1. Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Operations Management - 5 th Edition Chapter 12 Supplement Roberta Russell & Bernard W. Taylor, III Simulation

2. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-2 Lecture Outline   Monte Carlo Simulation   Computer Simulation with Excel   Areas of Simulation Application

3. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-3 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, trade-mills for tires   Mathematical-computerized simulation Computer-based replicated models

4. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-4 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

5. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-5 Distribution of Demand LAPTOPS DEMANDEDFREQUENCY OFPROBABILITY OF PER WEEK, xDEMANDDEMAND, P(x) 0200.20 1400.40 2200.20 3100.10 4100.10 1001.00

6. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-6 Roulette Wheel of Demand 90 80 60 200 x = 2 x = 0 x = 4 x = 3 x = 1

7. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-7 Generating Demand from Random Numbers DEMAND,RANGES OF RANDOM NUMBERS, xr 00-19 120-59r = 39 260-79 380-89 490-99

8. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-8 Random Number Table

9. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-9 Random Numbers in Excel

10. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-10 15 Weeks of Demand Average demand = 31/15 = 2.07 laptops/week WEEKrDEMAND (x)REVENUE (S) 13914,300 27328,600 37228,600 47528,600 53714,300 60200 787312,900 898417,200 91000 104714,300 1193417,200 122114,300 1395417,200 1497417,200 156928,600  = 31$133,300

11. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-11 Computing Expected Demand 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)Difference between 1.5 and 2.07 is due to small number of periods analyzed (only 15 weeks) Steady-state result an average result that remains constant after enough trials

12. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-12 Simulation in Excel Enter this formula in G6 and copy to G7:G20 Enter “=4300*G6” in H6 and copy to H7:H20 Generate random numbers for cells F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20 = AVERAGE (G6:G20)

13. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-13 Simulation in Excel (cont.)

14. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-14 Decision Making with Simulation This formula entered in G7 and copied to G8:G105 =VLOOKUP (F6,LOOKUP,2) in H6 and copied to H7:H105 =G6*50 entered into cell L6 and copied to L7:L105 Shortages computed by entering =MIN(G6-H6,0) in I6 and copying to I7:I105

15. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-15 Decision Making with Simulation (cont.) New formula for two laptops ordered per week

16. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-16 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 Simulation is widely used to analyze JIT without having to implement it physically

17. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-17 Areas of Simulation Application (cont.)  Production and Manufacturing Systems Examples: 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

18. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-18 Areas of Simulation Application (cont.)  Logistics Typically include numerous random variables, such as distance, different modes of transport, shipping rates, and schedules to analyze different distribution channels  Service Operations Examples: police departments, fire departments, post offices, hospitals, court systems, airports Complex operations that no technique except simulation can be employed  Environmental and Resource Analysis Examples: impact of manufacturing plants, waste-disposal facilities, nuclear power plants, waste and population conditions, feasibility of alternative energy sources

19. Copyright 2006 John Wiley & Sons, Inc.Supplement 12-19 Copyright 2006 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.