1. Operational Decision-Making Tools: Simulation
Chapter 13
Operational Decision-Making Tools:
Simulation
Russell and Taylor
Operations and Supply Chain Management, 8th Edition

2. Lecture Outline Monte Carlo Simulation – Slide 4
Computer Simulation With Excel – Slide 11
Areas of Simulation Application – Slide 16
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

3. Simulation
Mathematical and computer modeling technique for replicating real-world problem situations
Modeling approach primarily used to analyze probabilistic problems
It does not normally provide a solution; instead it provides information that is used to make a decision
Physical simulation
Space flights, wind tunnels, treadmills for tires
Mathematical-computerized simulation
Computer-based replicated models
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

4. Monte Carlo Simulation
Select numbers randomly from a probability distribution
Use these values to observe how a model performs over time
Random numbers each have an equal likelihood of being selected at random
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

5. Probability Distribution of Demand
LAPTOPS DEMANDED FREQUENCY OF PROBABILITY OF
PER WEEK, x DEMAND DEMAND, P(x)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

6. Roulette Wheel of Demand90
x = 4
x = 0
x = 3 20 80
x = 2
x = 1 60
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

7. Generating Demand from Random Numbers
DEMAND, RANGES OF RANDOM NUMBERS,
x r
0 0-19
r = 39
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

8. Random Number Table
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

9. 15 Weeks of Demand
WEEK r DEMAND (x) REVENUE (S)
,300
,600
,600
,600
,300
,900
,200
,300
,200
,300
,200
,200
,600
 = 31 $133,300
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

10. Computing Expected Demand
Estimated average demand = 31/15 = 2.07 laptops/week
E(x) = (0.20)(0) + (0.40)(1) + (0.20)(2)
+ (0.10)(3) + (0.10)(4)
= 1.5 laptops per week
Difference between 1.5 and 2.07 is due to small number of periods analyzed (only 15 weeks)
Steady-state result
average result which stays constant after enough trials
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

11. Computer Simulation With Excel
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

12. Simulation in Excel Enter this formula in G6 and copy to G7:G20
Enter “=4300*G6” in H6 can copy to H7:H20
Generate random number for cells F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20
=AVERAGE(G6:G20)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

13. Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6
Simulation in Excel
Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

14. Decision Making with Simulation
=G6*50 entered into cell L6 and copied to L7:L105
This formula entered in G7 and copied to G8:G105
=VLOOKUP (F6,LOOKUP,2) in H6 and copied to H7:H105
Shortages computed by entering =MIN(G6-H6,0) in I6 and copying to I7:I105
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

15. Decision Making with Simulation
New formula for two laptops ordered per week.
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

16. Areas of Simulation Application
Waiting Lines/Service
Complex systems for which it is difficult to develop analytical formulas
Determine how many registers and servers are needed to meet customer demand
Inventory Management
Traditional models make the assumption that customer demand is certain
Simulation is widely used to analyze JIT without having to implement it physically
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

17. Areas of Simulation Application
Production and Manufacturing Systems
Production scheduling, production sequencing, assembly line balancing, plant layout, and plant location analysis
Machine breakdowns typically occur according to some probability distributions
Capital Investment and Budgeting
Capital budgeting problems require estimates of cash flows, often resulting from many random variables
Simulation has been used to generate values of cash flows, market size, selling price, growth rate, and market share
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

18. Areas of Simulation Application
Logistics
Random variables include, distance, transport modes, shipping rates, and schedules
Allows analysis of different distribution channels
Service Operations
Police departments, fire departments, post offices, hospitals, court systems, airports
Complex operations where only simulation can be employed
Environmental and Resource Analysis
Impact of manufacturing plants, waste-disposal facilities, nuclear power plants, waste and population conditions, feasibility of alternative energy sources
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

19. Copyright 2014 John Wiley & Sons, Inc. All rights reserved
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© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e