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1 Chapter 4 Decision Making

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2 Advanced Organizer

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3 Chapter Objectives Discuss how decision making relates to planning Explain the process of engineering problem solving Be able to solve problems using three types of decision making tools Discuss the differences between decision making under certainty, risk, and uncertainty Describe the basics of other decision making techniques

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4 Relation to Planning Managerial decision making is the process of making a conscious choice between two or more rational alternatives

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5 Types of Decisions Routine and Non-Routine Decisions Objective vs. Bounded Rationality Level of Certainty

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6 Management Science Characteristics Systems view of the problem Team approach Emphasis on use of formal mathematical models and statistical and quantitative techniques

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7 Models & Analysis Formulate the problem Construct a mathematical model Test the models ability Derive a solution from the model Apply models solution to real system

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8 Categories of Decision Making Decision Making under Certainty (Only one state of nature exists.) Decision Making under Risk (Probabilities for states of natures are known.) Decision Making under Uncertainty (Probabilities for states of natures are unknown.)

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9 Payoff Table O mn....O mj.... O in....O ij.... O 2n....O 2j.... O 1n....O 1j.... O m2.... O i2.... O 22 O 12 O m1.... O i1.... O 21 O 11 (P n )....(P j )....(P 2 )(P 1 ) NnNn....NjNj N2N2 N1N1 AmAm AiAi A2A2 A1A1 Alt.

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10 Payoff Table for Decision Making under Certainty O mn....O mj.... O in....O ij.... O 2n....O 2j.... O 1n....O 1j.... O m2.... O i2.... O 22 O 12 O m1.... O i1.... O 21 O 11 (P n )....(P j )....(P 2 )(P 1 ) NnNn....NjNj N2N2 N1N1 AmAm AiAi A2A2 A1A1 Alt. 1.0

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11 Tools for Decision Making under Certainty Linear programming –Graphical solution –Simplex method –Computer software Non-linear programming Engineering Economic Analysis

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12 Linear Programming Decision Variables Objective Function (Maximizing or Minimizing) –Example: A factory produces two products, product X and product Y. If we can realize $10 profit per unit of product X and $14 per unit of Y, what should be the production level for product X and product Y? –Maximize P = 10x + 14y

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13 Linear Programming Constrains –Example: 3 machinists 2 assemblers Each works 40 hours/week Product X requires 3 hours of machining and 1 hour of assembly per unit Product Y requires 2 hours of machining and 2 hours of assembly per unit –For machining time: 3x + 2y 3(40) –For assembly time: 1x + 2y 2(40)

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14 Linear programming Graphical solution (Constraints) 3x+2y120 (40,0) (0,60) 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Y X x+2y80 (80,0) (0,40) Feasible Region Corner Solutions

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15 Linear programming Graphical solution (Objective Function) 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Y X P=10x+14y P=1050 P=700 P=350

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16 Linear programming Graphical solution (Objective Function) 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Y X P=10x+14y P=1050 P=700 P=350

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17 Linear programming Graphical solution 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 Y X Optimal Solution (20, 30)

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18 Linear programming Simplex method BV Coefficient of RS Ratio PXYS1S1 S2S2 P 1-10-14000 S1S1 0321012060 S2S2 012018040 P 1 -3007560 S1S1 02014020 Y01/210 4080 P 1003/211/2620 X0101/2-1/220 Y001-1/43/430

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19 Linear programming Computer Software Excel: Solver LINDO: www.lindo.comwww.lindo.com max 10x + 14 y subject to M) 3x + 2y <= 120 A) x + 2y <= 80 end

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20 Engineering Economic Analysis Time Value of Money Minimum Acceptable Rate of Return Decision Criteria –Net Present Worth –Equivalent Annual Worth –Internal Rate of Return –Benefit / Cost Ratio

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21 Payoff Table for Decision Making under Risk O mn....O mj.... O in....O ij.... O 2n....O 2j.... O 1n....O 1j.... O m2.... O i2.... O 22 O 12 O m1.... O i1.... O 21 O 11 (P n )....(P j )....(P 2 )(P 1 ) NnNn....NjNj N2N2 N1N1 AmAm AiAi A2A2 A1A1 Alt.

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22 Expected value Tools for Decision Making under Risk Decision trees Decision Node Chance Node Queuing theory Simulation

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23 Payoff Table & Expected Value (Fire Insurance) -$100 -$200 -$100,0000 -$200 Expected Value A 2 =Self-Ins. A 1 =Buy Ins. (Fire)(No Accident) P 2 =0.001P 1 =0.999 N2N2 N1N1

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24 Decision Trees Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities. Decision Node D1D1 D2D2 DXDX Chance Node C1C1 C2C2 CYCY p1p1 p2p2 pypy Outcome Node Pruned Branch

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25 Decision Tree (Fire Insurance) -$200 Fire P=0.001 $0 -$100,000 No accident P=0.999 Fire P=0.001 Buy Insurance $200 Self-Insure $0 EV=-$200 EV=-$100 No accident P=0.9 No accident P=0.999

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26 Payoff Table & Expected Value (Car Insurance) $36$500$300$0 $411$13,000$300$0 A 1 =Buy Ins. ($800) A 2 =Self-Ins. ($500 Deduc.) Expected Value (Totaled)(Small Accident) (No Accident) P 3 =0.03P 2 =0.07P 1 =0.90 N3N3 N2N2 N1N1

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27 Decision Tree (Car Insurance) $0 $300 (<$500 deductible) $500 Totaled P=0.03 $0 $300 $13,000 No accident P=0.9 Small accident P=0.07 Totaled P=0.03 Buy Insurance $800 Self-Insure $0 EV=$36 EV=$411 No accident P=0.9 No accident P=0.9 Small accident P=0.07 Small accident P=0.07

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28 Payoff Table & Expected Value (Well Drilling) Value Expected $162.5k$1,250k$125k$0 $720k$9,300k$300k-$500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill P 3 =0.1P 2 =0.3P 1 =0.6 BigSmallDry N3N3 N2N2 N1N1

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29 Decision Tree (Well Drilling) $0 Big well P=0.1 Dont drill $0 Farm out $0 EV=$0 EV=$162.5k Dry P=0.6 Small well P=0.3 -$500k $300k $9,300k Big well P=0.1 Dry P=0.6 Small well P=0.3 $0 $125k $1,250k Big well P=0.1 Dry P=0.6 Small well P=0.3 Drill alone $500k EV=$720k

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30 Decision Tree (New Product Development) 1.Build New Product 2. Volume for New Product 3.$0 No Yes First cost=$1M 4. Net Revenue Year 1=$100K 7. Revenue=$0 8.Revenue=$100K/yr 6. Net Revenue Year 1=$400K 9. Revenue=$600K/yr 10.Revenue=$400K/yr 5. Revenue Year 1, 2..8 =$200K Low Volume P=0.3 Med. Volume P=0.6 High Volume P=0.1 Terminate Continue Expand First cost=$800K t=0 t=1 t=2, …,

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31 Decision Tree (New Product Development) 1.Build New Product 2. Volume for New Product 3.$0 No Yes First cost=$1M 4. Net Revenue Year 1=$100K 7. Revenue=$0 8.Revenue=$100K/yr 6. Net Revenue Year 1=$400K 9. Revenue=$600K/yr 10.Revenue=$400K/yr 5. Revenue Year 1, 2..8 =$200K Low Volume P=0.3 Med. Volume P=0.6 High Volume P=0.1 Terminate Continue Expand First cost=$800K t=0 t=1 t=2, …, PW 1 =$550,000 PW 1 =$486,800 PW=$590,915 PW=$1,067,000 PW 1 =$2,120,800 PW 1 =$1,947,200 PW=$2,291,660 EV=$1,046,640

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32 Queuing Theory Basics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times. a9a9 a8a8 a7a7 a6a6 a5a5 a4a4 a3a3 a2a2 a1a1 Server Queue

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33 Queuing Theory - Terminology Customers independent entities that arrive at random times to a Server and wait for service, then leave. Server can only service one customer at a time; length of time to provide service depends on type of service; customers are served in FIFO order. Time real, continuous, time. Queue customers that have arrived at server but are waiting for their service to start are in the queue. Queue Length at time t number of customers in the queue at time t. Waiting Time for a given customer, how long that customer has to wait between arriving at the server and when the server actually starts the service (total time is waiting time plus service time).

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34 Types of Queuing Models M/M/1 exponential arrival rate and service times, with 1 server (like office hours). M/M/m exponential arrival rate and service times, with m servers (like grocery store with many checkout lanes). M/M/m/m exponential arrival rate and service times, with m servers, but nobody waits in queue (if all m servers are busy when a customer arrives, that customer gives up and leaves). M/M/ exponential arrival rate and service times, with unlimited number of servers (customers never wait in queue).

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35 Types of Queuing Models M/D/1 service times are deterministic (e.g. a constant, fixed service time regardless of customer). M/G/1 exponential arrival rate, but service rate has a general (arbitrary) probability distribution, and a single server. M/G/m same as above, but with m servers.

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36 Simulation To study a system Experiment with actual system – Live Simulation Experiment with a model of system Physical model Virtual Simulation Mathematical model Analytical Solution Computer Simulation

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37 Simulation Simulation modeling seeks to: Describe the behavior of a system Use the model to predict future behavior, i.e. the effects that will be produced by changes in the system or in its method of operation.

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38 Simulation Types of Simulation Modes: Continuous Simulation –For systems vary continually with time Discrete Simulation –For systems change only at discrete set of points in time (state changes) Hybrid

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39 Applications of Simulation Testing new designs, layouts without committing resources to their implementation Exploring new policies, procedures, rules, structures, information flows, without disrupting the ongoing operations. Identifying bottlenecks in information, material and product flows and test options for increasing the flow rates. Testing hypothesis about how or why certain phenomena occur in the system. Gaining insights into how a system works and which variables are most important to performance. Experimenting with new and unfamiliar situations and to answer "what if" questions.

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40 Advantages and Limitations of Simulation +Easy to comprehend +Credible because the behavior can be validated +Fewer simplifying assumptions - Requires specialized training and skills -Utility of the study depends upon the quality of the model -Data Gathering reliable input data can be time consuming -Run" rather than solved. -Do not yield an optimal solution, rather they serve as a tool for analysis

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41 Simulation Tools General purpose language –C, C++, Java, Visual BASIC General simulation language –Discrete simulation: AutoMod, Arena, GASP, GPSS, SIMAN, SimPy, SIMSCRIPT II.5 –Continuous simulation: ACSL, Dynamo, SLAM,VisSim –Hybrid: EcosimPro Language (EL), Saber-Simulator, Simulink, Z simulation language, Flexsim 4.0 Special purpose simulation package –Chemical process, electrical circuits, transportation

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42 Risk as Variance $4000 Mean $1140$548Std. Deviation $60000.10 $30000.25 $40000.30 Cash F.Prob. $50000.25 $20000.10 Project Y $50000.10 $35000.20 $40000.40 Cash F.Prob. $45000.20 $30000.10 Project X

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43 Risk as Variance Probability Cash Flow X Y

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44 Payoff Table for Decision Making under Uncertainty O mn....O mj.... O in....O ij.... O 2n....O 2j.... O 1n....O 1j.... O m2.... O i2.... O 22 O 12 O m1.... O i1.... O 21 O 11 (P n )....(P j )....(P 2 )(P 1 ) NnNn....NjNj N2N2 N1N1 AmAm AiAi A2A2 A1A1 Alt.

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45 Tools for Decision Making under Uncertainty Laplace criteria (Equally likely) Maximax criteria Maximin criteria Hurwicz criteria Minimax regret criteria Game theory

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46 Laplace criteria (Equally likely) N1N1 N2N2....NjNj NnNn Max Alt.(P 1 )(P 2 )....(P j )....(P n ) A1A1 O 11 O 12....O 1j....O 1n EV 1 A2A2 O 21 O 22....O 2j....O 2n EV 2.... AiAi O i1 O i2....O ij....O in EV i.... AmAm O m1 O m2....O mj....O mn EV m 1/n

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47 Payoff Table (Well Drilling – Equally likely) $458k$1,250k$125k$0 $3033k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill Value Expected BigSmallDry N3N3 N2N2 N1N1 $9,300k$300k-$500k

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48 Maximax Criteria MAX m O mn....O mj....O m2 O m1.... MAX i O in....O ij....O i2 O i1.... MAX 2 MAX 1 Max. AmAm.... AiAi A2A2 A1A1 Alt. NnNn....NjNj N2N2 N1N1 O 1n....O 1j....O 12 O 11 O 2n....O 2j....O 22 O 21

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49 Payoff Table (Well Drilling - Maximax) Max. $1,250k $125k$0 $9,300k $300k-$500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill BigSmallDry N3N3 N2N2 N1N1

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50 Maximin Criteria MIN m O mn....O mj....O m2 O m1.... MIN i O in....O ij....O i2 O i1.... MIN 2 MIN 1 Max. AmAm.... AiAi A2A2 A1A1 Alt. NnNn....NjNj N2N2 N1N1 O 1n....O 1j....O 12 O 11 O 2n....O 2j....O 22 O 21

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51 Payoff Table (Well Drilling - Maximin) Min. $0$1,250k$125k$0 -$500k$9,300k$300k-$500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill BigSmallDry N3N3 N2N2 N1N1

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52 Hurwicz Criteria MAX m MIN m MAX 2 MIN 2 MAX 1 MIN 1 (1- ) ImIm....O mn....O mj O m2 O m1.... IiIi O in....O ij O i2 O i1.... I2I2 O 2n....O 2j O 22 O 21 I1I1....O 1n....O 1j O 12 O 11 Max AmAm.... AiAi A2A2 A1A1 Alt. Index....NnNn NjNj N2N2 N1N1 MAX i MIN i Index = (MAX) + (1 - )(MIN)

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53 Payoff Table (Well Drilling - Hurwicz) $1,250k$0 $9,300k-$500k $0 Max.Min. $250k$1,250k$125k$0 $1460k$9,300k$300k-$500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill Index ( =0.2) BigSmallDry N3N3 N2N2 N1N1

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54 Minimax Regret Criteria First convert payoff table to regret table O mn....O mj.... O in....O ij.... O 2n....O 2j.... O 1n....O 1j.... O m2.... O i2.... O 22 O 12 O m1.... O i1.... O 21 O 11 NnNn....NjNj N2N2 N1N1 AmAm AiAi A2A2 A1A1 Alt. Work on one state of nature at a time Identify the maximum output in that state Regret = Max. output - output Repeat for all states of nature

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55 Minimax Regret Criteria R mn.... R in.... R 2n R 1n NnNn MAX m.... MAX i.... MAX 2 MAX 1 AmAm.... AiAi A2A2 A1A1 Alt. Min..... R mj.... R ij.... R 2j R 1j NjNj.... R m2.... R i2.... R 22 R 12 N2N2 R m1.... R i1.... R 21 R 11 N1N1

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56 Payoff Table & Regret Table (Well Drilling – Minimax Regret) Payoff $1,250k$125k$0 $9,300k$300k-$500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill BigSmallDry N3N3 N2N2 N1N1 MaxRegret $8,050k $500k $9,300k $8,050k $0 $9,300k $175k $0 $300k $0 $500k $0 A 3 :Farm out A 2 :Drill alone A 1 :Dont drill BigSmallDry N3N3 N2N2 N1N1

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57 Game theory Game theory attempts to mathematically capture behavior in strategic situations, where an individuals success in making choices depends on the choices of others. Traditional applications of game theory attempt to find equilibria in these gamessets of strategies where individuals are unlikely to change their behavior.

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58 Game theory (Example) 2nd-best for U.S.S.R. 2nd-best for U.S. Best for U.S.S.R. Worst for U.S. Worst for U.S.S.R. Best for U.S. 3 rd -best for U.S.S.R. 3 rd -best for U.S. Disarm Arm U.S. Strategy DisarmArm Soviet Strategy

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59 Computer-Based Information Systems Integrated Database CAD/CAM Management Information Systems (MIS) Decision Support Systems (DSS) Expert Systems

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