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## Chapter 4 Decision Making

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**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**Relation to Planning**• Managerial decision making is the process of making a conscious choice between two or more rational alternatives**Types of Decisions**• Routine and Non-Routine Decisions • Objective vs. Bounded Rationality • Level of Certainty**Management ScienceCharacteristics**• Systems view of the problem • Team approach • Emphasis on use of formal mathematical models and statistical and quantitative techniques**Models & Analysis**• Formulate the problem • Construct a mathematical model • Test the model’s ability • Derive a solution from the model • Apply model’s solution to real system**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.)**N1**N2 .... Nj .... Nn Alt. (P1) (P2) .... (Pj) .... (Pn) A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Payoff Table**N1**N2 .... Nj .... Nn Alt. (P1) (P2) .... (Pj) .... (Pn) A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Payoff Tablefor Decision Making under Certainty 1.0**Tools for Decision Making under Certainty**• Linear programming • Graphical solution • Simplex method • Computer software • Non-linear programming • Engineering Economic Analysis**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**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)**60**50 40 30 20 10 Linear programming Graphical solution (Constraints) Y (0,60) (0,40) 3x+2y≤120 Corner Solutions x+2y≤80 Feasible Region (40,0) (80,0) X 0 10 20 30 40 50 60 70 80 90**60**50 40 30 20 10 Linear programming Graphical solution (Objective Function) Y P=10x+14y P=1050 P=700 P=350 X 0 10 20 30 40 50 60 70 80 90**60**50 40 30 20 10 Linear programming Graphical solution (Objective Function) Y P=10x+14y P=1050 P=700 P=350 X 0 10 20 30 40 50 60 70 80 90**60**50 40 30 20 10 Linear programming Graphical solution Y Optimal Solution (20, 30) X 0 10 20 30 40 50 60 70 80 90**BV**Coefficient of RS Ratio P X Y S1 S2 P 1 -10 -14 0 0 0 S1 0 3 2 1 0 120 60 S2 0 1 2 0 1 80 40 P 1 -3 0 0 7 560 S1 0 2 0 1 -1 40 20 Y 0 1/2 1 0 1/2 40 80 P 1 0 0 3/2 11/2 620 X 0 1 0 1/2 -1/2 20 Y 0 0 1 -1/4 3/4 30 Linear programmingSimplex method**Linear programming Computer Software**• Excel: Solver • LINDO: www.lindo.com max 10x + 14 y subject to M) 3x + 2y <= 120 A) x + 2y <= 80 end**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**N1**N2 .... Nj .... Nn Alt. (P1) (P2) .... (Pj) .... (Pn) A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Payoff Tablefor Decision Making under Risk**Tools for Decision Making under Risk**• Expected value • Decision trees Decision Node Chance Node • Queuing theory • Simulation**N1**N2 (No Accident) (Fire) Expected P1=0.999 P2=0.001 Value A1=Buy Ins. -$200 -$200 A2=Self-Ins. 0 -$100,000 Payoff Table & Expected Value(Fire Insurance) -$200 -$100**p1**D1 C1 p2 Outcome Node Decision Node D2 Chance Node C2 py DX CY Pruned Branch Decision Trees • Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities.**No accident**P=0.9 No accident P=0.999 Buy Insurance $200 Fire P=0.001 No accident P=0.999 Fire P=0.001 Decision Tree(Fire Insurance) -$200 EV=-$200 -$200 $0 Self-Insure $0 EV=-$100 -$100,000**N1**N2 N3 (No Accident) (Small Accident) (Totaled) Expected P1=0.90 P2=0.07 P3=0.03 Value A1=Buy Ins. ($800) $0 $300 $500 ($500 Deduc.) A2=Self-Ins. $0 $300 $13,000 Payoff Table & Expected Value(Car Insurance) $36 $411**No accident**P=0.9 No accident P=0.9 Small accident P=0.07 Small accident P=0.07 Buy Insurance $800 Totaled P=0.03 No accident P=0.9 Small accident P=0.07 Totaled P=0.03 Decision Tree(Car Insurance) $0 EV=$36 $300 (<$500 deductible) $500 $0 Self-Insure $0 EV=$411 $300 $13,000**N1**N2 N3 Dry Small Big Expected P1=0.6 P2=0.3 P3=0.1 Value A1:Don’t drill $0 $0 $0 A2:Drill alone -$500k $300k $9,300k A3:Farm out $0 $125k $1,250k Payoff Table & Expected Value(Well Drilling) $0 $720k $162.5k**Dry P=0.6**Small well P=0.3 Big well P=0.1 Don’t drill $0 Dry P=0.6 Small well P=0.3 Drill alone $500k Big well P=0.1 Farm out $0 Dry P=0.6 Small well P=0.3 Big well P=0.1 Decision Tree(Well Drilling) $0 EV=$0 $0 $0 -$500k EV=$720k $300k $9,300k $0 EV=$162.5k $125k $1,250k**7. Revenue=$0**Terminate 4. Net Revenue Year 1=$100K Low Volume P=0.3 8.Revenue=$100K/yr Continue 2. Volume for New Product Med. Volume P=0.6 5. Revenue Year 1, 2..8 =$200K High Volume P=0.1 Yes First cost=$1M 9. Revenue=$600K/yr Expand First cost=$800K 6. Net Revenue Year 1=$400K • Build New • Product 10.Revenue=$400K/yr Continue No 3. $0 Decision Tree(New Product Development) t=0 t=2, …, t=1**7. Revenue=$0**Terminate 4. Net Revenue Year 1=$100K Low Volume P=0.3 8.Revenue=$100K/yr Continue 2. Volume for New Product Med. Volume P=0.6 5. Revenue Year 1, 2..8 =$200K High Volume P=0.1 Yes First cost=$1M 9. Revenue=$600K/yr Expand First cost=$800K 6. Net Revenue Year 1=$400K • Build New • Product 10.Revenue=$400K/yr Continue No 3. $0 t=0 t=2, …, t=1 Decision Tree (New Product Development) PW1=$550,000 PW=$590,915 PW1=$486,800 EV=$1,046,640 PW=$1,067,000 PW1=$2,120,800 PW=$2,291,660 PW1=$1,947,200**Queue**a9 a8 a7 a6 a5 a4 a3 a2 a1 Queuing Theory • Basics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times. Server**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).**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).**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.**To study a system**Experiment with actual system – Live Simulation Experiment with a model of system Mathematical model Physical model —Virtual Simulation Analytical Solution Computer Simulation Simulation**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.**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**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.**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**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**Project X**Project Y Prob. Cash F. Prob. Cash F. 0.10 $3000 0.10 $2000 0.20 $3500 0.25 $3000 0.40 $4000 0.30 $4000 0.20 $4500 0.25 $5000 0.10 $5000 0.10 $6000 Mean $4000 $4000 Std. Deviation $548 $1140 Risk as Variance**Probability**Cash Flow Risk as Variance X Y**N1**N2 .... Nj .... Nn Alt. (P1) (P2) .... (Pj) .... (Pn) A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Payoff Table for Decision Making under Uncertainty**Tools for Decision Making under Uncertainty**• Laplace criteria (Equally likely) • Maximax criteria • Maximin criteria • Hurwicz criteria • Minimax regret criteria • Game theory**Laplace criteria (Equally likely)**1/n 1/n 1/n 1/n**N1**N2 N3 Expected Dry Small Big Value A1:Don’t drill $0 $0 $0 A2:Drill alone -$500k $300k $9,300k A3:Farm out $0 $125k $1,250k Payoff Table(Well Drilling – Equally likely) $0 $3033k $458k**N1**N2 .... Nj .... Nn Alt. A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Maximax Criteria Max. MAX1 MAX2 .... MAXi .... MAXm**N1**N2 N3 Dry Small Big A1:Don’t drill $0 $0 $0 A2:Drill alone -$500k $300k $9,300k A3:Farm out $0 $125k $1,250k Payoff Table(Well Drilling - Maximax) Max. $0 $9,300k $1,250k**N1**N2 .... Nj .... Nn Alt. A1 O11 O12 .... O1j .... O1n A2 O21 O22 .... O2j .... O2n .... .... .... .... .... .... .... Ai Oi1 Oi2 .... Oij .... Oin .... .... .... .... .... .... .... Am Om1 Om2 .... Omj .... Omn Maximin Criteria Max. MIN1 MIN2 .... MINi .... MINm