1. Chapter 13 Operational Decision-Making Tools: Simulation

2. Copyright 2011 John Wiley & Sons, Inc Lecture Outline Monte Carlo Simulation Computer Simulation with Excel Areas of Simulation Application Supplement 13-2

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 Copyright 2011 John Wiley & Sons, IncSupplement 13-3

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 Copyright 2011 John Wiley & Sons, IncSupplement 13-4

5. Probability Distribution of Demand Copyright 2011 John Wiley & Sons, IncSupplement 13-5 LAPTOPS DEMANDEDFREQUENCY OFPROBABILITY OF PER WEEK, xDEMANDDEMAND, P(x) 0200.20 1400.40 2200.20 3100.10 4100.10 1001.00

6. Roulette Wheel of Demand Copyright 2011 John Wiley & Sons, IncSupplement 13-6 90 80 60 20 0 x = 2 x = 0 x = 4 x = 3 x = 1

7. Generating Demand from Random Numbers Copyright 2011 John Wiley & Sons, IncSupplement 13-7 DEMAND,RANGES OF RANDOM NUMBERS, xr 00-19 120-59r = 39 260-79 380-89 490-99

8. Random Number Table Copyright 2011 John Wiley & Sons, IncSupplement 13-8

9. 15 Weeks of Demand Copyright 2011 John Wiley & Sons, IncSupplement 13-9 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

10. Computing Expected Demand Copyright 2011 John Wiley & Sons, IncSupplement 13-10 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 Estimated average demand = 31/15 = 2.07 laptops/week

11. Random Numbers in Excel Copyright 2011 John Wiley & Sons, IncSupplement 13-11

12. Simulation in Excel Copyright 2011 John Wiley & Sons, IncSupplement 13-12 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)

13. Simulation in Excel Copyright 2011 John Wiley & Sons, IncSupplement 13-13 Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6

14. Decision Making with Simulation Copyright 2011 John Wiley & Sons, IncSupplement 13-14 =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

15. Decision Making with Simulation Copyright 2011 John Wiley & Sons, IncSupplement 13-15 New formula for two laptops ordered per week.

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 Copyright 2011 John Wiley & Sons, IncSupplement 13-16

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 Copyright 2011 John Wiley & Sons, IncSupplement 13-17

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 Copyright 2011 John Wiley & Sons, IncSupplement 13-18

19. Copyright 2011 John Wiley & Sons, IncSupplement 13-19 Copyright 2011 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.