OPERATIONS MANAGEMENT: Creating Value Along the Supply Chain, Canadian Edition Robert S. Russell, Bernard W. Taylor III, Ignacio Castillo, Navneet Vidyarthi CHAPTER 13 SUPPLEMENT Operational Decision-Making Tools: Simulation

Lecture Outline Monte Carlo Simulation Computer Simulation with Excel Areas of Simulation Application

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

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

Probability Distribution of Demand LAPTOPS 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 1.00

Roulette Wheel of Demand 90 80 60 20 x = 2 x = 0 x = 4 x = 3 x = 1

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 90-99

Random Number Table

15 Weeks of Demand WEEK r DEMAND (x) REVENUE (S) 1 39 1 4,300 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 $133,300

Computing Expected Demand + (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

Random Numbers in Excel

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)

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

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

Decision Making with Simulation New formula for two laptops ordered per week.

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

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

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

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