3 Chapter Objectives Discuss how decision making relates to planning Explain the process of engineering problem solvingBe able to solve problems using three types of decision making toolsDiscuss the differences between decision making under certainty, risk, and uncertaintyDescribe the basics of other decision making techniques
4 Relation to PlanningManagerial decision making is the process of making a conscious choice between two or more rational alternatives
5 Types of Decisions Routine and Non-Routine Decisions Objective vs. Bounded RationalityLevel of Certainty
6 Management Science Characteristics Systems view of the problemTeam approachEmphasis on use of formal mathematical models and statistical and quantitative techniques
7 Models & Analysis Formulate the problem Construct a mathematical model Test the model’s abilityDerive a solution from the modelApply model’s solution to real system
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.)
9 Payoff Table Am .... Ai A2 A1 Alt. Nn .... Nj N2 N1 (Pn) .... (Pj) Om1....Oi1O21O11Om2....Oi2O22O12Omn....OmjOinOijO2nO2jO1nO1j
10 Payoff Table for Decision Making under Certainty Omn....OmjOinOijO2nO2jO1nO1jOm2Oi2O22O12Om1Oi1O21O11(Pn)(Pj)(P2)(P1)NnNjN2N1AmAiA2A1Alt.1.0
11 Tools for Decision Making under Certainty Linear programmingGraphical solutionSimplex methodComputer softwareNon-linear programmingEngineering Economic Analysis
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
13 Linear Programming Constrains Example: 3 machinists2 assemblersEach works 40 hours/weekProduct X requires 3 hours of machining and 1 hour of assembly per unitProduct Y requires 2 hours of machining and 2 hours of assembly per unitFor machining time: 3x + 2y 3(40)For assembly time: 1x + 2y 2(40)
14 Linear programming Graphical solution (Constraints) Y102030405060(0,60)(0,40)3x+2y≤120Corner Solutionsx+2y≤80Feasible Region(40,0)(80,0)X
15 Linear programming Graphical solution (Objective Function) Y102030405060P=10x+14yP=1050P=700P=350X
16 Linear programming Graphical solution (Objective Function) Y102030405060P=10x+14yP=1050P=700P=350X
17 Linear programming Graphical solution Y102030405060Optimal Solution(20, 30)X
18 Linear programming Simplex method BVCoefficient ofRSRatioPXYS1S2P1-10-14S13212060S28040P1-37560S12-14020Y1/280P13/211/2620X1/2-1/220Y-1/43/430
20 Engineering Economic Analysis Time Value of MoneyMinimum Acceptable Rate of ReturnDecision CriteriaNet Present WorthEquivalent Annual WorthInternal Rate of ReturnBenefit / Cost Ratio
21 Payoff Table for Decision Making under Risk Omn....OmjOinOijO2nO2jO1nO1jOm2Oi2O22O12Om1Oi1O21O11(Pn)(Pj)(P2)(P1)NnNjN2N1AmAiA2A1Alt.
22 Tools for Decision Making under Risk Expected valueDecision treesDecision NodeChance NodeQueuing theorySimulation
23 Payoff Table & Expected Value (Fire Insurance) (No Accident)P2=0.001P1=0.999N2N1ExpectedValueA2=Self-Ins.A1=Buy Ins.-$100,000-$200-$200-$100
24 Decision TreesDecision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities.Decision NodeD1D2DXOutcome NodeChance NodeC1C2CYp1p2pyPruned Branch
25 Decision Tree (Fire Insurance) No accidentP=0.9P=0.999-$200EV=-$200Buy Insurance$200FireP=0.001-$200No accidentP=0.999Self-Insure$0$0EV=-$100FireP=0.001-$100,000
29 Decision Tree (Well Drilling) $0EV=$0Dry P=0.6$0Small well P=0.3Don’t drill $0Big well P=0.1$0EV=$720kDry P=0.6-$500kSmall well P=0.3$300kFarm out $0Drill alone $500kBig well P=0.1$9,300kEV=$162.5k$0Dry P=0.6$125kSmall well P=0.3Big well P=0.1$1,250k
30 Decision Tree (New Product Development) 7. Revenue=$0Terminate4. Net RevenueYear 1=$100KLow VolumeP=0.3Continue8.Revenue=$100K/yr2. Volume forNew ProductMed. VolumeP=0.65. Revenue Year 1, 2..8 =$200KYesFirst cost=$1MHigh VolumeP=0.19. Revenue=$600K/yrExpandFirst cost=$800K6. Net RevenueYear 1=$400KBuild NewProductNoContinue10.Revenue=$400K/yr3. $0t=0t=1t=2, …,
31 Decision Tree (New Product Development) Build NewProduct2. Volume forNew Product3. $0NoYesFirst cost=$1M4. Net RevenueYear 1=$100K7. Revenue=$08.Revenue=$100K/yr6. Net RevenueYear 1=$400K9. Revenue=$600K/yr10.Revenue=$400K/yr5. Revenue Year 1, 2..8 =$200KLow VolumeP=0.3Med. VolumeP=0.6High VolumeP=0.1TerminateContinueExpandFirst cost=$800Kt=0t=1t=2, …,PW1=$550,000PW=$590,915PW1=$486,800EV=$1,046,640PW=$1,067,000PW1=$2,120,800PW=$2,291,660PW1=$1,947,200
32 Queuing TheoryBasics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times.Queuea9a8a7a6a5a4a3a2a1Server
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).
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).
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.
36 Physical model —Virtual Simulation To study a systemExperiment with actual system – Live SimulationExperiment with a model of systemPhysical model —Virtual SimulationMathematical modelAnalytical SolutionComputer Simulation
37 Simulation Simulation modeling seeks to: Describe the behavior of a systemUse 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.
38 Simulation Types of Simulation Modes: Continuous Simulation For systems vary continually with timeDiscrete SimulationFor systems change only at discrete set of points in time (state changes)Hybrid
39 Applications of Simulation Testing new designs, layouts without committing resources to their implementationExploring 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.
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
41 Simulation Tools General purpose language General simulation language C, C++, Java, Visual BASICGeneral simulation languageDiscrete simulation: AutoMod, Arena, GASP, GPSS, SIMAN, SimPy, SIMSCRIPT II.5Continuous simulation: ACSL, Dynamo, SLAM ,VisSimHybrid: EcosimPro Language (EL), Saber-Simulator, Simulink, Z simulation language, Flexsim 4.0Special purpose simulation packageChemical process, electrical circuits, transportation
42 Risk as Variance $5000 0.10 $3500 0.20 $4000 0.40 Cash F. Prob. $4500 $3000Project X$60000.10$30000.25$40000.30Cash F.Prob.$5000$2000Project Y$4000Mean$1140$548Std. Deviation
54 Minimax Regret Criteria First convert payoff table to regret tableOmn....OmjOinOijO2nO2jO1nO1jOm2Oi2O22O12Om1Oi1O21O11NnNjN2N1AmAiA2A1Alt.Work on one state of nature at a timeIdentify the maximum output in that stateRegret = Max. output - outputRepeat for all states of nature
57 Game theoryGame theory attempts to mathematically capture behavior in strategic situations, where an individual’s success in making choices depends on the choices of others.Traditional applications of game theory attempt to find equilibria in these games—sets of strategies where individuals are unlikely to change their behavior.
58 Game theory (Example) Disarm Arm Soviet Strategy Disarm Arm U.S. Strategy3rd-best for U.S.S.R.3rd-best for U.S.Worst for U.S.S.R.Best for U.S.Best for U.S.S.R.Worst for U.S.2nd-best for U.S.S.R.2nd-best for U.S.
59 Computer-Based Information Systems Integrated DatabaseCAD/CAMManagement Information Systems (MIS)Decision Support Systems (DSS)Expert Systems