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C13s

1. 1. Chapter 13Operational Decision-Making Tools: Simulation
2. 2. Lecture Outline• Monte Carlo Simulation• Computer Simulation with Excel• Areas of Simulation ApplicationCopyright 2011 John Wiley & Sons, Inc Supplement 13-2
3. 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 modelsCopyright 2011 John Wiley & Sons, Inc Supplement 13-3
4. 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 randomCopyright 2011 John Wiley & Sons, Inc Supplement 13-4
5. 5. Probability Distribution of DemandLAPTOPS DEMANDED FREQUENCY OF PROBABILITY OF PER WEEK, x DEMAND DEMAND, P(x) 0 20 0.20 1 40 0.40 2 20 0.20 3 10 0.10 4 10 0.10 100 1.00Copyright 2011 John Wiley & Sons, Inc Supplement 13-5
6. 6. Roulette Wheel of Demand 0 90 x=4 x=0 80 x=3 20 x=2 x=1 60Copyright 2011 John Wiley & Sons, Inc Supplement 13-6
7. 7. Generating Demand from Random Numbers DEMAND, RANGES OF RANDOM NUMBERS, x r 0 0-19 1 20-59 r = 39 2 60-79 3 80-89 4 90-99Copyright 2011 John Wiley & Sons, Inc Supplement 13-7
8. 8. Random Number TableCopyright 2011 John Wiley & Sons, Inc Supplement 13-8
9. 9. 15 Weeks of Demand WEEK r DEMAND (x) REVENUE (S) 1 39 1 4,300 2 73 2 8,600 3 72 2 8,600 4 75 2 8,600 5 37 1 4,300 6 02 0 0 7 87 3 12,900 8 98 4 17,200 9 10 0 0 10 47 1 4,300 11 93 4 17,200 12 21 1 4,300 13 95 4 17,200 14 97 4 17,200 15 69 2 8,600 = 31 \$133,300Copyright 2011 John Wiley & Sons, Inc Supplement 13-9
10. 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 trialsCopyright 2011 John Wiley & Sons, Inc Supplement 13-10
11. 11. Random Numbers in ExcelCopyright 2011 John Wiley & Sons, Inc Supplement 13-11
12. 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 =AVERAGE(G6:G20) F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20Copyright 2011 John Wiley & Sons, Inc Supplement 13-12
13. 13. Simulation in Excel Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6Copyright 2011 John Wiley & Sons, Inc Supplement 13-13
14. 14. Decision Making with Simulation This formula entered in G7 and copied to G8:G105 =G6*50 entered into cell L6 and copied to L7:L105 =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:I105Copyright 2011 John Wiley & Sons, Inc Supplement 13-14
15. 15. Decision Making with Simulation New formula for two laptops ordered per week.Copyright 2011 John Wiley & Sons, Inc Supplement 13-15
16. 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 physicallyCopyright 2011 John Wiley & Sons, Inc Supplement 13-16
17. 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 shareCopyright 2011 John Wiley & Sons, Inc Supplement 13-17
18. 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 sourcesCopyright 2011 John Wiley & Sons, Inc Supplement 13-18
19. 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.Copyright 2011 John Wiley & Sons, Inc Supplement 13-19