The Genus Datura: From Research Subject to Powerful Hallucinogen :: Botany

The Genus Datura: From Research Subject to Powerful Hallucinogen Datura is one of the most intriguing plants with stimulating properties. In spite of having a notoriety for being one of the 'darker' stimulants, it has been generally utilized by social orders truly in both the Old World and the New, and keeps on being today. For those keen on ethnobotanical employments of this plant around the world, Datura is an interesting theme. While being restricted in its uses monetarily, the alkaloids contained in the plant have been sought after previously and its application as a subject for plant research is huge. Heiser has expressed that Datura is a variety of differences - from foul weeds to exquisite ornamentals. This paper will endeavor to give a diagram of this changed class, with explicit consideration being given to Datura stramonium, generally basic in North America. Datura has a place with the family Solanaceae, the nightshades, which Includes somewhere in the range of 2,400 species altogether (Siegel 1989:36). Different plants with opiate properties in this family are mandrake (Mandrogora), belladonna (Atropa), henbane (Hyoscyamus), and tobacco (Nicotiana). Suitably called the dumbfounding plants by Heiser, this family likewise incorporates such normal food plants as the tomato, potato, and eggplant (Safford 1922:539). There is by all accounts some difference with regards to what number of segments and species have a place with the variety Datura. Conklin (1976:3-4) expresses that herbaceous Datura is presently partitioned into five areas, while the more seasoned reference by Avery (1959:18) asserts just four. regardless, this variety contains around ten diverse herbaceous species, the most significant ones being D. stramonium, D. inoxia, D. metel, and D. ceratocaula (Schultes 1979:41-42). Basic names for Datura are various, the absolute most basic ones being raving nightshade, thistle apple, stinkweed, Devil's apple, Jimson weed, and holy messenger's trumpet (Heiser 1969:140 and Avery 1959:19). Datura can be found all through Asia, Europe, and the Americas as either local or unusual plants, and some have additionally been found in Africa and Australia (Conklin 1976:5). The focal point of assorted variety of this plant is in the New World, explicitly in Andean South America and in the southwestern United States/Mexico area (Lewis 1977:423-4). This information corresponds with the for the most part endless supply of Datura, despite the fact that this theme was bantered for quite a while. Analysts currently accept the plant started and advanced in Mexico and the American Southwest, trailed by versatile radiation into new desert situations (Conklin 1976:5). Today, Datura (primarily the species stramonium) can be discovered all over North America as a side of the road weed, yet never in uneven or forested environments (Hutchens 1991:166).

Project risk analysis and assessment in oil and gas industry Essay

Task chance investigation and evaluation in oil and gas industry - Essay Example In any case, the principle point of this paper is to concentrate on restrictions and issues of the instruments and methods of task hazard examination and assessment.â Hazard and vulnerability assessment has a couple of restriction and traps in the chief thought. All of these procedures makes strong part of intercession and nonappearance of vital reason in hazard and vulnerability assessment. These deficiencies will achieve despicable treatment of vulnerabilities. Those cutoff points are displayed here to give the follower a reflection on the use of current hazard and vulnerability examination in the sensible occasion of the sensible endeavor stage (Perminova et al, 2008). Center the segregating parameter for subject of assessment. This premise can be tended to. Affectability assessment isn't defenselessness examination. Affectability just worries on yield result as change of data parameter. Questionable information parameter isn't chosen through use of affectability assessment. The examination on how questionable data parameter is avoided in this examination. The objective of hazard and vulnerability assessment is to envision future execution of questionable recognizable sums that are not known at the period of assessment. Imagine the effect of oil stores to consolidated NPV of a field. In the occasion that recoveries has generous proportion of oil contained, adventure NPV might be certain. Something different, NPV might be negative in light of the fact that cost will be higher than oil bargains given that recoveries are underneath certain proportion of worth. Affectability examination is directed to investigate how oil stores influences NPV. It has n othing to do with how uncertain the stores, helplessness of stores underneath certain quality, or absolute probability of stores in high and low regard. Affectability examination isn't utilized to center mysterious information parameter for hazard and vulnerability

corporate governance Essay examples -- essays research papers

Corporate administration is an inadequately characterized idea; it covers such huge numbers of various financial issues. It is hard to give a top of the line definition in one sentence. Corporate administration has prevailing with regards to pulling in a lot of interests of the open as a result of its conspicuous significance for the monetary wellbeing of enterprises and society as a rule. Accordingly, various individuals have thought of various definitions that essentially reflect their exceptional enthusiasm for the field. It is hard to see that this 'issue' will be any extraordinary later on so the most ideal approach to characterize the idea is maybe to list a couple of the various definitions instead of simply referencing one definition. "Corporate administration is a field in financial aspects that researches how to make sure about/persuade productive administration of enterprises by the utilization of motivator systems, for example, contracts, hierarchical plans and enactment. This is regularly restricted to the subject of improving monetary execution, for instance, how the corporate proprietors can make sure about/rouse that the corporate chiefs will convey a serious pace of return.† www.encycogov.com, Mathiesen [2002].      According to Shleifer and Vishny in The Journal of Finance, â€Å"corporate administration manages the manners by which providers of account to enterprises guarantee themselves of getting an arrival on their investment.† J. Wolfensohn, leader of the Word bank, cited by an article in Financial Times in June of 1999 that "corporate administration is tied in with advancing corporate decency, straightforwardness and accountability."      Ã¢â‚¬Å"Corporate Governance takes a gander at the institutional and strategy system for enterprises - from their very beginnings, in business, through their administration structures, organization law, privatization, to showcase exit and bankruptcy. The honesty of organizations, monetary establishments and markets is especially integral to the wellbeing of our economies and their stability.† (www.oecd.org)      What does this all mean and how can it influence the business world today is the thing that might be inquired. Analysis of corporate administration is back furiously in the post-Enron period. Is the whole administration framework separated and needing change, or was it simply an inappropriate activities of a couple of individuals that has prompted this new instance of critisms? E... ...an Administration are driving the route for change, which is uncommon â€Å"given the run of the mill star business feelings of these groups.† Some individuals feel that the present administration is filling in as well as can be expected and that more noteworthy guideline won't forbid the untrustworthy and indecent activities of a couple of individuals. Notwithstanding, representatives need more noteworthy assurance. They need to be guaranteed that the standards for selling organization stock are not diverse for top directors that they are for representatives. Speculators likewise need to be taken care of. They need to be sure that the open data accessible to them is â€Å"an precise and reasonable portrayal of the company’s money related status.†       (Business Week 116)       www.encycogov.com. Mathiesen 2000 www.oecd.org. Association for Economic Co-activity and Development. Building Partnerships for Progress Booker, Katrina. â€Å"Trouble in the Boardroom.† Fortune Magazine. May 13, 2002 Luoma, Patrice. â€Å"Enron and Beyond.† Corporate Self-Governance and the Corporate Checks and Balances System. CCH Incorporated. 2002 â€Å"Corporate Governance: The Road Back.† Business Week. May 6, 2002. p. 116

International Banking Essay - 825 Words

International Banking (Essay Sample) Content: International BankingName of Student:Instructor:Course:Institution:Date:International BankingInternational banking involves aspects in terms of services and operations involving the facilitation of international trade, loans, and grants to governments and other private institutions, and the manner in which money flows both for investments and for making payments. The United States banks involvement in international banking remains limited to the large banks in which the volume of the markets is concentrated. However, despite the late entry into international banking for American banks, which made entry late, though the banksà ¢Ã¢â€š ¬ participation in international banking has witnessed a significant growth over period with volumes going well beyond the elementary levels in offering of services both to the domestic firms and to individuals in equal measure. Based on such a perspective, it is an aspect of substantive importance that indeed international banking remain s a core issue of the global economy. This paper, therefore, discusses the various aspects pertaining to international banking, in terms of initiatives includingÂVolcker rule, Vickers proposal, andÂLiikanen.ÂInternational banking is indeed a different kind of banking and, therefore, requires appropriate structures and operative mechanisms for the realization of success in the industry. Following the current financial crisis, different economies are working on instituting various banking regulations in the international perspective, in the form of different initiatives, all aimed towards the establishment of stable international banking relations (Gambacorta and Rixtel, 2013, 19). As such, legislation on the European Unionà ¢Ã¢â€š ¬s banking structural reform is currently being determined, from which European Union banks are required to have a distinction between investment businesses from the retail businesses. However, in the case of United States banks, a different pe rspective is visible, especially on the separation aspect of investment business and the retail businesses. In the United States, the distance aspect is not a requirement for United States banks; however, for the other banks of non-American origin operating in U.S., would require that the banks have operations under a single U.S. holding company (Gambacorta and Rixtel, 2013, 14). For the achievement of such an aspect, a number of modifications would be necessary, especially for the EU banks with affiliated US businesses. In order to achieve such a perspective, a number of aspects have appeared including the Volcker rule, Vickers proposal, Liikanen, as well as other recent European initiatives.The primary reason for the development of the different initiatives is to establish an insulation of various financial aspects of substantive importance to the economy. Equally, the efforts seek to offer protection to consumers from risky, though less important activities. Despite the various n egatives associated with the separation aspect, it remains an aspect of substantive relevant on the benefits related to the separation. Such include, preventing the subsidies supporting protecting aspect from lowering risk-taking costs as a means of encouraging moral hazards in business, reduction in the scope of interest conflicts through preventing aggressive risk culture from getting infected by the traditional banking businesses (Gambacorta and Rixtel, 2013, 22). Others include the offering of protection to various institutions from participating in activities of losses emanating from sources other than those of the government operations as well as the reduction in complexity of the banking institutions as a means of enhancing management and strengthening of the market discipline .In order to achieve the above aspects, it is clear that the initiatives have to come in handy. For Volcker rule, despite being narrow, has very strict regulations. The law operates in such a way that i t opens up for market-making activities while limiting proprietary trading. Volcker rule works to offer protection from investments in entities that expose the investing institutions to significant danger including private equity funds (Gambacorta and Rixtel, 2013, 18). Currently, the United States legislation limits activities of depository institutions, therefore, works in unison with Volcker rule on the restrictions on banking institutions. Volcker rule is indeed a strict piece of legislation as it exempts the transaction of certain financial instruments including agency securities while at the same time limiting various activities with other subsidiaries within the same group.In the case of Vickers proposals, a different perspective is evident from that of the rule. Ideally, Vickers proposals are broader in terms of their operative mechanisms, which include the exception of a wider array of business involved in banking from the protected entity including the elements such as the purchase of various financial instruments as well as loan purchases for secondary markets. In comparison to the Volcker rule, it emanates that Volcker proposals appear stricter as restrictions extend to intragroup and inter-firms available (G...

The Bible Is True And Not Myths - 1258 Words

Archaeology has verified that the bible is true but how? First, archeology has confirmed the biblical stories are true and not myths, as the world believed, because of ancient sites and civilizations discovered. Second, manuscripts that were found and translated has shown people today how the people back in the bible lived and worked. Last but not least, archeology has shown where major events, like battles, have gone on and during what year, they happened. According to Archeology and the Old Testament, the book of Judges took place around the Iron Age period, which was 1200 – 586 BC. Excavations have provided some useful information about daily life in ancient Israel during Judges, including the land, climate and people. However, before we learn about how people lived their daily lives in Israel during the Iron Ages, we should learn about the geography of Israel. The land of Israel stretches from Dan in the North to Beersheba in the South and from the Mediterranean Sea in the west to the Transjordan in the east. Israel s landscape is divided into five main regions and even though the regions are in the same place they all receive different amounts of rain, which produce different crops. The first region, the coastal plain, goes along the Mediterranean coast to Rosh HaNiqura, receives about 25 to 16 inches of rain which is a great place to grow grain. The second region, is the central mountain range that goes from Galilee to Negev Highlands; this region receives from 20 toShow MoreRelatedThe Bible Is True And Not Myths1258 Words   |  6 PagesArchaeology has verified that the bible is true but how? First, archeology has confirmed the biblical stories are true and not myths, as the world believed, because of ancient sites and civilizations discovered. Second, manuscripts that were found and translated has shown people today how the people back in the bible lived and worked. Last but not least, archeology has shown where major events, like battles, have gone on and during what year, they happened. According to Archeology and the Old TestamentRead MoreReligion and Myth1007 Words   |  5 PagesA biblical myth is defined by Burrows, (1946) as a symbolic, approximate expression of truth which the human mind cannot perceive sharply and completely, but can only glimpse vaguely, and therefore cannot adequately express. In bibilical interpretation a myth is a story which communicates a set of values or beliefs through imagery. The most important thing in the myth is the message and not the literal truth of the imagery. . Good examples in the bible include: Jonah and the Whale Noah’s ArkRead MoreHum 105 WORLD MYTHOLOGY Essay779 Words   |  4 Pagesthe word myth used popularly? For example, what does the statement, â€Å"It’s a myth† mean? In contrast, how is the word myth used in the academic context? After considering the definition in your textbooks and course materials, write a definition in your own words. The word myth is used most popularly in tales and stories. These tales and stories have been passed down from generation to generation and are based on some truth, but mostly an idea or common theme. The statement â€Å"It’s a myth† means thatRead MoreUse Of Symbolic Communications For An Individual Act Of Faith1569 Words   |  7 PagesThe word â€Å"myth† is being used abundantly when indicating a false story, the spiritual world that hasn’t been proven is important to many different religions and is more real to a culture than the observable facts. In the Hebrew Bible, Qur’an, and New Testament the ancient people told stories that are recorded in these scriptures. God, angels or demons aren’t able to be physically seen which all religions can agree on. However during prayer or any acts of religious service the unknown presence ofRead MoreBible vs. Mythology994 Words   |  4 Pages Bible vs. Myth There are many similarities and differences between Greek Mythology and The Bible. Whether it’s the creation of man and women, or the universe, stories have been told throughout time and some can be alike and others completely different. There are people that have gathered, translated and recorded all of these events for us now to learn about. Whether a person believes it is true or not is up to them but if a God is real how come the stories between these two different beliefsRead More Definition Essay1002 Words   |  5 PagesDefinition Essay The origin of the word myth seems to be a myth in itself. Myths have generally originated from a Greek history that used an oral tradition to explain events that occurred before the written word. Often supernatural beings or fictitious characters were used to explain popular ideas concerning phenomenas of nature or the history of people. The myths that were carried on from generation to generation were often very imaginative in an attempt to spark the interest of youngRead MoreMyths According to Joseph Campbell1161 Words   |  5 PagesKevin Gerbier What is a myth? When one thinks of a myth perhaps one thinks about a story being told by the fire, or a dramatic tale about an invincible hero, or perhaps a cosmological occurrence that caused everything to be. Personally, when I think of the word myth, I think of the ancient Greeks or Romans with their many gods and goddesses; however, to most, the story being told by a myth is simply that, just a story. To most the term â€Å"myth† has been confused for a legend or folklore. TheRead MoreTypes of Mythology Worksheet Essay1013 Words   |  5 PagesMaterial Types of Myths Worksheet Knowledge, Belief, Myth, and Religion Directions: Answer the following question on knowledge, belief, myth, and religion in 3 to 5 sentences. How are knowledge, belief, myth, and religion related to one another and how are they distinct from one another? Use an example from your life or popular culture to explain this relationship. Knowledge is made up of facts, truth, stories, and more. Belief is â€Å"the assertion that something is true without necessaryRead More Comparing Creation Myths of Ancient Egypt and The Christian Bible1218 Words   |  5 PagesComparing Creation Myths of Ancient Egypt and The Christian Bible Creation in Ancient Egyptian religion can be much different than the creation account taken from The Bible. Genesis has a set description of â€Å"The Beginning† while there are several different versions and variations in Egyptian mythology. The versions range from a â€Å"one god† myth (Ptah; see picture) to the more common creator out of Nun, which in itself has several derivations. The Ogdoad is a grouping of eight gods that existedRead MoreThere Is No Scientific Proof That A God Or God?1280 Words   |  6 Pagesgod or gods exist; therefore god is but a myth. There are many different types of beliefs in this huge world. No one is quite sure what will happen after I die. They say that this will happen, or that, but at the end of the day, are those beliefs false? This is where atheists come in. Atheists do not believe in a god. â€Å"They argue that scientific evidence proves that life on Earth evolved over many millennia, not according to the literal timetable of the Bible. They argue that there is no logical reason

Position As A Writer By John Edgar Wideman - 1211 Words

Position As a Writer John Edgar Wideman begins his piece, Our Time, with a description of the world he grew up in. He takes the reader through the story of his brother, Robby, using a variety of voices and points of view. In this narration of his brother’s life he brings to light his own dilemma with writing the piece. He uses a variety of voices and points of view to demonstrate the different perspectives of Robby s story. To contest the ethical dilemma of telling someone else’s story without exploiting it, Wideman addresses the issue head on. By reading Our Time, a writer could learn much from Wideman, and adopt a number of his methods for different writing styles. One of Wideman’s main writing methods is his use of multiple voices and points of view. This becomes apparent even in the first page of the text. Wideman introduces his essay with a letter. It is not addressed to anyone, neither is it signed, but, it is written as if every character in his story was speaking. The tone is his own, the subject is his brother, Robby, and parts of the letter reveal advise from Garth and his mother. This presentation of a multi-narrative style is present throughout the essay. It gives the reader a sense of authenticity that cannot be achieved through third person narration because it places the audience in the mindset of the person speaking. By switching points of view, Wideman is providing the reader with multiple perceptions of a scenario, giving a different lens of analysisShow MoreRelatedFinding Place : East Liberty Essay1915 Words   |  8 Pageshousing for its residents. Decades later, this neighborhood’s prosperity declined as resid ents began fleeing to other areas and businesses were forced to shut down. This left East Liberty in diminished conditions, like the conditions depicted in John Edgar Wideman’s story of Homewood in Our Time. Urban renewal efforts were quickly adopted for East Liberty, but these efforts failed. Today, the area is in a state of continuous revitalization, which is beneficial for the economy and some citizens,

the major systematic error sublimation of caffeine Essay Example For Students

the major systematic error sublimation of caffeine Essay Outline1 Introduction:2 Research Question:3 Background Information:4 Original Coffee beans:5 Caffeine:6 Phase Diagram:7 Roasting procedure:8 Light joint:9 Medium joint:10 Full joint:11 Double joint:12 Method:13 Variables:14 Procedures:15 Explanation of Stage 1 process:16 Premise in Stage 1 process:17 Separate caffeine from other chemicals in the solution18 Precaution of Stage 2:19 Explanation of Stage 2 process:20 Premises in Stage 2 process:21 Completion of caffeine infusion ( In fume board )22 Explanation for Stage 3 process:23 Premise in Stage 3 process:24 Raw informations:25 Decision and Analysis:26 Restrictions and Evaluations:27 Methods to decide the major systematic error- Sublimation of caffeine:28 Further unsolved inquiry and suggested probe:29 Bibliography:30 Appendix31 Chemicals in green java beans32 Degree of roasting Introduction: Coffee has been a popular drink since twentieth century, non merely because of its different colourss and spirits due to different grades of roasting, but besides the consequence on which it can maintain you to remain awake and to complete your occupation. It is normally known that the ground for java to possess this consequence is because of the caffeine inside the java beans. In general, there are four chief types of roasting methods in the industry, viz. , Light Roast, Medium Roast, Full Roast and Double Roast. There are a assortment of utilizations on caffeine presents. By interfering with adenosine in encephalon and organic structure, it moderates new transmittal of signals in CNS, Central Nervous System, and hence keeps people awake . Due to its short half life in human organic structure, around 4-10 hours on mean , it can be used to increase the consequence of anodyne for hurting control Besides it has consequence on detaining the musculus weariness. However, caffeine can do negative consequence on human organic structure, for illustration, increase the bosom rate, take a breathing rate and makes people experience more qui vive and energetic, which is besides the ground why International Olympic Committee forbid high caffeine ingestion. Furthermore, it is a mildly habit-forming drug, so some people can non command the ingestion of caffeine under overdose, which could take to caffeine intoxication. Besides, harmonizing to the a survey held by Montreal University, if pregnant adult fe male consume more than 1.5 cup of java, the opportunity of abortion is doubled ; if consume more than four, the opportunity of abortion is tripled. Therefore, the pick of caffeine ingestion from java becomes critical due to its harmful consequence on human organic structure. It is advised that, if necessary, 100-300 milligram per twenty-four hours of caffeine ingestion is acceptable. However, people are normally lack of cognition about the caffeine content in the java and have no thought what sum precisely is in the java they are imbibing. Therefore, they frequently use their senses to place the caffeine content in java relation to each other. However, there are a batch of myths about this method. For illustration, those darker java has more caffeine than lighter java due to its darkness or that the caffeine is destroyed during roasting in higher temperature, so the caffeine content in lighter java is higher than that of darker java. To forestall over-dosing of caffeine from java, it is critical for people to hold the general thought of comparing the caffeine content in different java when purchasing a them. In this essay, the caffeine contents in java beans roasted in different grades are examined by experiment through the extraction of caffeine by chemical agencies. The consequence would be interpreted by concentrating on the roasting procedure, as java beans experience greatest alteration in physical or chemical alteration during roasting. Although there are a batch of sub-degrees of the chief four roasting grades, merely one sub-degree from each grade would be selected as representative. Research Question: Does different roasting grade affect the caffeine content in java beans? Background Information: Original Coffee beans: The original java beans are green in colour. They contain non-volatile alkaloids, proteins and amino acid, saccharides, lipoids, non-volatile chlorogenic acid, and volatile compounds. Among the non-volatile alkaloids, caffeine is the most abundant. It contains 1-2.5 % w/w of green java been. Caffeine: Caffeine is a white, crystalline odorless and acrimonious savoring solid. It exists in the works of java beans as a natural pesticide. Its formal name is trimethylxanthine, or in systematic calling 1,3,7-trimethylxanthine or 3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione. The chemical expression of caffeine is C8H10N4O2. It is a polar organic compound that contains C, N, H and O. Its denseness in solid signifier is 1.23 g/cm3. Due to the presence of N in the compound, caffeine is base in nature. Since it is a polar molecule, it is soluble to H2O, particularly in hot H2O. The solubility of caffeine in H2O is 22 at 25, 180 at 80, and 670 at 100. Under force per unit area of standard ambient temperature and force per unit area , the runing point of caffeine is 238 and it can besides sublimate at 178in about vacuity , which will be explained by stage diagram following. Phase Diagram: Three general stages of affair are solid, liquid and gas. Change of stage does non merely depend on the temperature, but besides the surrounding force per unit area moving on the chemicals. For illustration, the boiling point of H2O is 100, under standard ambient temperature and force per unit area. However, if the is placed in a lower atmospheric force per unit area, the boiling point of H2O is decreased since the vapour force per unit area is already greater than the atmospheric force per unit area, so H2O molecules can get away from the H2O surface in a lower required energy. Therefore, each compound can undergo stage alteration to the three stages in different combination of temperature and force per unit area. Figure 2 is a phase diagram of. The lines spliting the diagram into subdivisions represent that under certain temperature and force per unit area, would undergo alteration of stage, which is equilibrium between the two stages that the line is spliting. For illustration, th e ruddy line, if A A ; lt ; 1, so the matching thaw point additions, while the corresponding boiling point, A , lessenings. Each component has their ain stage diagram to exemplify the passage of stages under different combination of temperature and force per unit area. Figure 3 is a stage diagram exemplifying the stage passages of caffeine, which is different from. This is critical in ulterior reading of the consequence in the experiment. It is because roasting procedure involves temperature and force per unit area alteration. Roasting procedure: The chief intent of roasting java beans is to take toxins, heighten the gustatory sensation and concentrate the olfactory property wanted. Since green java beans are difficult, small odor and incorporate a batch of compounds that are acrimonious in gustatory sensation. Therefore, by roasting, it can ensue in both physical and chemical alteration in the green java beans. Since caffeine is the chief factor that is concerned in this essay, other chemical alteration will non be discussed. Although there are a batch different roasting procedures in the industry, such as fluidized bed roasting, fast roasting or horizontal rotating membranophone, the basic procedure of roasting is similar. During roasting, there are 10 % to 20 % lost in weight from the green java beans. Here is a sum-up of roasting procedure of java beans: Heating of Green Coffee Beans from 3-5 proceedingss ( about 25 to 100 ) The green java beans are heated so that the H2O in the original java beans evaporates at a really fast rate. As this point, the green java beans turn from green to yellow due to caramelization of sugar in the java beans. Heating of Yellow Coffee Beans from 5th-9th proceedingss ( about 170to 200 ) The xanthous java beans are farther heated and get down to turn to brown in colour as more sugar being caramelized. Carbon dioxide and H2O are forced to get away out of the java beans due to the high force per unit area indoors, as the temperature is really high, which besides causes the enlargement in size of java beans. The olfactory property besides starts to give out at this phase. First cleft from 10th-11th proceedingss ( about 210 ) A first sound of cleft gives out as the java beans expand to about duplicate in size from green java beans in high temperature. Familiar olfactory property is given out and the java beans turn aureate brown at this phase. After this phase, harmonizing to different grades of roasting required, the java beans will undergo different temperatures and clip periods for farther warming. During the procedure, the sugar is caramelized farther and coffee oil is released. Light joint: To get visible radiation roasted java beans, the beans from phase 3 are to be roasted about one more minute in approximately 215 before the 2nd cleft. Medium joint: For farther half to one minute from light roasted in approximately 230, a 2nd cleft occurs and it means average joint is finished. Full joint: If continued for half to one minute from medium roasted in approximately 240, full roasted java beans are collected. Double joint: This is the most common concluding measure that java beans would be roasted, which is acquired from go oning the roasting from full roasted java beans for about half a minute more in approximately 245. The sugar in the java beans at this phase is started to fire and degraded. The above warming procedure can be achieved by either roasting the java beans on a hot home base, which is a traditional roasting method in industry or in place roasting, or go throughing the java beans by high temperature steam. Method: Variables: Mugwump: Degree of roasted java beans Dependant: Caffeine extracted from the java beans ( g ) Controlled: Mass of roasted java beans ( g ) Brand of java beans ( Starbucks ) Apparatus: The undermentioned setup are used in this experiment. Chemicals: The undermentioned chemicals are used in this experiment. Procedures: Extracting chemicals compounds out of java beans Measure 100mL of distilled H2O by graduated cylinder Pour the H2O into a 200mL beaker. Topographic point the beaker on a hot home base and heat the hot home base to 100. Topographic point a weighing boat on an electronic graduated table and tare it. Measure 3g of java beans, in signifier of pulverization, on the electronic graduated table and record it. Add the 3g of java pulverization into the boiling H2O. Use glass rod to stir the solution during warming. After the H2O furuncles, which means it reaches 100, set the temperature to 80 and let the solution to stand for 20 proceedingss to pull out as much caffeine as possible. The Benetton Group EssayTo reason, high temperature and force per unit area in roasting procedure are the grounds that the caffeine content is non affected irrespective the grade of roasting that the java beans have achieved. Therefore, even different grade of roasted java beans is used to brew java, the caffeine ingestion is the same no affair which type of java you prefer. Indeed, decaffeinated java is non taken into history. Restrictions and Evaluations: Random mistakes: Random mistake arises since caffeine may non be all dissolved in methylene chloride since it still has a small solubility in room temperature H2O. Furthermore, the caffeine extracted by methylene chloride may incorporate drosss, which affect the mass of caffeine recorded. Besides, the measuring utilizing graduated cylinder causes uncertainnesss. Furthermore, the usage of other equipments such as electronic balance, which causes 0.01g on the mass measured. Systematic mistakes: The measure of sample is excessively little, which causes ill-defined consequences obtained since big difference may be obtained if sample has larger measure. If there is any difference of caffeine content, it would be more obvious if increase the sum of each java pulverization sample used. However, due to the fact that school research lab do non hold a big beaker at the clip the experiment was performed, which required more than 200mL, merely little sum of sample in each test can be used in order to maintain a big ratio between the volume of H2O and the mass of the java pulverization. Furthermore, the major systematic mistake is the separation of two beds in dividing funnel. Since the running of methylene chloride into a beaker is manipulated by custodies and through the observation. To guarantee that all methylene chloride is collected, the closing of the separating funnel is a small delayed due to the bubbles in the separating line, which blurred the exact dividing degree. Therefore, a small solution of the upper portion, which contains the drosss from java beans, is added into the methylene chloride in the beaker. After the vaporization, since Na carbonate is added before and it has high boiling point due to its ionic construction, its mass contributes to the mass weighed on the electronic balance. Methods to decide the major systematic error- Sublimation of caffeine: In order to decide the major systematic mistake, a farther measure can be done if equipment is allowed in school research lab. Since caffeine sublimes good under vacuity at 178, as no air molecules against the vapor force per unit area of caffeine, the gathered caffeine can be placed into a flask linking to a aspirator, which keeps the status in vacuity, and have a cold finger above it and a heat beginning below the flask. Caffeine can so sublimate and precipitate on the cold finger. Therefore, pure caffeine can be collected and weighed. Further unsolved inquiry and suggested probe: Although the caffeine content is non affected by roasting, a measure rearward can ensue in an unsolved inquiry, which is whether green java beans grown from different topographic points contain different degree of caffeine inside? A suggested manner to make so is that ; purchase different java beans of same roasted degree from different locations around the universe. This can be done by utilizing cyberspace shopping. After, extract caffeine from each illustration and compare the caffeine content in each java bean from different location. Since there are more and more methods of roasting in the industry, such as fluidized bed roasting and fast roasting , it would be interesting to look into whether these new methods of roasting can impact the caffeine content in the java beans even they are claimed to be same grade of roasting after all. Bibliography: A, Nehlig ; JL, Daval ; G, Debry ( 1992 ) . Caffeine and the cardinal nervous system: Mechanisms of action, biochemical, metabolic, and psychostimulant effects . Brain Res Rev FP, Meyer ; E, Canzler ; H, Giers ; H. Walther ( 1991 ) . Time class of suppression of caffeine riddance in response to the unwritten terminal prophylactic agent Deposiston. Hormonal preventives and caffeine riddance . Zentralbl Gynakol Oxford A-Z of Medicinal Drugs Oxford Press. Kent, Michael ( 1997 ) . Oxford Food A ; Fitness ( A Dictionary of diet and exercising ) Oxford University Press. Anderson, Jean ; Deslein, Barbara. The Nutrition Bible William Marrow and Company, Inc. LEUNG, T. M. ; LEE, C. C. Inorganic Chemistry and Chemistry in Action Fillans. Library for Science . A ; lt ; hypertext transfer protocol: //www.chromatography-online.org/directory/analt-235/page.html gt ; . About.com amp ; lt ; hypertext transfer protocol: //chemistry.about.com/od/moleculescompounds/a/caffeine.htm gt ; Drug bank amp ; lt ; hypertext transfer protocol: //www.drugbank.ca/cgi-bin/getCard.cgi? CARD=DB00201 gt ; Purdue University Online Writing Lab amp ; lt ; hypertext transfer protocol: //employees.oneonta.edu/knauerbr/chem226/226expts/226_expt06_pro.pdf gt ; Look for chemicals amp ; lt ; hypertext transfer protocol: //www.lookchem.com/Caffeine/ gt ; Carleton College » A ; lt ; hypertext transfer protocol: //serc.carleton.edu/research_education/equilibria/other_diagrams.html gt ; University of British Columbia amp ; lt ; hypertext transfer protocol: //www.chem.ubc.ca/courseware/123/tutorials/exp10A/sublimation/ gt ; Coffee-Makers-Caf A ; eacute ; amp ; lt ; hypertext transfer protocol: //www.coffee-makers-cafe.com/coffee-roasting.html # roastHome gt ; Coffee-Tea amp ; lt ; hypertext transfer protocol: //www.coffee-tea.co.uk/commercial-roasting.php gt ; Sweet Marias amp ; lt ; hypertext transfer protocol: //www.sweetmarias.com/roasting-VisualGuideV2.php gt ; Sonora Environmental Research Institute, Inc. amp ; lt ; www.seriaz.org/downloads/4-caffiene.pdf gt ; The Scripps Research Institute amp ; lt ; hypertext transfer protocol: //www.scripps.edu/chem/finn/Scipdfiles/dipolemoments.pdf gt ; City Collegiate amp ; lt ; hypertext transfer protocol: //www.citycollegiate.com/dipolemoment.htm gt ; New Mexico Tech amp ; lt ; hypertext transfer protocol: //infohost.nmt.edu/~jaltig/Chem333LCaffeine.pdf gt ;  «Ezine Article » A ; lt ; hypertext transfer protocol: //ezinearticles.com/ ? A-Look-at-the-Coffee-Roasting-Process A ; id=1802022 gt ; Beverage.cc A ; lt ; hypertext transfer protocol: //www.beverages.cc/Coffea/encyclopedia.htm gt ; PubMed database A ; lt ; hypertext transfer protocol: //www.ncbi.nlm.nih.gov/pubmed/7361718? dopt=Abstract gt ; Appendix Chemicals in green java beans Non-volatile alkaloids: Caffeine, Elixophyllin, theobromine, paraxanthine, liberine, and methylliberine are present, while caffeine is the most abundant non-volatile alkaloid, which is about 1-2.5 % w/w of a green java bean. Besides, caffeine Acts of the Apostless as a natural insect powder for the works. Furthermore, caffeine s half life is 5.7 hours in a normal grownup organic structure. Proteins and amino acids Proteins and aminic acids make up 8-12 % w/w of a green java bean. Carbohydrates Carbohydrates account for 50 % w/w of a green java bean, largely polysaccharides. Lipids Lipids, ester, long chained unsaturated fatty acids and amides are found in green java beans. The fatty acid is saturated during roasting procedure, which accounts for the java oil. Non-volatine chlorogenic acids Chlorogenic acids are antioxidant. They are good for wellness, but 70 % of them are destroyed during roasting procedure. Volatile compounds Volatile compounds are found in green java beans as aldehydes, short-chained fatty acids and N incorporating aromatic molecules. However, the aromatic molecules in green java beans are unpleasant, which is the ground that java beans are roasted in order to organize pleasant olfactory property of aromatic molecules. Degree of roasting It can be seen that although dipole minute of caffeine is really big, larger than H2O, the size of the molecule is really big compared to H2O and methylene chloride. Therefore, charges are spread widely, which makes the mutual opposition of caffeine molecule less polar. Therefore, caffeine dissolves more readily in methylene chloride than in H2O or Na carbonate, which is ionic compound. Sodium carbonate is used to respond and do some compound other than caffeine to be more soluble to H2O, such as tannic acid. Nehlig, A, Daval JL, Debry G ( 1992 ) . Caffeine and the cardinal nervous system: Mechanisms of action, biochemical, metabolic, and psychostimulant effects . Brain Res Rev Meyer, FP, Canzler E, Giers H, Walther H. ( 1991 ) . Time class of suppression of caffeine riddance in response to the unwritten terminal prophylactic agent Deposiston. Hormonal preventives and caffeine riddance . Zentralbl Gynakol Oxford A-Z of Medicinal Drugs, Oxford Press. Michael Kent ( 1997 ) . Oxford Food A ; Fitness ( A Dictionary of diet and exercising ) . Oxford University Press. Jean Anderson, Barbara Deslein. The Nutrition Bible . William Marrow and Company, Inc. Volatile means inclination of vaporisation. w/w = weight/volume per centum solution Library for Science: hypertext transfer protocol: //www.chromatography-online.org/directory/analt-235/page.html About.com: hypertext transfer protocol: //chemistry.about.com/od/moleculescompounds/a/caffeine.htm Drug bank: hypertext transfer protocol: //www.drugbank.ca/cgi-bin/getCard.cgi? CARD=DB00201 Electrons are unevenly distributed. Purdue University Online Writing Lab: hypertext transfer protocol: //employees.oneonta.edu/knauerbr/chem226/226expts/226_expt06_pro.pdf 25and 1 standard pressure T. M. LEUNG, C. C. LEE, Inorganic Chemistry and Chemistry in Action , Fillans. Expression for chemicals: hypertext transfer protocol: //www.lookchem.com/Caffeine/ Original from Carleton College: hypertext transfer protocol: //serc.carleton.edu/research_education/equilibria/other_diagrams.html Red line added as illustration. Original from University of British Columbia: hypertext transfer protocol: //www.chem.ubc.ca/courseware/123/tutorials/exp10A/sublimation/ Coffee-Makers-Cafe: hypertext transfer protocol: //www.coffee-makers-cafe.com/coffee-roasting.html # roastHomeCoffee-Tea: hypertext transfer protocol: //www.coffee-tea.co.uk/commercial-roasting.php Sweet Marias: hypertext transfer protocol: //www.sweetmarias.com/roasting-VisualGuideV2.php The method of pull outing caffeine from java is improved by myself from originally design from Sonora Environmental Research Institute, Inc. : www.seriaz.org/downloads/4-caffiene.pdf All java beans are from same brand- Starbucks. Using dividing funnel is more accurate than pouring the solution in another beaker by manus and utilizing filter paper to take the staying unwanted solution from the original design. Fig. 4 dividing funnel s diagram is from Jindal Medical A ; Scientific Instrument D = Debye = unit of dipole minute. Look for chemical: hypertext transfer protocol: //www.lookchem.com/Caffeine/ Dipole minute is the vector amount of mutual opposition. The Scripps Research Institute: hypertext transfer protocol: //www.scripps.edu/chem/finn/Scipdfiles/dipolemoments.pdf City Collegiate: hypertext transfer protocol: //www.citycollegiate.com/dipolemoment.htm Calcium sulfate is non used as mentioned in the original process, since it can non be removed after wards, which could impact the mass of caffeine collected. Exothermic reaction agencies there is a net energy given out as heat. New Mexico Tech: hypertext transfer protocol: //infohost.nmt.edu/~jaltig/Chem333LCaffeine.pdf Ezine Articles: hypertext transfer protocol: //ezinearticles.com/ ? A-Look-at-the-Coffee-Roasting-Process A ; id=1802022 Beverage.cc A ; lt ; hypertext transfer protocol: //www.beverages.cc/Coffea/encyclopedia.htm gt ; PubMed database A ; lt ; hypertext transfer protocol: //www.ncbi.nlm.nih.gov/pubmed/7361718? dopt=Abstract gt ; Sweet Marias amp ; lt ; hypertext transfer protocol: //www.sweetmarias.com/roasting-VisualGuideV2.php gt ; Rare instance that the java beans are wholly blackened. Sonora Environmental Research Institute, Inc. A ; lt ; www.seriaz.org/downloads/4-caffiene.pdf gt ;

Patricide Essays - Death, Homicide, Law, Fatherhood, Patricide

Patricide In the time of the Romans, the punishment for patricide was to be sewn up in a sack that had a monkey, snake, rooster, and dog inside, and then to be thrown in a river. Each of the animals in the bag had some specific meaning to them, and being sewn up in a sack and tossed into the river also had a specific function to the murderer. Thus this punishment became the proper way to punish the guilty. In the Roman era, patricide had become a major problem, so it was decided that for whomever held a title in Rome, there would be a meeting to discuss how to get rid of the problem and punish appropriately. The title holders decided that the best way to punish the young men, and to stop them from thinking of committing the sin, was to make them die, as well as make them feel everything their father had, and to regret their crime. This decision then became the chosen consequence for the crime of patricide. The significance of the animals was to torture the perpetrator in a particular way for his crime. The importance of the snake was that the snake was evil, dating back to the Garden of Eden, where it posed as the Devil and deceived Eve. While the victim was alive, the snake would be there to remind him of the ultimate sin-the deception of one's own father. The rooster is primarily known for his crowing, and thus his crows would remind the sinner of his guilt, so that he couldn't escape from what he did. The dog's function in the sack would be to howl, not only to be deafening and frightening, but also to evoke the wrath of the gods upon him. The monkey represents torture, because it is capable of mimicking human actions. It would mimic the son's behavior and re-enact the murder of the son's All four of these animals perform at least one role in torturing the boy, and so that he would be forced to think about what he had done to his father. The purpose of the sack was to increase tenfold the agony which his father suffered, and also to make him regret his decision to kill his father. With each passing moment, the torment would get progressively worse, so that the boy would get a taste of the Hell that was to be his afterlife, as punishment for committing patricide. The sack represented a way in which to make the boy suffer much more, and quickly before he drowned. The son was thrown into the river so that he could feel the way his father's panic when he killed him. The water would serve to scare the son in the way his father felt when he realized that his own son had turned on him. The sewn sack would prevent the son's escape so he would realize there would be no turning back from his actions. These different elements of punishment combined to make the murderer truly suffer each aspect of the crime through the torture. The closed sack with animal reminders of different aspects of the murder would serve as a deterrent to living observers. This ritual is a fitting punishment for the crime.

Free Essays on Market Segmentation

Market segmentation is briefley the process of breaking down a larger target market into smaller segments with specific characteristics. Each group requires different promotional strategies and marketing mixes because each group has different wants and needs. Segmentation will help us customize our product, such as advertising or to reach and meet the specific needs of a narrowly defined customer group. Before deciding to fund a market research we must be sure that the market is, Big enough: Market must be large enough for segmentation. We can not split a market that is already very small. Different: Differences must exist between members of the market and these differences must be measurable with data collection methods. Reachable: Each segment must be reachable through one or more media. You must be able to get your message in front of the right market segments for it to be effective. If one-eyed, green aliens are your best marketing opportunity, make certain there is a magazine, cable program or some other medium that targets these people (or be prepared to create one). Profitable: The expected profits from expanding your markets and more effectively reaching buyer segments must exceed the costs of developing multiple marketing programs, re-designing existing products or creating new products to reach those segments. And we should mostly look for differences in the 5 categories which are, Demographics: Refers to age, sex, income, education, race, martial status, size of household, geographic location, size of city, and profession. Psychographics: Refers to personality and emotionally based behavior linked to purchase choices; for example, whether customers are risk-takers or risk-avoiders, impulsive buyers, etc. Lifestyle: Refers to the collective choice of hobbies, recreational pursuits, entertainment, vacations, and other non-work time hobbies Belief and value systems: Includes religious, political, ... Free Essays on Market Segmentation Free Essays on Market Segmentation Market segmentation is briefley the process of breaking down a larger target market into smaller segments with specific characteristics. Each group requires different promotional strategies and marketing mixes because each group has different wants and needs. Segmentation will help us customize our product, such as advertising or to reach and meet the specific needs of a narrowly defined customer group. Before deciding to fund a market research we must be sure that the market is, Big enough: Market must be large enough for segmentation. We can not split a market that is already very small. Different: Differences must exist between members of the market and these differences must be measurable with data collection methods. Reachable: Each segment must be reachable through one or more media. You must be able to get your message in front of the right market segments for it to be effective. If one-eyed, green aliens are your best marketing opportunity, make certain there is a magazine, cable program or some other medium that targets these people (or be prepared to create one). Profitable: The expected profits from expanding your markets and more effectively reaching buyer segments must exceed the costs of developing multiple marketing programs, re-designing existing products or creating new products to reach those segments. And we should mostly look for differences in the 5 categories which are, Demographics: Refers to age, sex, income, education, race, martial status, size of household, geographic location, size of city, and profession. Psychographics: Refers to personality and emotionally based behavior linked to purchase choices; for example, whether customers are risk-takers or risk-avoiders, impulsive buyers, etc. Lifestyle: Refers to the collective choice of hobbies, recreational pursuits, entertainment, vacations, and other non-work time hobbies Belief and value systems: Includes religious, political, ...

Online learning bibliography Annotated Example | Topics and Well Written Essays - 500 words

Online learning - Annotated Bibliography Example For instance, knowledge construction via collaborative discussion is vital since collaboration methods sequence, define, and assign learning activities to distinct learners and can in turn facilitate activities such as construction of arguments during discussions. Leer, R., & Ivanov, S. (2013). Rethinking the future of learning: The possibilities and limitations of technology in education in the 21st century. International Journal of Organizational Innovation, 5(4), 14-20. In this article, the author argues that technology is very important in data analysis. By the use of computers, one can assess quantitative data of great magnitude and at a very fast speed much faster than any person can accomplish. Moreover, technology saves on time in data analysis with certain appropriate software in that one can easily analyze data by just entering it in a computer specifying the characteristic to be checked and within no time, the results are ready. Therefore, via online learning, students will be able to access important data at a fast rate and easily. Marchetti, C., & Long, G. (2011). The Importance of Interaction for Academic Success in Online Courses with Hearing, Deaf, and Hard-of-Hearing Students. Retrieved 16 March 2014 from http://www.irrodl.org/index.php/irrodl/article/view/1015/1952 In this article, the authors state that online learning is rapidly growing because of advancement in technology. The authors argue that online learning is the best method of learning since it gives a student more interaction options. For instance, online learning promotes student-student interaction and student-instructor socialization, which increases quality of information dissemination. Via online learning, students are in a position to talk directly to their teachers and fellow students using discussion forum features and chat messaging of

Tom DeLay indictment Essay Example | Topics and Well Written Essays - 500 words

Tom DeLay indictment - Essay Example While it is not a criminal offence to receive additional funding, becoming charged of conspiracy in a campaign finance scheme has serious implications. Unlawful transfer of company's assets or property to finance election campaigns is strongly prohibited in Texas State. Nevertheless, it was found that the sum $190,000 was transferred from associates of DeLay and companies to the accounts of seven candidates. John Colyandro and Jim Ellis were also accused in violation Texas election law. In spite this fact, "no evidence to support the conspiracy charge was cited in the indictment, which says only that DeLay and two named associates entered "into an agreement with one or more of each other" or with the committee to conduct the funds transfer" (Smith, 2005). The only evidence presented to the a Texas grand jury was the check in corporate money, but Tom Delay denies the fact that he used corporate funds illegally and conspiringly. DeLay told "I have done nothing wrong. ... I am innocent" He added that "the charges amounted to "one of the weakest and most baseless indictments in American history." (DeLay indicted, steps down as majority leader, 2005). Tom DeLay's attorney, Dick DeGuerin, stated that the money transferred were "lawfully collected from individuals who knew what they were contributing to".

The importance of Cromwells military role Essay Example for Free

The importance of Cromwells military role Essay Using these four passages and your own knowledge, assess the view that the importance of Cromwell’s military role in the Civil War has been exaggerated. Oliver Cromwell was born in 1599 into a middle class gentry family in Huntingdon. He began his career as a Member of Parliament for Cambridge in 1628; he went on to fight in the Civil War as part of the Parliamentarian army, with a number of roles as he rose through the ranks from captain to lieutenant-general. Cromwell fought in numerous battles with great success and was seen to have had great military and leadership skills. In my opinion, I believe that Cromwell’s military role in the Civil War was not exaggerated; the further analysis and evaluation of the passages will help me to prove this view. One view of Cromwell’s military role would agree that the importance he held was a result of his unusual military approach and his characteristics. The approaches that he used made him stand out as they were seen as ‘unique’. Interpretation C states ‘he raised such men as had the fear of God before them and made them conscience of what they did’. This relates to Cromwell’s use of religion within his cavalry as he was a devout Puritan himself. He believed that he was undertaking God’s work and saw every military victory as being won with the help of God. The use of religion would have been a strong motivation for any of the troops, which made them differ from any other cavalry at the time. Another Interpretation that shares evidence of this is Interpretation D as it states ‘he seems to have been instinctively aware that, in war, moral forces can far outweigh the physical’. This belief in God was thought to have been the driving force behind Cromwell which gave him the determination in battle that others did not possess. This determination is apparent within the battle of Marston Moor as Interpretation A mentions that he ‘kept such control over his man and over the battle when all three of his commanding generals had given it up for lost’. The actions of Marston Moor were seen to recognise Cromwell as an ‘extraordinary character’. Interpretations A, C and D all show evidence of Cromwell’s use of religion within war and how it was successful in his cavalry. The mention of religion in these sources appear to give the impression that these religious tactics set him out from others cavalry commander at the time. Therefore, this shows the difference between him and other military leaders, proving the view that he was a unique character, which is ultimately a factor in his military success. Cromwell also used other military approaches that were seen as unusual at the time, such as his use of discipline. He was seen to have total control over his cavalry in which they followed every order such as his ability to ‘regroup his forces into a tight formation’. There is further evidence of his disciplinary actions within Interpretation C, ‘an unusually high degree of discipline on, as well as off, the battlefield’. This discipline allowed him to carry out coordinated military manoeuvres with great success. The battle of Marston Moor in July 1644 was seen as a ‘dramatic struggle’ as the Royalists held many advantages but Cromwell’s decision to rally his cavalry after victory and aid the other side of the battlefield was the decisive tactic that won the Parliamentarians the battle. Without the discipline that Cromwell used in his cavalry he would not have been able to rally his men the way he did. The battle of Marston Moor was prearranged which was a disadvantage to both the Parliamentarians and the Royalists. However, Cromwell’s cavalry waited until early evening in order to obtain the element of surprise. This decision was a major factor in the victory over the Royalists in this battle as they were unprepared for the attack. The actions throughout the battle were unique and cunning and from the evidence appeared to have won the Parliamentarians their victory. Therefore, Ashley’s interpretation shows he was of great importance to the military success of the Parliamentarians through his decisions on the battlefield. Therefore, confirming that his military reputation has not been exaggerated. However, this view that Cromwell’s military role was not exaggerated is simply based on the numerous victories that he was a part of in his time of being a soldier. However, Ashley acknowledges that Cromwell held all the advantage at the Battle of Marston Moor. Yet, he does not take this into account in the interpretation. He focuses upon Cromwell’s tactics being exceptional rather than considering that all Cromwell’s advantages won the victory and not his tactics. This unbalanced interpretation is, therefore, limited and it undermines its reliability. Interpretation A recalls the events of the battle of Marston Moor and states that ‘it lacked coordinated command’, which was before the New Model Army, thus weakening the interpretation that Cromwell was such a good general. Yet, the New Model Army was created in order to control the numerous Parliamentarian armies throughout the country, the bases of the Army was to become disciplined, trained and mot ivated. These characteristics were very apparent within Cromwell’s cavalry during the battle of Marston Moor and could have been the reasoning behind the structuring of the New Model Army as it was proven to be successful. However, we need to consider whether this success as a cavalry commander was equally matched by his career as a general. Interpretation C also shows evidence of further military victories such as the defeat of Rupert at the battle of Naseby in June 1645 and a following success at the battle of Langport, which gave the Parliamentarians control over the West of England. This proves evidence that he was equally successful as a general and therefore deserves his reputation. Further evidence of military success is also apparent within Interpretation D, regarding ‘the Preston campaign of 1648’, this was a battle in which Cromwell was the main commander of the force and defeated the attacking Royalists and Scottish armies. This victory was seen to be the defeat of the Royalists that lead to the end of the Civil War. These numerous military successes are evidence that Cromwell showed importance to the military cause of the Parliamentarians. We also know of another military success that took place in 1649, this was Cromwell’s conquest of Ireland where he took Wexford in a massacre of 3,500 troops and civilians with only a small number of Parliamentarian casualties in comparison. These numerous victories indicate that the use of Cromwell’s military approach through the New Model Army proved successful. However, it is difficult to make a judgement with this evidence, as it could be argued that it was possible that these victories could have been achieved without Cromwell’s role in them, if another strong leader was present. These other military victories are not mentioned within the interpretations, this implies that they were not taken into account in judging the capability of Cromwel l as a military leader and could hinder the opinion presented from the interpretation. It is also believed that Cromwell was not in fact the military success that people saw him as. Interpretation D mentions his ‘atypical Cromwellian aggression’ that came out during battles, the interpretation implies his aggression and drive was the main factors that lead him to such success. The interpretation does not see him as an outstanding tactician as interpretation A and C imply but name his as a ‘very sound and capable tactician’, which seems to offer a more convincing view of Cromwell. The repeated use of positive language in these interpretations could be an indicator of Cromwell’s ability. However, interpretation D does not believe that Cromwell was the genius that interpretation A does, stating that he ‘never really reached the heights of a master of the strategic manoeuvre’. This shows that the evidence in interpretation D most strongly agrees with the view that the importance of Cromwell’s military role was exaggerated than any of the other interpretation. I disagree with the view that interpretation D implies, that Cromwell’s military role was exaggerated as the evidence regarding the battle of Marston Moor in both interpretation A and C outweighs the view presented in source D. The interpretation also describes him as ‘hasty’ and ‘unsubtle’ in his tactics on the battlefield, these negative phrases emphasise that the evidence does not agree with the importance of Cromwell’s military role. This idea is contradicted within the evidence shown in interpretation A as it states ‘led them across the battlefield to the aid of his right wing, had a crucial move with the hall-mark of genius upon it’, this was relating to the battle of Marston Moor in 1644. The tactics of Marston Moor were seen this way as they were very unique at the time and no other cavalry commanders managed their cavalries in this way. Cromwell’s use of his religion and confidence in his belief were seen to be the reason behind his success as implied in interpretation D, ‘sheer force of will; he seems to have been instinctively aware’. This could be a reason for and against the exaggeration of his military role as it set him apart from other which may have made him more successful. It may prove to be for the view that the role was an exaggeration as it could be implied that Cromwell relied on his religious beliefs, as he did not hold the tactical skills of his fellow cavalry commanders. Interpretation B shows the importance of Cromwell’s military role in a different way to the other interpretation as it only seems to concentrates on the political successes within his career as he rose to power to become Lord Protector. It explains that the major political success of Cromwell grew from the victories throughout his military career. His military success in the Civil War made him stand out and come to a spotlight within the government, allowing him to successfully work his way up politically, as interpretation B states ‘the well-deserved rise to fame, which in turn enhanced his position in the political world’. The fact that Cromwell was so success in his political career could be the reasoning to imply that his military role was also success as a result of a simple assumption. Cromwell’s main successes that are identified in the evidence are from Cromwell’s victories as a cavalry commander rather than as a general. As a cavalry commander, he proved numerously successful in battle yet his victories in the role of a general are not mentioned within the source in the same way as the cavalry commander role. This could be because he did not reach the peak of a military career as he changed his focused himself on the political issues within England at the time. This fact could indicate that his military career was exaggerated as the evidence focuses on his success as a cavalry commander rather than a general in a higher ranked position. However, a clear judgement regarding this cannot be made, as further evidence regarding his victories as a general would need to be assessed. In conclusion, it is possible that the importance of Cromwell’s military role was slightly exaggerated but he was important to the Parliamentarian side through the numerous victorious battles that he was a part of, which are shown in interpretation A, C and D. His unusual military approach such as the use of discipline and religion, as well as his own personality set him apart from others cavalry commanders. All these characteristics made Cromwell a success and as source B states, went on to help him in his political career, it could be said that this political career was a result of his actions in a military role. Ultimately, Cromwell’s importance in a military role was not exaggerated and he proved to be a very successful asset within the Civil War due to his numerous military victories.

American Slavery Essay -- Slavery in the United States

Enormous changes swept through nearly every facet of American society in the years between the American Revolution and the Civil War, and the institution of slavery was no exception to this rule. Prior to the Revolution, slavery existed in every American colony. The growing population of settlers was founded on and maintained by notions of inequality, in which indentured servants and slaves provided the necessary manpower for the development of a largely agricultural economy and the settlement of an ever-diminishing frontier. First- and second generation whites began to equate race and servitude as white indentured servitude waned and black slaves came to represent the primary source of forced labor in the Americas. In the seventeenth and eighteenth centuries, many whites and blacks negotiated the terms of slavery for the first time – new slaveholders sought to define the status of slaves and to create a viable workforce out of individuals unfamiliar with the language, land, or expectations of their keepers; new slaves, still intimately tied to their native languages and cultures, struggled to comprehend the new status forced on them in a strange land. As each group viewed the other as hostile strangers, dehumanization and brutality were commonly employed by new masters to conform African behavior to their expectations and needs. After the American Revolution, slavery underwent significant transformations in concert with larger changes sweeping the political, economic, and religious structure of the nation. The spirit of liberty in which the revolution was fought gave pause to whites who had begun to take the status of bondsmen for granted and elicited different responses in the North and South. Gradual emancipation in ... ... different from that of the colonial years – it was a distinctly Southern institution, grounded in the accepted tradition of generations past, bringing masters and slaves into closer contact, and eliciting radical opposition for the first time in the North. In other ways, antebellum slavery was a product of its earlier embodiment, shaped and transformed by the political, economic, and religious revolutions of the interwar years, just as the rest of society was. By 1861, an even greater revolution would be necessary to form a society free from its yoke. Works Consulted Douglas, Frederick. Narrative of the Life of an American Slave, Written by Himself. New York: Signet, 1968. Ginzberg, Lori D. Women in Antebellum Reform. Wheeling, IL: Harlan Davidson, Inc., 2000. Kolchin, Peter. American Slavery, 1619-1877. New York: Hill and Wang, 2003. American Slavery Essay -- Slavery in the United States Enormous changes swept through nearly every facet of American society in the years between the American Revolution and the Civil War, and the institution of slavery was no exception to this rule. Prior to the Revolution, slavery existed in every American colony. The growing population of settlers was founded on and maintained by notions of inequality, in which indentured servants and slaves provided the necessary manpower for the development of a largely agricultural economy and the settlement of an ever-diminishing frontier. First- and second generation whites began to equate race and servitude as white indentured servitude waned and black slaves came to represent the primary source of forced labor in the Americas. In the seventeenth and eighteenth centuries, many whites and blacks negotiated the terms of slavery for the first time – new slaveholders sought to define the status of slaves and to create a viable workforce out of individuals unfamiliar with the language, land, or expectations of their keepers; new slaves, still intimately tied to their native languages and cultures, struggled to comprehend the new status forced on them in a strange land. As each group viewed the other as hostile strangers, dehumanization and brutality were commonly employed by new masters to conform African behavior to their expectations and needs. After the American Revolution, slavery underwent significant transformations in concert with larger changes sweeping the political, economic, and religious structure of the nation. The spirit of liberty in which the revolution was fought gave pause to whites who had begun to take the status of bondsmen for granted and elicited different responses in the North and South. Gradual emancipation in ... ... different from that of the colonial years – it was a distinctly Southern institution, grounded in the accepted tradition of generations past, bringing masters and slaves into closer contact, and eliciting radical opposition for the first time in the North. In other ways, antebellum slavery was a product of its earlier embodiment, shaped and transformed by the political, economic, and religious revolutions of the interwar years, just as the rest of society was. By 1861, an even greater revolution would be necessary to form a society free from its yoke. Works Consulted Douglas, Frederick. Narrative of the Life of an American Slave, Written by Himself. New York: Signet, 1968. Ginzberg, Lori D. Women in Antebellum Reform. Wheeling, IL: Harlan Davidson, Inc., 2000. Kolchin, Peter. American Slavery, 1619-1877. New York: Hill and Wang, 2003.

Dai Park Textbook

Stochastic Manufacturing & Service Systems Jim Dai and Hyunwoo Park School of Industrial and Systems Engineering Georgia Institute of Technology October 19, 2011 2 Contents 1 Newsvendor Problem 1. 1 Pro? t Maximization 1. 2 Cost Minimization . 1. 3 Initial Inventory . . 1. 4 Simulation . . . . . . 1. 5 Exercise . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Queueing Theory 2. 1 Introduction . . . . . . . 2. 2 Lindley Equation . . . . 2. 3 Tra? c Intensity . . . . . 2. 4 Kingman Approximation 2. 5 Little’s Law . . . . . . . 2. 6 Throughput . . . . . . . 2. 7 Simulation . . . . . . . . 2. 8 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Discrete Time Markov Chain 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . 3. 1. 1 State Space . . . . . . . . . . . . . . . . 3. 1. 2 Transition Probability Matrix . . . . . . 3. 1. 3 Initial Distribution . . . . . . . . . . . . 3. 1. 4 Markov Property . . . . . . . . . . . . . 3. 1. 5 DTMC Models . . . . . . . . . . . . . . 3. 2 Stationary Distribution . . . . . . . . . . . . . 3. 2. 1 Interpretation of Stationary Distribution 3. 2. 2 Function of Stationary Distribution . . 3. 3 Irreducibility . . . . . . . . . . . . . . . . . . . 3. 3. 1 Transition Diagram . . . . . . . . . . 3. 3. 2 Accessibility of States . . . . . . . . . . 3. 4 Periodicity . . . . . . . . . . . . . . . . . . . . . 3. 5 Recurrence and Transience . . . . . . . . . . . 3. 5. 1 Geometric Random Variable . . . . . . 3. 6 Absorption Probability . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. 7 3. 8 3. 9 3. 0 Computing Stationary Distribution Using Cut Method Introduction to Binomial Stock Price Model . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . . . . . Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS . . . . . . . . . . . . . . . . . . . . 59 61 62 63 71 71 72 73 75 78 80 80 80 82 84 91 91 96 97 100 101 103 103 104 106 107 107 108 109 111 111 117 117 130 135 148 159 4 Poisson Process 4. 1 Exponential Distribution . . . . . . . 4. 1. 1 Memoryless Property . . . . 4. 1. 2 Comparing Two Exponentials 4. 2 Homogeneous Poisson Process . . . . 4. 3 Non-homogeneous Poisson Process . 4. Thinning and Merging . . . . . . . . 4. 4. 1 Merging Poisson Process . . . 4. 4. 2 Thinning Poisson Process . . 4. 5 Simulation . . . . . . . . . . . . . . . 4. 6 Exercise . . . . . . . . . . . . . . . . 5 Continuous Time Markov Chain 5. 1 Introduction . . . . . . . . . . . 5. 1. 1 Holding Times . . . . . 5. 1. 2 Generator Matrix . . . . 5. 2 Stationary Distribution . . . . 5. 3 M/M/1 Queue . . . . . . . . . 5. 4 Variations of M/M/1 Queue . . 5. 4. 1 M/M/1/b Queue . . . . 5. 4. 2 M/M/? Queue . . . . . 5. 4. 3 M/M/k Queue . . . . . 5. 5 Open Jackson Network . . . . . 5. 5. 1 M/M/1 Queue Review . 5. 5. 2 Tandem Queue . . . . . 5. 5. Failure Inspection . . . 5. 6 Simulation . . . . . . . . . . . . 5. 7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Exercise Answers 6. 1 Newsvendor Problem . . . . . . . 6. 2 Queueing Theory . . . . . . . . . 6. 3 Discrete Time Markov Chain . . 6. 4 Poisson Process . . . . . . . . . . 6. 5 Continuous Time Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Newsvendor Problem In this course, we will learn how to design, analyze, and manage a manufacturing or service system with uncertainty. Our ? rst step is to understand how to solve a single period decision problem containing uncertainty or randomness. 1. 1 Pro? t Maximization We will start with the simplest case: selling perishable items. Suppose we are running a business retailing newspaper to Georgia Tech campus. We have to order a speci? c number of copies from the publisher every evening and sell those copies the next day.One day, if there is a big news, the number of GT people who want to buy and read a paper from you may be very high. Another day, people may just not be interested in reading a paper at all. Hence, you as a retailer, will encounter the demand variability and it is the primary un certainty you need to handle to keep your business sustainable. To do that, you want to know what is the optimal number of copies you need to order every day. By intuition, you know that there will be a few other factors than demand you need to consider. †¢ Selling price (p): How much will you charge per paper? Buying price (cv ): How much will the publisher charge per paper? This is a variable cost, meaning that this cost is proportional to how many you order. That is why it is denoted by cv . †¢ Fixed ordering price (cf ): How much should you pay just to place an order? Ordering cost is ? xed regardless of how many you order. †¢ Salvage value (s) or holding cost (h): There are two cases about the leftover items. They could carry some monetary value even if expired. Otherwise, you have to pay to get rid of them or to storing them. If they have some value, it is called salvage value. If you have to pay, it is called 5 6 CHAPTER 1.NEWSVENDOR PROBLEM holding cost. Hence , the following relationship holds: s = ? h. This is per-item value. †¢ Backorder cost (b): Whenever the actual demand is higher than how many you prepared, you lose sales. Loss-of-sales could cost you something. You may be bookkeeping those as backorders or your brand may be damaged. These costs will be represented by backorder cost. This is per-item cost. †¢ Your order quantity (y): You will decide how many papers to be ordered before you start a day. That quantity is represented by y. This is your decision variable. As a business, you are assumed to want to maximize your pro? t. Expressing our pro? t as a function of these variables is the ? rst step to obtain the optimal ordering policy. Pro? t can be interpreted in two ways: (1) revenue minus cost, or (2) money you earn minus money you lose. Let us adopt the ? rst interpretation ? rst. Revenue is represented by selling price (p) multiplied by how many you actually sell. The actual sales is bounded by the realized dema nd and how many you prepared for the period. When you order too many, you can sell at most as many as the number of people who want to buy. When you order too few, you can only sell what you prepared. Hence, your revenue is minimum of D and y, i. . min(D, y) or D ? y. Thinking about the cost, ? rst of all, you have to pay something to the publisher when buying papers, i. e. cf +ycv . Two types of additional cost will be incurred to you depending on whether your order is above or below the actual demand. When it turns out you prepared less than the demand for the period, the backorder cost b per every missed sale will occur. The amount of missed sales cannot be negative, so it can be represented by max(D ? y, 0) or (D ? y)+ . When it turns out you prepared more, the quantity of left-over items also cannot go negative, so it can be expressed as max(y ? D, 0) or (y ? D)+ .In this way of thinking, we have the following formula. Pro? t =Revenue ? Cost =Revenue ? Ordering cost ? Holding c ost ? Backorder cost =p(D ? y) ? (cf + ycv ) ? h(y ? D)+ ? b(D ? y)+ (1. 1) How about the second interpretation of pro? t? You earn p ? cv dollars every time you sell a paper. For left-over items, you lose the price you bought in addition to the holding cost per paper, i. e. cv + h. When the demand is higher than what you prepared, you lose b backorder cost. Of course, you also have to pay the ? xed ordering cost cf as well when you place an order. With this logic, we have the following pro? t function. Pro? t =Earning ?Loss =(p ? cv )(D ? y) ? (cv + h)(y ? D)+ ? b(D ? y)+ ? cf (1. 2) 1. 1. PROFIT MAXIMIZATION 7 Since we used two di? erent approaches to model the same pro? t function, (1. 1) and (1. 2) should be equivalent. Comparing the two equations, you will also notice that (D ? y) + (y ? D)+ = y. Now our quest boils down to maximizing the pro? t function. However, (1. 1) and (1. 2) contain a random element, the demand D. We cannot maximize a function of random element if we all ow the randomness to remain in our objective function. One day demand can be very high. Another day it is also possible nobody wants to buy a single paper. We have to ? ure out how to get rid of this randomness from our objective function. Let us denote pro? t for the nth period by gn for further discussion. Theorem 1. 1 (Strong Law of Large Numbers). Pr g1 + g2 + g3 +  ·  ·  · + gn = E[g1 ] n>? n lim =1 The long-run average pro? t converges to the expected pro? t for a single period with probability 1. Based on Theorem 1. 1, we can change our objective function from just pro? t to expected pro? t. In other words, by maximizing the expected pro? t, it is guaranteed that the long-run average pro? t is maximized because of Theorem 1. 1. Theorem 1. 1 is the foundational assumption for the entire course.When we will talk about the long-run average something, it involves Theorem 1. 1 in most cases. Taking expectations, we obtain the following equations corresponding to (1. 1) and ( 1. 2). E[g(D, y)] =pE[D ? y] ? (cf + ycv ) ? hE[(y ? D)+ ] ? bE[(D ? y)+ ] =(p ? cv )E[D ? y] ? (cv + h)E[(y ? D)+ ] ? bE[(D ? y)+ ] ? cf (1. 4) (1. 3) Since (1. 3) and (1. 4) are equivalent, we can choose either one of them for further discussion and (1. 4) will be used. Before moving on, it is important for you to understand what E[D? y], E[(y? D)+ ], E[(D ? y)+ ] are and how to compute them. Example 1. 1. Compute E[D ? 18], E[(18 ? D)+ ], E[(D ? 8)+ ] for the demand having the following distributions. 1. D is a discrete random variable. Probability mass function (pmf) is as follows. d Pr{D = d} 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 Answer: For a discrete random variable, you ? rst compute D ? 18, (18 ? D)+ , (D ? 18)+ for each of possible D values. 8 d CHAPTER 1. NEWSVENDOR PROBLEM 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 Pr{D = d} D ? 18 (18 ? D)+ (D ? 18)+ 10 8 0 15 3 0 18 0 2 18 0 7 18 0 12 Then, you take the weighted average using corresponding Pr{D = d} for each possible D. 1 1 1 1 1 125 (10) + (15) + (18) + (18) + (18) = 4 8 8 4 4 8 1 1 1 1 1 19 + E[(18 ?D) ] = (8) + (3) + (0) + (0) + (0) = 4 8 8 4 4 8 1 1 1 1 1 + E[(D ? 18) ] = (0) + (0) + (2) + (7) + (12) = 5 4 8 8 4 4 E[D ? 18] = 2. D is a continuous random variable following uniform distribution between 10 and 30, i. e. D ? Uniform(10, 30). Answer: Computing expectation of continuous random variable involves integration. A continuous random variable has probability density function usually denoted by f . This will be also needed to compute the expectation. In this case, fD (x) = 1 20 , 0, if x ? [10, 30] otherwise Using this information, compute the expectations directly by integration. ? E[D ? 18] = ? 30 (x ? 18)fD (x)dx (x ? 18) 10 18 = = 10 18 1 dx 20 1 20 dx + 30 (x ? 18) x 10 dx + 18 30 (x ? 18) 1 20 dx 1 20 dx = = x2 40 1 20 + 18 x=18 x=10 18x 20 18 x=30 x=18 The key idea is to remove the ? operator that we cannot handle by separating the integration interval into two. The other two expectations can 1. 1. PROFIT MAXIMIZATION be computed in a similar way. 9 ? E[(18 ? D)+ ] = 30 (18 ? x)+ fD (x)dx (18 ? x)+ 10 18 = = 10 18 1 dx 20 1 20 1 20 +0 30 (18 ? x)+ (18 ? x) 10 x2 2 x=18 dx + 18 30 (18 ? x)+ 0 18 1 20 dx = dx + 1 20 dx 18x ? = 20 x=10 ? E[(D ? 18)+ ] = 30 (18 ? x)+ fD (x)dx (x ? 8)+ 10 18 = = 10 18 1 dx 20 1 20 30 (x ? 18)+ 0 10 x2 2 dx + 18 30 (x ? 18)+ 1 20 dx 1 20 dx = =0 + 1 20 dx + 18 x=30 (x ? 18) ? 18x 20 x=18 Now that we have learned how to compute E[D? y], E[(y? D)+ ], E[(D? y)+ ], we have acquired the basic toolkit to obtain the order quantity that maximizes the expected pro? t. First of all, we need to turn these expectations of the pro? t function formula (1. 4) into integration forms. For now, assume that the demand is a nonnegative continuous random variable. 10 CHAPTER 1. NEWSVENDOR PROBLEM E[g(D, y)] =(p ? cv )E[D ? y] ? (cv + h)E[(y ? D)+ ] ? bE[(D ? y)+ ] ? f ? =(p ? cv ) 0 (x ? y)fD (x)dx ? ? (cv + h) 0 ? (y ? x)+ fD (x)dx ?b 0 (x ? y)+ fD (x)dx ? cf y ? =(p ? cv ) 0 xfD (x)dx + y y yfD (x)dx ? (cv + h) 0 ? (y ? x)fD (x)dx ?b y (x ? y)fD (x)dx ? cf y y =(p ? cv ) 0 xfD (x)dx + y 1 ? 0 y y fD (x)dx xfD (x)dx ? (cv + h) y 0 y fD (x)dx ? 0 y ? b E[D] ? 0 xfD (x)dx ? y 1 ? 0 fD (x)dx ? cf (1. 5) There can be many ways to obtain the maximum point of a function. Here we will take the derivative of (1. 5) and set it to zero. y that makes the derivative equal to zero will make E[g(D, y)] either maximized or minimized depending on the second derivative.For now, assume that such y will maximize E[g(D, y)]. We will check this later. Taking the derivative of (1. 5) will involve di? erentiating an integral. Let us review an important result from Calculus. Theorem 1. 2 (Fundamental Theorem of Calculus). For a function y H(y) = c h(x)dx, we have H (y) = h(y), where c is a constant. Theorem 1. 2 can be translated as follows for our case. y d xfD (x)dx =yfD (y) dy 0 y d fD (x)dx =fD (y) dy 0 (1. 6) (1. 7) Also remember the relationship between cd f and pdf of a continuous random variable. y FD (y) = fD (x)dx (1. 8) 1. 1. PROFIT MAXIMIZATION Use (1. 6), (1. 7), (1. ) to take the derivative of (1. 5). d E[g(D, y)] =(p ? cv ) (yfD (y) + 1 ? FD (y) ? yfD (y)) dy ? (cv + h) (FD (y) + yfD (y) ? yfD (y)) ? b (? yfD (y) ? 1 + FD (y) + yfD (y)) =(p + b ? cv )(1 ? FD (y)) ? (cv + h)FD (y) =(p + b ? cv ) ? (p + b + h)FD (y) = 0 If we di? erentiate (1. 9) one more time to obtain the second derivative, d2 E[g(D, y)] = ? (p + b + h)fD (y) dy 2 11 (1. 9) which is always nonpositive because p, b, h, fD (y) ? 0. Hence, taking the derivative and setting it to zero will give us the maximum point not the minimum point. Therefore, we obtain the following result. Theorem 1. 3 (Optimal Order Quantity).The optimal order quantity y ? is the smallest y such that FD (y) = p + b ? cv ? 1 or y = FD p+b+h p + b ? cv p+b+h . for continuous demand D. Looking at Theorem 1. 3, it provides the following intuitions. †¢ Fixed cost cf does not a? ect the o ptimal quantity you need to order. †¢ If you can procure items for free and there is no holding cost, you will prepare as many as you can. †¢ If b h, b cv , you will also prepare as many as you can. †¢ If the buying cost is almost as same as the selling price plus backorder cost, i. e. cv ? p + b, you will prepare nothing. You will prepare only upon you receive an order.Example 1. 2. Suppose p = 10, cf = 100, cv = 5, h = 2, b = 3, D ? Uniform(10, 30). How many should you order for every period to maximize your long-run average pro? t? Answer: First of all, we need to compute the criterion value. p + b ? cv 10 + 3 ? 5 8 = = p+b+h 10 + 3 + 2 15 Then, we will look up the smallest y value that makes FD (y) = 8/15. 12 1 CHAPTER 1. NEWSVENDOR PROBLEM CDF 0. 5 0 0 5 10 15 20 25 30 35 40 D Therefore, we can conclude that the optimal order quantity 8 62 = units. 15 3 Although we derived the optimal order quantity solution for the continuous demand case, Theorem 1. applies to t he discrete demand case as well. I will ? ll in the derivation for discrete case later. y ? = 10 + 20 Example 1. 3. Suppose p = 10, cf = 100, cv = 5, h = 2, b = 3. Now, D is a discrete random variable having the following pmf. d Pr{D = d} 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 What is the optimal order quantity for every period? Answer: We will use the same value 8/15 from the previous example and look up the smallest y that makes FD (y) = 8/15. We start with y = 10. 1 4 1 1 3 FD (15) = + = 4 8 8 1 1 1 1 FD (20) = + + = 4 8 8 2 1 1 1 1 3 FD (25) = + + + = 4 8 8 4 4 ? Hence, the optimal order quantity y = 25 units.FD (10) = 8 15 8 < 15 8 < 15 8 ? 15 < 1. 2 Cost Minimization Suppose you are a production manager of a large company in charge of operating manufacturing lines. You are expected to run the factory to minimize the cost. Revenue is another person’s responsibility, so all you care is the cost. To model the cost of factory operation, let us set up variables in a slightly di? erent way. 1. 2. COST MINIMIZATION 13 †¢ Understock cost (cu ): It occurs when your production is not su? cient to meet the market demand. †¢ Overstock cost (co ): It occurs when you produce more than the market demand.In this case, you may have to rent a space to store the excess items. †¢ Unit production cost (cv ): It is the cost you should pay whenever you manufacture one unit of products. Material cost is one of this category. †¢ Fixed operating cost (cf ): It is the cost you should pay whenever you decide to start running the factory. As in the pro? t maximization case, the formula for cost expressed in terms of cu , co , cv , cf should be developed. Given random demand D, we have the following equation. Cost =Manufacturing Cost + Cost associated with Understock Risk + Cost associated with Overstock Risk =(cf + ycv ) + cu (D ? )+ + co (y ? D)+ (1. 10) (1. 10) obviously also contains randomness from D. We cannot minimize a random objective itself. Instead, based on Theorem 1. 1, we will minimize expected cost then the long-run average cost will be also guaranteed to be minimized. Hence, (1. 10) will be transformed into the following. E[Cost] =(cf + ycv ) + cu E[(D ? y)+ ] + co E[(y ? D)+ ] ? ? =(cf + ycv ) + cu 0 ? (x ? y)+ fD (x)dx + co 0 y (y ? x)+ fD (x)dx (y ? x)fD (x)dx (1. 11) 0 =(cf + ycv ) + cu y (x ? y)fD (x)dx + co Again, we will take the derivative of (1. 11) and set it to zero to obtain y that makes E[Cost] minimized.We will verify the second derivative is positive in this case. Let g here denote the cost function and use Theorem 1. 2 to take the derivative of integrals. d E[g(D, y)] =cv + cu (? yfD (y) ? 1 + FD (y) + yfD (y)) dy + co (FD (y) + yfD (y) ? yfD (y)) =cv + cu (FD (y) ? 1) + co FD (y) ? (1. 12) The optimal production quantity y is obtained by setting (1. 12) to be zero. Theorem 1. 4 (Optimal Production Quantity). The optimal production quantity that minimizes the long-run average cost is the smallest y such tha t FD (y) = cu ? cv or y = F ? 1 cu + co cu ? cv cu + co . 14 CHAPTER 1. NEWSVENDOR PROBLEM Theorem 1. can be also applied to discrete demand. Several intuitions can be obtained from Theorem 1. 4. †¢ Fixed cost (cf ) again does not a? ect the optimal production quantity. †¢ If understock cost (cu ) is equal to unit production cost (cv ), which makes cu ? cv = 0, then you will not produce anything. †¢ If unit production cost and overstock cost are negligible compared to understock cost, meaning cu cv , co , you will prepare as much as you can. To verify the second derivative of (1. 11) is indeed positive, take the derivative of (1. 12). d2 E[g(D, y)] = (cu + co )fD (y) dy 2 (1. 13) (1. 13) is always nonnegative because cu , co ? . Hence, y ? obtained from Theorem 1. 4 minimizes the cost instead of maximizing it. Before moving on, let us compare criteria from Theorem 1. 3 and Theorem 1. 4. p + b ? cv p+b+h and cu ? cv cu + co Since the pro? t maximization problem solved previously and the cost minimization problem solved now share the same logic, these two criteria should be somewhat equivalent. We can see the connection by matching cu = p + b, co = h. In the pro? t maximization problem, whenever you lose a sale due to underpreparation, it costs you the opportunity cost which is the selling price of an item and the backorder cost.Hence, cu = p + b makes sense. When you overprepare, you should pay the holding cost for each left-over item, so co = h also makes sense. In sum, Theorem 1. 3 and Theorem 1. 4 are indeed the same result in di? erent forms. Example 1. 4. Suppose demand follows Poisson distribution with parameter 3. The cost parameters are cu = 10, cv = 5, co = 15. Note that e? 3 ? 0. 0498. Answer: The criterion value is cu ? cv 10 ? 5 = = 0. 2, cu + co 10 + 15 so we need to ? nd the smallest y such that makes FD (y) ? 0. 2. Compute the probability of possible demands. 30 ? 3 e = 0. 0498 0! 31 Pr{D = 1} = e? 3 = 0. 1494 1! 32 ? Pr{D = 2} = e = 0. 2241 2! Pr{D = 0} = 1. 3. INITIAL INVENTORY Interpret these values into FD (y). FD (0) =Pr{D = 0} = 0. 0498 < 0. 2 FD (1) =Pr{D = 0} + Pr{D = 1} = 0. 1992 < 0. 2 FD (2) =Pr{D = 0} + Pr{D = 1} + Pr{D = 2} = 0. 4233 ? 0. 2 Hence, the optimal production quantity here is 2. 15 1. 3 Initial Inventory Now let us extend our model a bit further. As opposed to the assumption that we had no inventory at the beginning, suppose that we have m items when we decide how many we need to order. The solutions we have developed in previous sections assumed that we had no inventory when placing an order.If we had m items, we should order y ? ? m items instead of y ? items. In other words, the optimal order or production quantity is in fact the optimal order-up-to or production-up-to quantity. We had another implicit assumption that we should order, so the ? xed cost did not matter in the previous model. However, if cf is very large, meaning that starting o? a production line or placing an order i s very expensive, we may want to consider not to order. In such case, we have two scenarios: to order or not to order. We will compare the expected cost for the two scenarios and choose the option with lower expected cost.Example 1. 5. Suppose understock cost is $10, overstock cost is $2, unit purchasing cost is $4 and ? xed ordering cost is $30. In other words, cu = 10, co = 2, cv = 4, cf = 30. Assume that D ? Uniform(10, 20) and we already possess 10 items. Should we order or not? If we should, how many items should we order? Answer: First, we need to compute the optimal amount of items we need to prepare for each day. Since cu ? cv 1 10 ? 4 = , = cu + co 10 + 2 2 the optimal order-up-to quantity y ? = 15 units. Hence, if we need to order, we should order 5 = y ? ? m = 15 ? 10 items. Let us examine whether we should actually order or not. . Scenario 1: Not To Order If we decide not to order, we will not have to pay cf and cv since we order nothing actually. We just need to conside r understock and overstock risks. We will operate tomorrow with 10 items that we currently have if we decide not to order. E[Cost] =cu E[(D ? 10)+ ] + co E[(10 ? D)+ ] =10(E[D] ? 10) + 2(0) = $50 16 CHAPTER 1. NEWSVENDOR PROBLEM Note that in this case E[(10 ? D)+ ] = 0 because D is always greater than 10. 2. Scenario 2: To Order If we decide to order, we will order 5 items. We should pay cf and cv accordingly. Understock and overstock risks also exist in this case.Since we will order 5 items to lift up the inventory level to 15, we will run tomorrow with 15 items instead of 10 items if we decide to order. E[Cost] =cf + (15 ? 10)cv + cu E[(D ? 15)+ ] + co E[(15 ? D)+ ] =30 + 20 + 10(1. 25) + 2(1. 25) = $65 Since the expected cost of not ordering is lower than that of ordering, we should not order if we already have 10 items. It is obvious that if we have y ? items at hands right now, we should order nothing since we already possess the optimal amount of items for tomorrow’s op eration. It is also obvious that if we have nothing currently, we should order y ? items to prepare y ? tems for tomorrow. There should be a point between 0 and y ? where you are indi? erent between order and not ordering. Suppose you as a manager should give instruction to your assistant on when he/she should place an order and when should not. Instead of providing instructions for every possible current inventory level, it is easier to give your assistant just one number that separates the decision. Let us call that number the critical level of current inventory m? . If we have more than m? items at hands, the expected cost of not ordering will be lower than the expected cost of ordering, so we should not order.Conversely, if we have less than m? items currently, we should order. Therefore, when we have exactly m? items at hands right now, the expected cost of ordering should be equal to that of not ordering. We will use this intuition to obtain m? value. The decision process is s ummarized in the following ? gure. m* Critical level for placing an order y* Optimal order-up-to quantity Inventory If your current inventory lies here, you should order. Order up to y*. If your current inventory lies here, you should NOT order because your inventory is over m*. 1. 4. SIMULATION 17 Example 1. 6.Given the same settings with the previous example (cu = 10, cv = 4, co = 2, cf = 30), what is the critical level of current inventory m? that determines whether you should order or not? Answer: From the answer of the previous example, we can infer that the critical value should be less than 10, i. e. 0 < m? < 10. Suppose we currently own m? items. Now, evaluate the expected costs of the two scenarios: ordering and not ordering. 1. Scenario 1: Not Ordering E[Cost] =cu E[(D ? m? )+ ] + co E[(m? ? D)+ ] =10(E[D] ? m? ) + 2(0) = 150 ? 10m? 2. Scenario 2: Ordering In this case, we will order.Given that we will order, we will order y ? ?m? = 15 ? m? items. Therefore, we will start tomorrow with 15 items. E[Cost] =cf + (15 ? 10)cv + cu E[(D ? 15)+ ] + co E[(15 ? D)+ ] =30 + 4(15 ? m? ) + 10(1. 25) + 2(1. 25) = 105 ? 4m? At m? , (1. 14) and (1. 15) should be equal. 150 ? 10m? = 105 ? 4m? ? m? = 7. 5 units (1. 15) (1. 14) The critical value is 7. 5 units. If your current inventory is below 7. 5, you should order for tomorrow. If the current inventory is above 7. 5, you should not order. 1. 4 Simulation Generate 100 random demands from Uniform(10, 30). p = 10, cf = 30, cv = 4, h = 5, b = 3 1 p + b ? v 10 + 3 ? 4 = = p + b + h 10 + 3 + 5 2 The optimal order-up-to quantity from Theorem 1. 3 is 20. We will compare the performance between the policies of y = 15, 20, 25. Listing 1. 1: Continuous Uniform Demand Simulation # Set up parameters p=10;cf=30;cv=4;h=5;b=3 # How many random demands will be generated? n=100 # Generate n random demands from the uniform distribution 18 Dmd=runif(n,min=10,max=30) CHAPTER 1. NEWSVENDOR PROBLEM # Test the policy where we order 15 it ems for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 33. 4218 # Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 44. 37095 # Test the policy where we order 25 items for every period y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 32. 62382 You can see the policy with y = 20 maximizes the 100-period average pro? t as promised by the theory. In fact, if n is relatively small, it is not guaranteed that we have maximized pro? t even if we run based on the optimal policy obtained from this section.The underlying assumption is that we should operate with this policy for a long time. Then, Theorem 1. 1 guarantees that the average pro? t will be maximized when we use the optimal ordering policy. Discrete demand case can also be simulated. Suppose the demand has the following distribution. All other parameters remain same. d Pr{D = d} 10 1 4 15 1 8 20 1 4 25 1 8 30 1 4 The theoretic optimal order-up-to quantity in this case is also 20. Let us test three policies: y = 15, 20, 25. Listing 1. 2: Discrete Demand Simulation # Set up parameters p=10;cf=30;cv=4;h=5;b=3 # How many random demands will be generated? =100 # Generate n random demands from the discrete demand distribution Dmd=sample(c(10,15,20,25,30),n,replace=TRUE,c(1/4,1/8,1/4,1/8,1/4)) # Test the policy where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 19. 35 # Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 31. 05 # Test the policy where we order 25 items for every period 1. 5. EXERCISE y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 26. 55 19There are other distributions such as triangular, normal, Poisson or binomial distributions available in R. When you do your senior project, for example, you will observe the demand for a departm ent or a factory. You ? rst approximate the demand using these theoretically established distributions. Then, you can simulate the performance of possible operation policies. 1. 5 Exercise 1. Show that (D ? y) + (y ? D)+ = y. 2. Let D be a discrete random variable with the following pmf. d Pr{D = d} Find (a) E[min(D, 7)] (b) E[(7 ? D)+ ] where x+ = max(x, 0). 3. Let D be a Poisson random variable with parameter 3.Find (a) E[min(D, 2)] (b) E[(3 ? D)+ ]. Note that pmf of a Poisson random variable with parameter ? is Pr{D = k} = ? k e . k! 5 1 10 6 3 10 7 4 10 8 1 10 9 1 10 4. Let D be a continuous random variable and uniformly distributed between 5 and 10. Find (a) E[max(D, 8)] (b) E[(D ? 8)? ] where x? = min(x, 0). 5. Let D be an exponential random variable with parameter 7. Find (a) E[max(D, 3)] 20 (b) E[(D ? 4)? ]. CHAPTER 1. NEWSVENDOR PROBLEM Note that pdf of an exponential random variable with parameter ? is fD (x) = ? e x for x ? 0. 6. David buys fruits and vegetables wholesal e and retails them at Davids Produce on La Vista Road.One of the more di? cult decisions is the amount of bananas to buy. Let us make some simplifying assumptions, and assume that David purchases bananas once a week at 10 cents per pound and retails them at 30 cents per pound during the week. Bananas that are more than a week old are too ripe and are sold for 5 cents per pound. (a) Suppose the demand for the good bananas follows the same distribution as D given in Problem 2. What is the expected pro? t of David in a week if he buys 7 pounds of banana? (b) Now assume that the demand for the good bananas is uniformly distributed between 5 and 10 like in Problem 4.What is the expected pro? t of David in a week if he buys 7 pounds of banana? (c) Find the expected pro? t if David’s demand for the good bananas follows an exponential distribution with mean 7 and if he buys 7 pounds of banana. 7. Suppose we are selling lemonade during a football game. The lemonade sells for $18 per g allon but only costs $3 per gallon to make. If we run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a value of $1. Assume that we believe the fans would buy 10 gallons with probability 0. 1, 11 gallons with probability 0. , 12 gallons with probability 0. 4, 13 gallons with probability 0. 2, and 14 gallons with probability 0. 1. (a) What is the mean demand? (b) If 11 gallons are prepared, what is the expected pro? t? (c) What is the best amount of lemonade to order before the game? (d) Instead, suppose that the demand was normally distributed with mean 1000 gallons and variance 200 gallons2 . How much lemonade should be ordered? 8. Suppose that a bakery specializes in chocolate cakes. Assume the cakes retail at $20 per cake, but it takes $10 to prepare each cake. Cakes cannot be sold after one week, and they have a negligible salvage value.It is estimated that the weekly demand for cakes is: 15 cakes in 5% of the weeks, 1 6 cakes in 20% of the weeks, 17 cakes in 30% of the weeks, 18 cakes in 25% of the weeks, 19 cakes in 10% of the weeks, and 20 cakes in 10% of the weeks. How many cakes should the bakery prepare each week? What is the bakery’s expected optimal weekly pro? t? 1. 5. EXERCISE 21 9. A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day.In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $600, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $25 fo r each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $480 each. (Assume that the order can only be made at the beginning of the month. (a) Assume that the demand has a discrete uniform distribution from 10 to 15 cameras a month (inclusive). If 12 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost? 10.Next month’s production at a manufacturing company will use a certain solvent for part of its production process. Assume that there is an ordering cost of $1,000 incurred whenever an order for the solvent is placed and the solvent costs $40 per liter. Due to short product life cycle, unused solvent cannot be used in following months. There will be a $10 disposal charge for each liter of solvent left over at the end of the month. If there is a shortage of solvent, the production process is seriously disrupted at a cost of $100 per liter short. Assume that the initial inventory level is m, where m = 0, 100, 300, 500 and 700 liters. a) What is the optimal ordering quantity for each case when the demand is discrete with Pr{D = 500} = Pr{D = 800} = 1/8, Pr{D = 600} = 1/2 and Pr{D = 700} = 1/4? (b) What is the optimal ordering policy for arbitrary initial inventory level m? (You need to specify the critical value m? in addition to the optimal order-up-to quantity y ? . When m ? m? , you make an order. Otherwise, do not order. ) (c) Assume optimal quantity will be ordered. What is the total expected cost when the initial inventory m = 0? What is the total expected cost when the initial inventory m = 700? 22 CHAPTER 1. NEWSVENDOR PROBLEM 11.Redo Problem 10 for the case where the demand is governed by the continuous uniform distribution varying between 400 and 800 liters. 12. An automotive company will make one last production run of parts for Part 947A and 947B, which are not interchangeable. These parts are no longer used in new cars, but will be needed as replacements for warranty work in existing cars. The demand during the warranty period for 947A is approximately normally distributed with mean 1,500,000 parts and standard deviation 500,000 parts, while the mean and standard deviation for 947B is 500,000 parts and 100,000 parts. (Assume that two demands are independent. Ignoring the cost of setting up for producing the part, each part costs only 10 cents to produce. However, if additional parts are needed beyond what has been produced, they will be purchased at 90 cents per part (the same price for which the automotive company sells its parts). Parts remaining at the end of the warr anty period have a salvage value of 8 cents per part. There has been a proposal to produce Part 947C, which can be used to replace either of the other two parts. The unit cost of 947C jumps from 10 to 14 cents, but all other costs remain the same. (a) Assuming 947C is not produced, how many 947A should be produced? b) Assuming 947C is not produced, how many 947B should be produced? (c) How many 947C should be produced in order to satisfy the same fraction of demand from parts produced in-house as in the ? rst two parts of this problem. (d) How much money would be saved or lost by producing 947C, but meeting the same fraction of demand in-house? (e) Is your answer to question (c), the optimal number of 947C to produce? If not, what would be the optimal number of 947C to produce? (f) Should the more expensive part 947C be produced instead of the two existing parts 947A and 947B. Why? Hint: compare the expected total costs.Also, suppose that D ? Normal( µ, ? 2 ). q xv 0 (x?  µ)2 1 e? 2? 2 dx = 2 q (x ?  µ) v 0 q (x?  µ)2 1 e? 2? 2 dx 2 + µ =  µ2 v 0 (q?  µ)2 (x?  µ)2 1 e? 2? 2 dx 2 t 1 v e? 2? 2 dt +  µPr{0 ? D ? q} 2 2 where, in the 2nd step, we changed variable by letting t = (x ?  µ)2 . 1. 5. EXERCISE 23 13. A warranty department manages the after-sale service for a critical part of a product. The department has an obligation to replace any damaged parts in the next 6 months. The number of damaged parts X in the next 6 months is assumed to be a random variable that follows the following distribution: x Pr{X = x} 100 . 1 200 . 2 300 . 5 400 . 2The department currently has 200 parts in stock. The department needs to decide if it should make one last production run for the part to be used for the next 6 months. To start the production run, the ? xed cost is $2000. The unit cost to produce a part is $50. During the warranty period of next 6 months, if a replacement request comes and the department does not have a part available in house, it has to buy a part from the spot-market at the cost of $100 per part. Any part left at the end of 6 month sells at $10. (There is no holding cost. ) Should the department make the production run? If so, how many items should it produce? 4. A store sells a particular brand of fresh juice. By the end of the day, any unsold juice is sold at a discounted price of $2 per gallon. The store gets the juice daily from a local producer at the cost of $5 per gallon, and it sells the juice at $10 per gallon. Assume that the daily demand for the juice is uniformly distributed between 50 gallons to 150 gallons. (a) What is the optimal number of gallons that the store should order from the distribution each day in order to maximize the expected pro? t each day? (b) If 100 gallons are ordered, what is the expected pro? t per day? 15. An auto company is to make one ? al purchase of a rare engine oil to ful? ll its warranty services for certain car models. The current price for the engine oil is $1 per g allon. If the company runs out the oil during the warranty period, it will purchase the oil from a supply at the market price of $4 per gallon. Any leftover engine oil after the warranty period is useless, and costs $1 per gallon to get rid of. Assume the engine oil demand during the warranty is uniformly distributed (continuous distribution) between 1 million gallons to 2 million gallons, and that the company currently has half million gallons of engine oil in stock (free of charge). a) What is the optimal amount of engine oil the company should purchase now in order to minimize the total expected cost? (b) If 1 million gallons are purchased now, what is the total expected cost? 24 CHAPTER 1. NEWSVENDOR PROBLEM 16. A company is obligated to provide warranty service for Product A to its customers next year. The warranty demand for the product follows the following distribution. d Pr{D = d} 100 . 2 200 . 4 300 . 3 400 . 1 The company needs to make one production run to satisfy the wa rranty demand for entire next year. Each unit costs $100 to produce; the penalty cost of a unit is $500.By the end of the year, the savage value of each unit is $50. (a) Suppose that the company has currently 0 units. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. (b) Suppose that the company has currently 100 units at no cost and there is $20000 ? xed cost to start the production run. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. 17. Suppose you are running a restaurant having only one menu, lettuce salad, in the Tech Square.You should order lettuce every day 10pm after closing. Then, your supplier delivers the ordered amount of lettuce 5am next morning. Store hours is from 11am to 9pm every day. The demand for the lettuce salad for a day (11am-9pm) has the following distribution. d Pr{D = d} 20 1/6 25 1/3 30 1/3 35 1/6 One lettu ce salad requires two units of lettuce. The selling price of lettuce salad is $6, the buying price of one unit of lettuce is $1. Of course, leftover lettuce of a day cannot be used for future salad and you have to pay 50 cents per unit of lettuce for disposal. (a) What is the optimal order-up-to quantity of lettuce for a day? b) If you ordered 50 units of lettuce today, what is the expected pro? t of tomorrow? Include the purchasing cost of 50 units of lettuce in your calculation. Chapter 2 Queueing Theory Before getting into Discrete-time Markov Chains, we will learn about general issues in the queueing theory. Queueing theory deals with a set of systems having waiting space. It is a very powerful tool that can model a broad range of issues. Starting from analyzing a simple queue, a set of queues connected with each other will be covered as well in the end. This chapter will give you the background knowledge when you read the required book, The Goal.We will revisit the queueing the ory once we have more advanced modeling techniques and knowledge. 2. 1 Introduction Think about a service system. All of you must have experienced waiting in a service system. One example would be the Student Center or some restaurants. This is a human system. A bit more automated service system that has a queue would be a call center and automated answering machines. We can imagine a manufacturing system instead of a service system. These waiting systems can be generalized as a set of bu? ers and servers. There are key factors when you try to model such a system.What would you need to analyze your system? †¢ How frequently customers come to your system? > Inter-arrival Times †¢ How fast your servers can serve the customers? > Service Times †¢ How many servers do you have? > Number of Servers †¢ How large is your waiting space? > Queue Size If you can collect data about these metrics, you can characterize your queueing system. In general, a queueing system can be denoted as follows. G/G/s/k 25 26 CHAPTER 2. QUEUEING THEORY The ? rst letter characterizes the distribution of inter-arrival times. The second letter characterizes the distribution of service times.The third number denotes the number of servers of your queueing system. The fourth number denotes the total capacity of your system. The fourth number can be omitted and in such case it means that your capacity is in? nite, i. e. your system can contain any number of people in it up to in? nity. The letter â€Å"G† represents a general distribution. Other candidate characters for this position is â€Å"M† and â€Å"D† and the meanings are as follows. †¢ G: General Distribution †¢ M: Exponential Distribution †¢ D: Deterministic Distribution (or constant) The number of servers can vary from one to many to in? nity.The size of bu? er can also be either ? nite or in? nite. To simplify the model, assume that there is only a single server and we have in? ni te bu? er. By in? nite bu? er, it means that space is so spacious that it is as if the limit does not exist. Now we set up the model for our queueing system. In terms of analysis, what are we interested in? What would be the performance measures of such systems that you as a manager should know? †¢ How long should your customer wait in line on average? †¢ How long is the waiting line on average? There are two concepts of average. One is average over time.This applies to the average number of customers in the system or in the queue. The other is average over people. This applies to the average waiting time per customer. You should be able to distinguish these two. Example 2. 1. Assume that the system is empty at t = 0. Assume that u1 = 1, u2 = 3, u3 = 2, u4 = 3, v1 = 4, v2 = 2, v3 = 1, v4 = 2. (ui is ith customer’s inter-arrival time and vi is ith customer’s service time. ) 1. What is the average number of customers in the system during the ? rst 10 minutes? 2 . What is the average queue size during the ? rst 10 minutes? 3.What is the average waiting time per customer for the ? rst 4 customers? Answer: 1. If we draw the number of people in the system at time t with respect to t, it will be as follows. 2. 2. LINDLEY EQUATION 3 2 1 0 27 Z(t) 0 1 2 3 4 5 6 7 8 9 10 t E[Z(t)]t? [0,10] = 1 10 10 Z(t)dt = 0 1 (10) = 1 10 2. If we draw the number of people in the queue at time t with respect to t, it will be as follows. 3 2 1 0 Q(t) 0 1 2 3 4 5 6 7 8 9 10 t E[Q(t)]t? [0,10] = 1 10 10 Q(t)dt = 0 1 (2) = 0. 2 10 3. We ? rst need to compute waiting times for each of 4 customers. Since the ? rst customer does not wait, w1 = 0.Since the second customer arrives at time 4, while the ? rst customer’s service ends at time 5. So, the second customer has to wait 1 minute, w2 = 1. Using the similar logic, w3 = 1, w4 = 0. E[W ] = 0+1+1+0 = 0. 5 min 4 2. 2 Lindley Equation From the previous example, we now should be able to compute each customerâ€℠¢s waiting time given ui , vi . It requires too much e? ort if we have to draw graphs every time we need to compute wi . Let us generalize the logic behind calculating waiting times for each customer. Let us determine (i + 1)th customer’s waiting 28 CHAPTER 2. QUEUEING THEORY time.If (i + 1)th customer arrives after all the time ith customer waited and got served, (i + 1)th customer does not have to wait. Its waiting time is 0. Otherwise, it has to wait wi + vi ? ui+1 . Figure 2. 1, and Figure 2. 2 explain the two cases. ui+1 wi vi wi+1 Time i th arrival i th service start (i+1)th arrival i th service end Figure 2. 1: (i + 1)th arrival before ith service completion. (i + 1)th waiting time is wi + vi ? ui+1 . ui+1 wi vi Time i th arrival i th service start i th service end (i+1)th arrival Figure 2. 2: (i + 1)th arrival after ith service completion. (i + 1)th waiting time is 0.Simply put, wi+1 = (wi + vi ? ui+1 )+ . This is called the Lindley Equation. Example 2. 2. Given the f ollowing inter-arrival times and service times of ? rst 10 customers, compute waiting times and system times (time spent in the system including waiting time and service time) for each customer. ui = 3, 2, 5, 1, 2, 4, 1, 5, 3, 2 vi = 4, 3, 2, 5, 2, 2, 1, 4, 2, 3 Answer: Note that system time can be obtained by adding waiting time and service time. Denote the system time of ith customer by zi . ui vi wi zi 3 4 0 4 2 3 2 5 5 2 0 2 1 5 1 6 2 2 4 6 4 2 2 4 1 1 3 4 5 4 0 4 3 2 1 3 2 3 1 4 2. 3. TRAFFIC INTENSITY 9 2. 3 Suppose Tra? c Intensity E[ui ] =mean inter-arrival time = 2 min E[vi ] =mean service time = 4 min. Is this queueing system stable? By stable, it means that the queue size should not go to the in? nity. Intuitively, this queueing system will not last because average service time is greater than average inter-arrival time so your system will soon explode. What was the logic behind this judgement? It was basically comparing the average inter-arrival time and the average serv ice time. To simplify the judgement, we come up with a new quantity called the tra? c intensity. De? nition 2. 1 (Tra? Intensity). Tra? c intensity ? is de? ned to be ? = 1/E[ui ] ? =  µ 1/E[vi ] where ? is the arrival rate and  µ is the service rate. Given a tra? c intensity, it will fall into one of the following three categories. †¢ If ? < 1, the system is stable. †¢ If ? = 1, the system is unstable unless both inter-arrival times and service times are deterministic (constant). †¢ If ? > 1, the system is unstable. Then, why don’t we call ? utilization instead of tra? c intensity? Utilization seems to be more intuitive and user-friendly name. In fact, utilization just happens to be same as ? if ? < 1.However, the problem arises if ? > 1 because utilization cannot go over 100%. Utilization is bounded above by 1 and that is why tra? c intensity is regarded more general notation to compare arrival and service rates. De? nition 2. 2 (Utilization). Utilization is de? ned as follows. Utilization = ? , 1, if ? < 1 if ? ? 1 Utilization can also be interpreted as the long-run fraction of time the server is utilized. 2. 4 Kingman Approximation Formula Theorem 2. 1 (Kingman’s High-tra? c Approximation Formula). Assume the tra? c intensity ? < 1 and ? is close to 1. The long-run average waiting time in 0 a queue E[W ] ? E[vi ] CHAPTER 2. QUEUEING THEORY ? 1 c2 + c2 a s 2 where c2 , c2 are squared coe? cient of variation of inter-arrival times and service a s times de? ned as follows. c2 = a Var[u1 ] (E[u1 ]) 2, c2 = s Var[v1 ] (E[v1 ]) 2 Example 2. 3. 1. Suppose inter-arrival time follows an exponential distribution with mean time 3 minutes and service time follows an exponential distribution with mean time 2 minutes. What is the expected waiting time per customer? 2. Suppose inter-arrival time is constant 3 minutes and service time is also constant 2 minutes. What is the expected waiting time per customer?Answer: 1. Tra? c intensity is ? = 1/E[ui ] 1/3 2 ? = = = .  µ 1/E[vi ] 1/2 3 Since both inter-arrival times and service times are exponentially distributed, E[ui ] = 3, Var[ui ] = 32 = 9, E[vi ] = 2, Var[vi ] = 22 = 4. Therefore, c2 = Var[ui ]/(E[ui ])2 = 1, c2 = 1. Hence, s a E[W ] =E[vi ] =2 ? c2 + c2 s a 1 2 2/3 1+1 = 4 minutes. 1/3 2 2. Tra? c intensity remains same, 2/3. However, since both inter-arrival times and service times are constant, their variances are 0. Thus, c2 = a c2 = 0. s E[W ] = 2 2/3 1/3 0+0 2 = 0 minutes It means that none of the customers will wait upon their arrival.As shown in the previous example, when the distributions for both interarrival times and service times are exponential, the squared coe? cient of variation term becomes 1 from the Kingman’s approximation formula and the formula 2. 5. LITTLE’S LAW 31 becomes exact to compute the average waiting time per customer for M/M/1 queue. E[W ] =E[vi ] ? 1 Also note that if inter-arrival time or service time distribution is deterministic, c2 or c2 becomes 0. a s Example 2. 4. You are running a highway collecting money at the entering toll gate. You reduced the utilization level of the highway from 90% to 80% by adopting car pool lane.How much does the average waiting time in front of the toll gate decrease? Answer: 0. 8 0. 9 = 9, =4 1 ? 0. 9 1 ? 0. 8 The average waiting time in in front of the toll gate is reduced by more than a half. The Goal is about identifying bottlenecks in a plant. When you become a manager of a company and are running a expensive machine, you usually want to run it all the time with full utilization. However, the implication of Kingman formula tells you that as your utilization approaches to 100%, the waiting time will be skyrocketing. It means that if there is any uncertainty or random ? ctuation input to your system, your system will greatly su? er. In lower ? region, increasing ? is not that bad. If ? near 1, increasing utilization a little bit can lead to a disaster. Atl anta, 10 years ago, did not su? er that much of tra? c problem. As its tra? c infrastructure capacity is getting closer to the demand, it is getting more and more fragile to uncertainty. A lot of strategies presented in The Goal is in fact to decrease ?. You can do various things to reduce ? of your system by outsourcing some process, etc. You can also strategically manage or balance the load on di? erent parts of your system.You may want to utilize customer service organization 95% of time, while utilization of sales people is 10%. 2. 5 Little’s Law L = ? W The Little’s Law is much more general than G/G/1 queue. It can be applied to any black box with de? nite boundary. The Georgia Tech campus can be one black box. ISyE building itself can be another. In G/G/1 queue, we can easily get average size of queue or service time or time in system as we di? erently draw box onto the queueing system. The following example shows that Little’s law can be applied in broade r context than the queueing theory. 32 CHAPTER 2. QUEUEING THEORY Example 2. 5 (Merge of I-75 and I-85).Atlanta is the place where two interstate highways, I-75 and I-85, merge and cross each other. As a tra? c manager of Atlanta, you would like to estimate the average time it takes to drive from the north con? uence point to the south con? uence point. On average, 100 cars per minute enter the merged area from I-75 and 200 cars per minute enter the same area from I-85. You also dispatched a chopper to take a aerial snapshot of the merged area and counted how many cars are in the area. It turned out that on average 3000 cars are within the merged area. What is the average time between entering and exiting the area per vehicle?Answer: L =3000 cars ? =100 + 200 = 300 cars/min 3000 L = 10 minutes ? W = = ? 300 2. 6 Throughput Another focus of The Goal is set on the throughput of a system. Throughput is de? ned as follows. De? nition 2. 3 (Throughput). Throughput is the rate of output ? ow from a system. If ? ? 1, throughput= ?. If ? > 1, throughput=  µ. The bounding constraint of throughput is either arrival rate or service rate depending on the tra? c intensity. Example 2. 6 (Tandem queue with two stations). Suppose your factory production line has two stations linked in series. Every raw material coming into your line should be processed by Station A ? rst.Once it is processed by Station A, it goes to Station B for ? nishing. Suppose raw material is coming into your line at 15 units per minute. Station A can process 20 units per minute and Station B can process 25 units per minute. 1. What is the throughput of the entire system? 2. If we double the arrival rate of raw material from 15 to 30 units per minute, what is the throughput of the whole system? Answer: 1. First, obtain the tra? c intensity for Station A. ?A = ? 15 = = 0. 75  µA 20 Since ? A < 1, the throughput of Station A is ? = 15 units per minute. Since Station A and Station B is linked in series, the throughput of Station . 7. SIMULATION A becomes the arrival rate for Station B. ?B = ? 15 = = 0. 6  µB 25 33 Also, ? B < 1, the throughput of Station B is ? = 15 units per minute. Since Station B is the ? nal stage of the entire system, the throughput of the entire system is also ? = 15 units per minute. 2. Repeat the same steps. ?A = 30 ? = = 1. 5  µA 20 Since ? A > 1, the throughput of Station A is  µA = 20 units per minute, which in turn becomes the arrival rate for Station B. ?B =  µA 20 = 0. 8 =  µB 25 ?B < 1, so the throughput of Station B is  µA = 20 units per minute, which in turn is the throughput of the whole system. 2. 7 SimulationListing 2. 1: Simulation of a Simple Queue and Lindley Equation N = 100 # Function for Lindley Equation lindley = function(u,v){ for (i in 1:length(u)) { if(i==1) w = 0 else { w = append(w, max(w[i-1]+v[i-1]-u[i], 0)) } } return(w) } # # u v CASE 1: Discrete Distribution Generate N inter-arrival times and service times = sample( c(2,3,4),N,replace=TRUE,c(1/3,1/3,1/3)) = sample(c(1,2,3),N,replace=TRUE,c(1/3,1/3,1/3)) # Compute waiting time for each customer w = lindley(u,v) w # CASE 2: Deterministic Distribution # All inter-arrival times are 3 minutes and all service times are 2 minutes # Observe that nobody waits in this case. 4 u = rep(3, 100) v = rep(2, 100) w = lindley(u,v) w CHAPTER 2. QUEUEING THEORY The Kingman’s approximation formula is exact when inter-arrival times and service times follow iid exponential distribution. E[W ] = 1  µ ? 1 We can con? rm this equation by simulating an M/M/1 queue. Listing 2. 2: Kingman Approximation # lambda = arrival rate, mu = service rate N = 10000; lambda = 1/10; mu = 1/7 # Generate N inter-arrival times and service times from exponential distribution u = rexp(N,rate=lambda) v = rexp(N,rate=mu) # Compute the average waiting time of each customer w = lindley(u,v) mean(w) > 16. 0720 # Compare with Kingman approximation rho = lambda/mu (1/mu)*(rho/(1-rho)) > 16. 33333 The Kingman’s approximation formula becomes more and more accurate as N grows. 2. 8 Exercise 1. Let Y be a random variable with p. d. f. ce? 3s for s ? 0, where c is a constant. (a) Determine c. (b) What is the mean, variance, and squared coe? cient of variation of Y where the squared coe? cient of variation of Y is de? ned to be Var[Y ]/(E[Y ]2 )? 2. Consider a single server queue. Initially, there is no customer in the system.Suppose that the inter-arrival times of the ? rst 15 customers are: 2, 5, 7, 3, 1, 4, 9, 3, 10, 8, 3, 2, 16, 1, 8 2. 8. EXERCISE 35 In other words, the ? rst customer will arrive at t = 2 minutes, and the second will arrive at t = 2 + 5 minutes, and so on. Also, suppose that the service time of the ? rst 15 customers are 1, 4, 2, 8, 3, 7, 5, 2, 6, 11, 9, 2, 1, 7, 6 (a) Compute the average waiting time (the time customer spend in bu? er) of the ? rst 10 departed customers. (b) Compute the average system time (waiting time plus service time) of the ? st 10 departed customers. (c) Compute the average queue size during the ? rst 20 minutes. (d) Compute the average server utilization during the ? rst 20 minutes. (e) Does the Little’s law of hold for the average queue size in the ? rst 20 minutes? 3. We want to decide whether to employ a human operator or buy a machine to paint steel beams with a rust inhibitor. Steel beams are produced at a constant rate of one every 14 minutes. A skilled human operator takes an average time of 700 seconds to paint a steel beam, with a standard deviation of 300 seconds.An automatic painter takes on average 40 seconds more than the human painter to paint a beam, but with a standard deviation of only 150 seconds. Estimate the expected waiting time in queue of a steel beam for each of the operators, as well as the expected number of steel beams waiting in queue in each of the two cases. Comment on the e? ect of variability in service time. 4. The arrival rate of customers to an ATM machi ne is 30 per hour with exponentially distirbuted in- terarrival times. The transaction times of two customers are independent and identically distributed.Each transaction time (in minutes) is distributed according to the following pdf: f (s) = where ? = 2/3. (a) What is the average waiting for each customer? (b) What is the average number of customers waiting in line? (c) What is the average number of customers at the site? 5. A production line has two machines, Machine A and Machine B, that are arranged in series. Each job needs to processed by Machine A ? rst. Once it ? nishes the processing by Machine A, it moves to the next station, to be processed by Machine B. Once it ? nishes the processing by Machine B, it leaves the production line.Each machine can process one job at a time. An arriving job that ? nds the machine busy waits in a bu? er. 4? 2 se? 2? s , 0, if s ? 0 otherwise 36 CHAPTER 2. QUEUEING THEORY (The bu? er sizes are assumed to be in? nite. ) The processing times fo r Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the inter-arrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes. (a) What is the utilization of Machine A?What is the utilization of Machine B? (b) What is the throughput of the production system? (Throughput is de? ned to be the rate of ? nal output ? ow, i. e. how many items will exit the system in a unit time. ) (c) What is the average waiting time at Machine A, excluding the service time? (d) It is known the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line? (e) Suppose that the mean inter-arrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, respectively?What is the throughput of the production system? 6. An auto collision shop has roughly 10 cars arriving per week for repairs. A car waits outside until it is brought inside for bumping. After bumping, the car is painted. On the average, there are 15 cars waiting outside in the yard to be repaired, 10 cars inside in the bump area, and 5 cars inside in the painting area. What is the average length of time a car is in the yard, in the bump area, and in the painting area? What is the average length of time from when a car arrives until it leaves? 7. A small bank is sta? d by a single server. It has been observed that, during a normal business day, the inter-arrival times of customers to the bank are iid having exponential distribution with mean 3 minutes. Also, the the processing times of customers are iid having the following distribution (in minutes): x Pr{X = x} 1 1/4 2 1/2 3 1/4 An arrival ? nding the server busy joins the queue. The waiting space is in? nite. (a) What is the long-run fraction of time that the server is busy? (b) What the the long-run average waiting tim e of each customer in the queue, excluding the processing time? c) What is average number of customers in the bank, those in queue plus those in service? 2. 8. EXERCISE (d) What is the throughput of the bank? 37 (e) If the inter-arrival times have mean 1 minute. What is the throughput of the bank? 8. You are the manager at the Student Center in charge of running the food court. The food court is composed of two parts: cooking station and cashier’s desk. Every person should go to the cooking station, place an order, wait there and pick up ? rst. Then, the person goes to the cashier’s desk to check out. After checking out, the person leaves the food court.The coo