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**Chapter 4 Decision Making**

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Advanced Organizer

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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

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

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**Types of Decisions Routine and Non-Routine Decisions**

Objective vs. Bounded Rationality Level of Certainty

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**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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**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

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**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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**Payoff Table Am .... Ai A2 A1 Alt. Nn .... Nj N2 N1 (Pn) .... (Pj)**

Om1 .... Oi1 O21 O11 Om2 .... Oi2 O22 O12 Omn .... Omj Oin Oij O2n O2j O1n O1j

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**Payoff Table for Decision Making under Certainty**

Omn .... Omj Oin Oij O2n O2j O1n O1j Om2 Oi2 O22 O12 Om1 Oi1 O21 O11 (Pn) (Pj) (P2) (P1) Nn Nj N2 N1 Am Ai A2 A1 Alt. 1.0

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**Tools for Decision Making under Certainty**

Linear programming Graphical solution Simplex method Computer software Non-linear programming Engineering Economic Analysis

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**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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**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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**Linear programming Graphical solution (Constraints)**

Y 10 20 30 40 50 60 (0,60) (0,40) 3x+2y≤120 Corner Solutions x+2y≤80 Feasible Region (40,0) (80,0) X

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**Linear programming Graphical solution (Objective Function)**

Y 10 20 30 40 50 60 P=10x+14y P=1050 P=700 P=350 X

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**Linear programming Graphical solution (Objective Function)**

Y 10 20 30 40 50 60 P=10x+14y P=1050 P=700 P=350 X

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**Linear programming Graphical solution**

Y 10 20 30 40 50 60 Optimal Solution (20, 30) X

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**Linear programming Simplex method**

BV Coefficient of RS Ratio P X Y S1 S2 P 1 -10 -14 S1 3 2 120 60 S2 80 40 P 1 -3 7 560 S1 2 -1 40 20 Y 1/2 80 P 1 3/2 11/2 620 X 1/2 -1/2 20 Y -1/4 3/4 30

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**Linear programming Computer Software**

Excel: Solver LINDO: max 10x + 14 y subject to M) 3x + 2y <= 120 A) x + 2y <= 80 end

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**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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**Payoff Table for Decision Making under Risk**

Omn .... Omj Oin Oij O2n O2j O1n O1j Om2 Oi2 O22 O12 Om1 Oi1 O21 O11 (Pn) (Pj) (P2) (P1) Nn Nj N2 N1 Am Ai A2 A1 Alt.

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**Tools for Decision Making under Risk**

Expected value Decision trees Decision Node Chance Node Queuing theory Simulation

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**Payoff Table & Expected Value (Fire Insurance)**

(No Accident) P2=0.001 P1=0.999 N2 N1 Expected Value A2=Self-Ins. A1=Buy Ins. -$100,000 -$200 -$200 -$100

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Decision Trees Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities. Decision Node D1 D2 DX Outcome Node Chance Node C1 C2 CY p1 p2 py Pruned Branch

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**Decision Tree (Fire Insurance)**

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

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**Payoff Table & Expected Value (Car Insurance)**

(Totaled) (Small Accident) (No Accident) P3=0.03 P2=0.07 P1=0.90 N3 N2 N1 Expected Value A1=Buy Ins. ($800) A2=Self-Ins. ($500 Deduc.) $500 $300 $0 $36 $13,000 $300 $0 $411

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**Decision Tree (Car Insurance)**

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

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**Payoff Table & Expected Value (Well Drilling)**

Big Small Dry N3 N2 N1 Value Expected A3:Farm out A2:Drill alone A1:Don’t drill $0 $0 $9,300k $300k -$500k $720k $1,250k $125k $0 $162.5k

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**Decision Tree (Well Drilling)**

$0 EV=$0 Dry P=0.6 $0 Small well P=0.3 Don’t drill $0 Big well P=0.1 $0 EV=$720k Dry P=0.6 -$500k Small well P=0.3 $300k Farm out $0 Drill alone $500k Big well P=0.1 $9,300k EV=$162.5k $0 Dry P=0.6 $125k Small well P=0.3 Big well P=0.1 $1,250k

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**Decision Tree (New Product Development)**

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

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**Decision Tree (New Product Development)**

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, …, 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

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Queuing Theory Basics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times. Queue a9 a8 a7 a6 a5 a4 a3 a2 a1 Server

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**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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**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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**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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**Physical model —Virtual 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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**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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**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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**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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**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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**Simulation Tools General purpose language General simulation 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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**Risk as Variance $5000 0.10 $3500 0.20 $4000 0.40 Cash F. Prob. $4500**

$3000 Project X $6000 0.10 $3000 0.25 $4000 0.30 Cash F. Prob. $5000 $2000 Project Y $4000 Mean $1140 $548 Std. Deviation

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Risk as Variance Probability Cash Flow X Y

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**Payoff Table for Decision Making under Uncertainty**

Omn .... Omj Oin Oij O2n O2j O1n O1j Om2 Oi2 O22 O12 Om1 Oi1 O21 O11 (Pn) (Pj) (P2) (P1) Nn Nj N2 N1 Am Ai A2 A1 Alt.

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**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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**Laplace criteria (Equally likely)**

N1 N2 .... Nj Nn Max Alt. (P1) (P2) (Pj) (Pn) A1 O11 O12 O1j O1n EV1 A2 O21 O22 O2j O2n EV2 Ai Oi1 Oi2 Oij Oin EVi Am Om1 Om2 Omj Omn EVm 1/n 1/n 1/n 1/n

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**Payoff Table (Well Drilling – Equally likely)**

Big Small Dry N3 N2 N1 Value Expected A3:Farm out A2:Drill alone A1:Don’t drill $0 $0 $9,300k $300k -$500k $3033k $1,250k $125k $0 $458k

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**Maximax Criteria Nn .... Nj N2 N1 Max. Am .... Ai A2 A1 Alt. O1n ....**

O1j O12 O11 MAX1 O2n .... O2j O22 O21 MAX2 .... .... Oin .... Oij Oi2 Oi1 MAXi .... .... Omn .... Omj Om2 Om1 MAXm

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**Payoff Table (Well Drilling - Maximax)**

Big Small Dry N3 N2 N1 Max. A3:Farm out A2:Drill alone A1:Don’t drill $0 $0 $9,300k $300k -$500k $9,300k $1,250k $125k $0 $1,250k

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**Maximin Criteria Nn .... Nj N2 N1 Max. Am .... Ai A2 A1 Alt. O1n ....**

O1j O12 O11 MIN1 O2n .... O2j O22 O21 MIN2 .... .... Oin .... Oij Oi2 Oi1 MINi .... .... Omn .... Omj Om2 Om1 MINm

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**Payoff Table (Well Drilling - Maximin)**

Big Small Dry N3 N2 N1 Min. A3:Farm out A2:Drill alone A1:Don’t drill $0 $0 $9,300k $300k -$500k -$500k $1,250k $125k $0 $0

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**Hurwicz Criteria .... Nn Nj N2 N1 (1-) Index Am .... Ai A2 A1 Alt.**

Max .... O1n O1j O12 O11 MAX1 MIN1 I1 .... O2n O2j O22 O21 MAX2 MIN2 I2 .... .... Oin Oij Oi2 Oi1 MAXi MINi Ii .... .... Omn Omj Om2 Om1 MAXm MINm Im Index = (MAX) + (1 - )(MIN)

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**Payoff Table (Well Drilling - Hurwicz)**

Big Small Dry N3 N2 N1 Index (=0.2) Max. Min. A3:Farm out A2:Drill alone A1:Don’t drill $0 $0 $0 $9,300k $300k -$500k $9,300k -$500k $1460k $1,250k $125k $0 $1,250k $0 $250k

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**Minimax Regret Criteria**

First convert payoff table to regret table Omn .... Omj Oin Oij O2n O2j O1n O1j Om2 Oi2 O22 O12 Om1 Oi1 O21 O11 Nn Nj N2 N1 Am Ai A2 A1 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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**Minimax Regret Criteria**

Rm1 .... Ri1 R21 R11 N1 Rm2 .... Ri2 R22 R12 N2 .... Rmj .... Rij R2j R1j Nj .... Rmn .... Rin R2n R1n Nn Min. Am .... Ai A2 A1 Alt. MAX1 MAX2 .... MAXi .... MAXm

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**Payoff Table & Regret Table (Well Drilling – Minimax Regret)**

Big Small Dry N3 N2 N1 Payoff A3:Farm out A2:Drill alone A1:Don’t drill $0 $9,300k $300k -$500k $1,250k $125k $0 Big Small Dry N3 N2 N1 Regret Max A3:Farm out A2:Drill alone A1:Don’t drill $0 $500k $175k $0 $300k $8,050k $0 $9,300k $9,300k $500k $8,050k

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Game theory Game 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.

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**Game theory (Example) Disarm Arm Soviet Strategy Disarm Arm**

U.S. Strategy 3rd-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.

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**Computer-Based Information Systems**

Integrated Database CAD/CAM Management Information Systems (MIS) Decision Support Systems (DSS) Expert Systems

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