Slide 1OptimizationChoice VariablesChoice: Hours of Study vs. GPAChoice: Size of Quality Dept. vs. DefectsSlide 6Optimization DefinitionsSlide 8Net BenefitUnconstrained Maximization with Discrete Choice VariablesIrrelevance of Sunk, Fixed, and Average CostsIrrelevance of Sunk, Fixed, and Average CostsSlide 13Constrained OptimizationSlide 15Continuous Choice Variables: Example from Notes RevisitedOptimal Level of Activity (Figure 3.1)Marginal AnalysisMarginal Benefit & Marginal CostMarginal Benefit & Marginal CostRelating Marginals to TotalsRelating Marginals to Totals (Figure 3.2)Using Marginal Analysis to Find A* (Figure 3.3)Using Marginal Analysis to Find Optimal Activity LevelsSlide 253-1Chapter 3:Marginal Analysis forOptimal Decisions3-2OptimizationAn optimization problem involves the specification of three things:~Objective function to be maximized or minimized~Activities or choice variables that determine the value of the objective function~Any constraints that may restrict the values of the choice variables3-3Choice VariablesActivities or choice variables determine the value of the objective functionDiscrete choice variables~Can only take specific integer valuesContinuous choice variables~Can take any value between two end points3-4Choice: Hours of Study vs. GPAHours of Study per weekGPA10 3.015 3.422 3.730 3.940 4.03-5Choice: Size of Quality Dept. vs. Defects # of Quality Control Inspectors % External Quality Rejects1 25%2 15%3 10%4 8%5 7.5%3-6KPI – Key Performance Indicatorssource: http://www.pnmsoft.com/resources/bpm-tutorial/key-performance-indicators/Performance Indicators are used in four main areas:•Revenue improvement•Cost reduction•Process cycle-time improvement•Increased customer satisfactionThe following are KPI examples from real-life scenarios for gauging business process performance. Using these KPIs will benefit in reducing overheads, errors, delays and costs.•Average process overdue time•Percentage of overdue processes•Average process age•Percentage of processes where the actual number assigned resources is less than planned number of assigned resources•Sum of deviation of time (e.g. in days) against planned schedule of all active projects3-7Optimization DefinitionsUnconstrained optimization~An optimization problem in which the decision maker can choose the level of activity from an unrestricted set of valuesConstrained optimization~An optimization problem in which the decision maker chooses values for the choice variables from a restricted set of valuesMaximization problem~An optimization problem that involves maximizing the objective functionMinimization problem~An optimization problem that involves minimizing the objective function3-8Question 1a from notes3-9Net BenefitNet Benefit (NB)~Difference between total benefit (TB) and total cost (TC) for the activity~ NB = TB – TCOptimal level of the activity (A*) is the level that maximizes net benefit3-10Unconstrained Maximization with Discrete Choice VariablesIncrease activity if MB > MCDecrease activity if MB < MCOptimal level of activity~Last level for which MB exceeds MC3-11Irrelevance of Sunk, Fixed, and Average CostsSunk costs~Previously paid & cannot be recoveredFixed costs~Constant & must be paid no matter the level of activityAverage (or unit) costs~Computed by dividing total cost by the number of units of activity3-12Irrelevance of Sunk, Fixed, and Average CostsDecision makers wishing to maximize the net benefit of an activity should ignore these costs, because none of these costs affect the marginal cost of the activity and so are irrelevant for optimal decisions3-13Question 1b from notes3-14Constrained OptimizationThe ratio MB/P represents the additional benefit per additional dollar spent on the activityRatios of marginal benefits to prices of various activities are used to allocate a fixed number of dollars among activities3-15Questions 2, 3 & 4 from notes3-16Continuous Choice Variables:Example from Notes Revisited3-17Optimal Level of Activity (Figure 3.1)NBTBTC1,000Level of activity2,0004,0003,000A01,000600200Total beneft and total cost (dollars)Panel A – Total benefit and total cost curvesA01,000600200Level of activityNet beneft (dollars)Panel B – Net benefit curve•G700•F••D’D••C’C••BB’2,3101,085NB* = $1,225•f’’350 = A*350 = A*•M1,225•c’’1,000•d’’6003-18Marginal AnalysisAnalytical technique for solving optimization problems that involves changing values of choice variables by small amounts to see if the objective function can be further improved3-19Marginal Benefit & Marginal CostMarginal benefit (MB)~Change in total benefit (TB) caused by an incremental change in the level of the activityMarginal cost (MC)~Change in total cost (TC) caused by an incremental change in the level of the activity3-20Marginal Benefit & Marginal CostDDChange in total benefitChange in activityTBMBA= =DDChange in total benefitChange in activityTCMCA= =3-21Relating Marginals to TotalsMarginal variables measure rates of change in corresponding total variables~Marginal benefit (marginal cost) of a unit of activity can be measured by the slope of the line tangent to the total benefit (total cost) curve at that point of activity3-22Relating Marginals to Totals (Figure 3.2)MC (= slope of TC)MB (= slope of TB)TBTC•F••D’D••C’CLevel of activity8001,000Level of activity2,0004,0003,000A01,000600200Total beneft and total cost (dollars)Panel A – Measuring slopes along TB and TCA01,000600200Marginal beneft and marginal cost (dollars)Panel B – Marginals give slopes of totals8002468350 = A*100520100520350 = A*••BB’b••G•g100320100820••d’ (600, $8.20)d (600, $3.20)100640100340••c’ (200, $3.40)c (200, $6.40)5.203-23Using Marginal Analysis to Find A* (Figure 3.3)NBA01,000600200Level of activityNet beneft (dollars)800•c’’•d’’100300100500350 = A*MB = MCMB > MC MB < MC•M3-24Using Marginal Analysis to Find Optimal Activity LevelsIf marginal benefit > marginal cost~Activity should be increased to reach highest net benefitIf marginal cost > marginal benefit~Activity should be decreased to reach highest net benefitOptimal level of activity~When no further increases in net benefit are possible~Occurs when MB = MC3-25Questions 5 & 6 from