Description Module 06: Reliability and Decision Theory Discussion Question Question Requirements: Capacity Planning Discuss the importance of capacity

Module 06: Reliability and Decision TheoryDiscussion QuestionQuestion Requirements:Capacity Planning1. Discuss the importance of capacity planning in deciding the number of police officers on dutyat any given time.2. How does capacity decisions influence productivity? Give an example.Directions:• Discuss the concepts, principles, and theories from your textbook. Cite your textbooks andcite any other sources.• Write a discussion that includes an introduction paragraph, the body, and a conclusionparagraph to address the assignment’s guide questions.• Your initial post should address all components of the question with a 600-word limit.Learning Outcomes• Evaluate the impact of product reliability on the decision-making process ofoperations management.• Differentiate the environments under which operations decisions are made.• Analyze the techniques that apply to decision making under uncertainty.ReadingsRequired:• Chapters 5 & 5S Decision Theory in Operations ManagementRecommended:• Liao, S., & Liu, Z., (2022). Enterprise financial influencing factors and early warningbased on decision model tree. Scientific Programming,2022, 1-8.• Kascelan, L., Pejic Bach, M., Rondovic, B., & Durickovic, T. (2020). The interactionbetween social media, knowledge management and service quality: A decision treeanalysis. PLoS ONE, 15(8), 1-30.• Dai, D., Wu, X., Si, F., Feng, Z., & Chu, W. (2023). The impact of tariff policies onvaccine supply chains: short-term and evolutionary game behaviors based onuncertain utility. Applied Mathematical Modelling, 115, 754–777.Strategic CapacityPlanning forProducts andServicesCopyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the priorwritten consent of McGraw-Hill Education.5-1You should be able to:LO 5.1LO 5.2LO 5.3LO 5.4LO 5.5Name the three key questions in capacity planningExplain the importance of capacity planningDescribe ways of defining and measuring capacityName several determinants of effective capacityDiscuss factors to consider when deciding whetherto perform in-house or outsourceLO 5.6 Discuss the major considerations related todeveloping capacity alternativesLO 5.7 Describe the steps used to resolve constraint issuesLO 5.8 Briefly describe approaches that are useful forevaluating capacity alternativesCopyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-2 Capacity The upper limit or ceiling on the load that an operatingunit can handle Capacity needs include Equipment Space Employee skillsLO 5.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-3 Goal To achieve a match between the long-term supplycapabilities of an organization and the predicted level oflong-term demand Overcapacity → operating costs that are too high Undercapacity → strained resources and possible loss ofcustomersLO 5.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-4 Key questions: What kind of capacity is needed? How much is needed to match demand? When is it needed? Related questions: How much will it cost? What are the potential benefits and risks? Are there sustainability issues? Should capacity be changed all at once, or through several smallerchanges? Can the supply chain handle the necessary changes?LO 5.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-5 Capacity decisions1.Impact the ability of the organization to meet future demands2. Affect operating costs3. Are a major determinant of initial cost4. Often involve long-term commitment of resources5. Can affect competitiveness6. Affect the ease of management7. Have become more important and complex due to globalization8. Need to be planned for in advance due to their consumption offinancial and other resourcesLO 5.2Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-6 Measure capacity in units that do not requireupdating Why is measuring capacity in dollars problematic? Two useful definitions of capacity Design capacity The maximum output rate or service capacity an operation,process, or facility is designed for Effective capacity Design capacity minus allowances such as personal time andmaintenanceLO 5.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-7BusinessInputsOutputsAutomanufacturingLabor hours,machine hoursNumber of cars per shiftSteel millFurnace sizeTons of steel per dayOil refineryRefinery sizeNumber of acres,number of cowsGallons of fuel per dayBushels of grain per acre peryear, gallons of milk per dayRestaurantNumber of tables,seating capacityTheaterNumber of seatsNumber of meals served perdayNumber of tickets sold perperformanceRetail salesSquare feet of floorspaceFarmingRevenue generated per dayTABLE 5.1 Measures of capacityLO 5.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-8 Actual output The rate of output actually achieved It cannot exceed effective capacity Efficiencyactual outputEfficiency =effective capacity Utilizationactual outputUtilizatio n =design capacityMeasured as percentagesLO 5.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-9 Design Capacity = 50 trucks per day Effective Capacity = 40 trucks per day Actual Output = 36 trucks per dayactual output36Efficiency === 90%effective capacity 40actual output36Utilizatio n === 72%design capacity 50LO 5.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-10 Facilities Product and service factors Process factors Human factors Policy factors Operational factors Supply chain factors External factorsLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-11TABLE 5.2 Factors that determine effective capacityLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-12 Strategies are typically based on assumptions andpredictions about: Long-term demand patterns Technological change Competitor behaviorLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-13 Leading Build capacity in anticipation of future demand increases Following Build capacity when demand exceeds current capacity Tracking Similar to the following strategy, but adds capacity in relativelysmall increments to keep pace with increasing demandLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-14 Capacity cushion Extra capacity used to offset demand uncertainty Capacity cushion = 100% − utilization Capacity cushion strategy Organizations that have greater demand uncertainty typicallyhave greater capacity cushions Organizations that have standard products and servicesgenerally have smaller capacity cushionsLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-151.Estimate future capacity requirements2.Evaluate existing capacity and facilities; identify gaps3.Identify alternatives for meeting requirements4.Conduct financial analyses5.Assess key qualitative issues6.Select the best alternative for the long term7.Implement alternative chosen8.Monitor resultsLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-16 Long-term considerations relate to overall level ofcapacity requirements Require forecasting demand over a time horizon andconverting those needs into capacity requirements Short-term considerations relate to probablevariations in capacity requirements Less concerned with cycles and trends than withseasonal variations and other variations from averageLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-17 Calculating processing requirements requiresreasonably accurate demand forecasts, standardprocessing times, and available work timekpDN R = i =1iiTwhereN R = number of required machinespi = standard processing time for product iDi = demand for product i during the planning horizonT = processing time available during the planning horizonLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-18 Service capacity planning can present a number ofchallenges related to: The need to be near customers Convenience The inability to store services Cannot store services for consumption later The degree of demand volatility Volume and timing of demand Time required to service individual customersLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-19 Strategies used to offset capacity limitations and thatare intended to achieve a closer match between supplyand demand Pricing Promotions Discounts Other tactics to shift demand from peak periods intoslow periodsLO 5.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-20 Once capacity requirements are determined, the organizationmust decide whether to produce a good or service itself oroutsource Factors to consider: Available capacity Expertise Quality considerations The nature of demand Cost RisksLO 5.5Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-21 Things that can be done to enhance capacity management: Design flexibility into systems Take stage of life cycle into account Take a “big-picture” approach to capacity changes Prepare to deal with capacity “chunks” Attempt to smooth capacity requirements Identify the optimal operating level Choose a strategy if expansion is involvedLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-22 An operation in asequence of operationswhose capacity is lowerthan that of the otheroperationsLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-23Average cost per unitMinimumcostOptimalOutputrateLO 5.6Rate of outputCopyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-24 Economies of scale If output rate is less than the optimal level, increasingthe output rate results in decreasing average per unitcosts Diseconomies of scale If the output rate is more than the optimal level,increasing the output rate results in increasing averagecosts per unitLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-25 Economies of scale If output rate is less than the optimal level, increasingthe output rate results in decreasing average per unitcosts Reasons for economies of scale: Fixed costs are spread over a larger number of units Construction costs increase at a decreasing rate as facility sizeincreases Processing costs decrease due to standardizationLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-26 Diseconomies of scale If the output rate is more than the optimal level, increasing theoutput rate results in increasing average per unit costs Reasons for diseconomies of scale Distribution costs increase due to traffic congestion andshipping from a centralized facility rather than multiple smallerfacilities Complexity increases costs Inflexibility can be an issue Additional levels of bureaucracyLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-27Average cost per unitMinimum cost & optimal operating rate arefunctions of size of production unit.SmallplantMediumplantLargeplantOutput rateLO 5.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-28 Constraint Something that limits the performance of a process or system inachieving its goals Categories Market Resource Material Financial Knowledge or competency PolicyLO 5.7Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-291.2.3.4.5.Identify the most pressing constraintChange the operation to achieve maximum benefit, giventhe constraintMake sure other portions of the process are supportive ofthe constraintExplore and evaluate ways to overcome the constraintRepeat the process until the constraint levels are atacceptable levelsLO 5.7Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-30 Alternatives should be evaluated from varyingperspectives Economic Is it economically feasible? How much will it cost? How soon can we have it? What will operating and maintenance costs be? What will its useful life be? Will it be compatible with present personnel and presentoperations? Non-economic Public opinionLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-31 Techniques for Evaluating Alternatives Cost-volume analysis Financial analysis Decision theory Waiting-line analysis SimulationLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-32 Cost-volume analysis Focuses on the relationship between cost, revenue, andvolume of output Fixed Costs (FC) Tend to remain constant regardless of output volume Variable Costs (VC) Vary directly with volume of output VC = Quantity(Q) × variable cost per unit (v) Total Cost TC = FC + VC Total Revenue (TR) TR = revenue per unit (R) × QLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-33 BEP The volume of output at which total cost and totalrevenue are equal Profit (P) = TR – TC = R × Q – (FC + v × Q)= Q(R – v) – FCFCQBEP =R−vLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-34.LO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-35 Capacity alternatives may involve step costs, which arecosts that increase stepwise as potential volumeincreases The implication of such a situation is the possible occurrence ofmultiple break-even quantitiesLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-36 Cost-volume analysis is a viable tool for comparingcapacity alternatives if certain assumptions aresatisfied One product is involved Everything produced can be sold The variable cost per unit is the same regardless of volume Fixed costs do not change with volume changes, or they are stepchanges The revenue per unit is the same regardless of volume Revenue per unit exceeds variable cost per unitLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-37 Cash flow The difference between cash received from sales andother sources and cash outflow for labor, material,overhead, and taxes Present value The sum, in current value, of all future cash flow of aninvestment proposalLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-38 Capacity planning impacts all areas of the organization It determines the conditions under which operations will have to function Flexibility allows an organization to be agile It reduces the organization’s dependence on forecast accuracy and reliability Many organizations utilize capacity cushions to achieve flexibility Bottleneck management is one way by which organizations can enhancetheir effective capacities Capacity expansion strategies are important organizational considerations Expand-early strategy Wait-and-see strategy Capacity contraction is sometimes necessary Capacity disposal strategies become important under theseconditionsLO 5.8Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5-39Decision TheoryCopyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior 5s-1written consent of McGraw-Hill Education.You should be able to:LO 5s.1LO 5s.2LO 5s.3LO 5s.4LO 5s.5LO 5s.6LO 5s.7Outline the steps in the decision processName some causes of poor decisionsDescribe and use techniques that apply to decision makingunder uncertaintyDescribe and use the expected-value approachConstruct a decision tree and use it to analyze a problemCompute the expected value of perfect informationConduct sensitivity analysis on a simple decision problemCopyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-2 A general approach to decision making that is suitableto a wide range of operations management decisions Capacity planning Product and service design Equipment selection Location planningLO 5s.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-3 Characteristics of decisions that are suitable for usingdecision theory A set of possible future conditions that will have abearing on the results of the decision A list of alternatives from which to choose A known payoff for each alternative under each possiblefuture conditionLO 5s.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-41.2.3.4.5.Identify the possible future states of natureDevelop a list of possible alternativesEstimate the payoff for each alternative for each possiblefuture state of natureIf possible, estimate the likelihood of each possible futurestate of natureEvaluate alternatives according to some decision criterionand select the best alternativeLO 5s.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-5A table showing the expected payoffs for eachalternative in every possible state of naturePossible Future DemandAlternativesLowModerateHighSmall facility$10$10$10Medium facility71212Large Facility(4)216• A decision is being made concerning which size facilityshould be constructed• The present value (in millions) for each alternative undereach state of nature is expressed in the body of the abovepayoff tableLO 5s.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-6 Steps:1.Identify the problem2. Specify objectives and criteria for a solution3. Develop suitable alternatives4. Analyze and compare alternatives5. Select the best alternative6. Implement the solution7. Monitor to see that the desired result is achievedLO 5s.1Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-7 Decisions occasionally turn out poorly due tounforeseeable circumstances; however, this is not thenorm More frequently poor decisions are the result of acombination of Mistakes in the decision process Bounded rationality SuboptimizationLO 5s.2Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-8 Errors in the Decision ProcessFailure to recognize the importance of each stepSkipping a stepFailure to complete a step before jumping to the next stepFailure to admit mistakesInability to make a decisionLO 5s.2Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-9 Bounded rationality The limitations on decision making caused by costs,human abilities, time, technology, and availability ofinformation Suboptimization The results of different departments each attempting toreach a solution that is optimum for that departmentLO 5s.2Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-10 There are three general environment categories: Certainty Environment in which relevant parameters have knownvalues Risk Environment in which certain future events haveprobabilistic outcomes Uncertainty Environment in which it is impossible to assess the likelihoodof various possible future eventsLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-11 Sometimes we know the exact outcome orenvironment. Under those situations, making adecision is easy. For example, if Investment 1 gives areturn of 3.4% and Investment 2 gives a return of 5.6%,then we know what to do. Uncertainty comes when there is a risk involved, forinstance, Investment 1 could be the return on a CDwhich is guaranteed, but Investment 2 could be amutual fund whose returned can’t be guaranteed.LO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-12 Decisions are sometimes made under completeuncertainty: No information is available on how likelythe various states of nature are. Decision criteria: Maximin Choose the alternative with the best of the worst possible payoffs Maximax Choose the alternative with the best possible payoff Laplace Choose the alternative with the best average payoff Minimax regret Choose the alternative that has the least of the worst regretsLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-13Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216•The worst payoff for each alternative isSmall facility:$10 millionMedium facility$7 millionLarge facility-$4 million•Choose to construct a small facilityLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-14Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216•The best payoff for each alternative isSmall facility:$10 millionMedium facility$12 millionLarge facility$16 million•Choose to construct a large facilityLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-15Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216•The average payoff for each alternative isSmall facility:(10 + 10 + 10) ÷ 3 = $10 millionMedium facility(7 + 12 + 12) ÷ 3 = $10.33 millionLarge facility(−4 + 2 + 16) ÷ 3 = $4.67 million•Choose to construct a medium facilityLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-16Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216•Construct a regret (or opportunity loss) table•The difference between a given payoff and the bestpayoff for a state of natureRegretsLO 5s.3AlternativesLowModerateHighSmall Facility$0$2$6Medium Facility304Large Facility14100Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-17RegretsAlternativesLowModerateHighSmall Facility$0$2$6Medium Facility304Large Facility14100•Identify the worst regret for each alternative•Small facility$6 million•Medium facility$4 million•Large facility$14 million•Select the alternative with the minimum of the maximumregrets•Build a medium facilityLO 5s.3Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-18 Decisions made under the condition that theprobability of occurrence for each state of nature canbe estimated A widely applied criterion is expected monetary value(EMV) EMV Determine the expected payoff of each alternative, and choosethe alternative that has the best expected payoff This approach is most appropriate when the decision maker isneither risk averse nor risk seekingLO 5s.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-19Possible Future DemandAlternativesLow (.30)Moderate (.50)High (.20)Small Facility$10$10$10Medium Facility71212Large Facility(4)216EMVsmall = .30(10) +.50(10) +.20(10) = 10EMVmedium = .30(7) + .50(12) + .20(12) = 10.5EMVlarge = .30(-4) + .50(2) + .20(16) = $3Build a medium facilityLO 5s.4Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-20 Decision tree A schematic representation of the available alternatives and theirpossible consequences Useful for analyzing sequential decisionsLO 5s.5Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-21 Composed of Nodes Decisions – represented by square nodes Chance events – represented by circular nodes Branches Alternatives – branches leaving a square node Chance events – branches leaving a circular node Analyze from right to left For each decision, choose the alternative that will yieldthe greatest return If chance events follow a decision, choose the alternativethat has the highest expected monetary value (or lowestexpected cost)LO 5s.5Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-22 A manager must decide on the size of a video arcade to construct. The managerhas narrowed the choices to two: large or small. Information has been collectedon payoffs, and a decision tree has been constructed. Analyze the decision treeand determine which initial alternative (build small or build large) should bechosen in order to maximize expected monetary value.$40$402Overtime$50$551($10)2$50$70LO 5s.5Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-23$40$402Overtime$50$551($10)2$50$70EVSmall = .4(40) + .6(55) = $49EVLarge = .4(50) + .6(70) = $62Build the large facilityLO 5s.5Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-24 Expected value of perfect information (EVPI) The difference between the expected payoff with perfectinformation and the expected payoff under risk Two methods for calculating EVPI EVPI = expected payoff under certainty – expected payoff under risk EVPI = minimum expected regretLO 5s.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-25Possible Future DemandAlternativesLow (.30)Moderate (.50)High (.20)Small Facility$10$10$10Medium Facility71212Large Facility(4)216EVwith perfect information = .30(10) + .50(12) + .20(16) = $12.2EMV = $10.5EVPI = EVwith perfect information – EMV= $12.2 – 10.5= $1.7You would be willing to spend up to $1.7 million to obtainperfect informationLO 5s.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-26RegretsAlternativesLow (.30)Moderate (.50)High (.20)Small Facility$0$2$6Medium Facility304Large Facility14100• Expected Opportunity Loss• EOLSmall = .30(0) + .50(2) + .20(6) = $2.2• EOLMedium = .30(3) + .50(0) + .20(4) = $1.7• EOLLarge = .30(14) + .50(10) + .20(0) = $9.2• The minimum EOL is associated with the building themedium size facility. This is equal to the EVPI, $1.7million.LO 5s.6Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-27 Sensitivity analysis Determining the range of probability for which analternative has the best expected payoff The approach illustrated is useful when there are twostates of nature It involves constructing a graph and then using algebra todetermine a range of probabilities over which a given solutionis bestLO 5s.7Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-28State ofNatureAlternative#1#2SlopeEquationA41212 – 4 = +84 + 8P(2)B1622 – 16 = −1416 – 14P(2)C1288 − 12 = −412 – 4P(2)LO 5s.7Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-2916 − 14P(2) = 12 − 4P(2)Rearranging terms yields4 = 10P(2)Solving yields P(2) = .40.Thus, alternative B is best from P(2) = 0 up toP(2) = .40. B and C are equivalent at P(2) = .40.Similar analysis can be used for alternative Aand C4 + 8P(2) = 12 − 4P(2 )Solving yields P(2) = .67.Thus, alternative C is best from P(2) > .40 up toP(2) = .67, where A and C are equivalent. Forvalues of P(2) greater than .67 up to P(2) = 1.0,A is best.LO 5s.7Copyright ©2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.5s-30
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• Click on the “Place Your Order” tab at the top or the “Order Now” button at the bottom. You’ll be directed to our order form.
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