Chapter 13 Operational DecisionMaking Tools Simulation Russell and

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

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 8 e Supplement 13 -2

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 8 e Supplement 13 -3

Simulation Yesterday and Tomorrow • During the 1940’s through 1990’s, if applied mathematicians could not derive a closedform analytical mathematical solution to a mathematized process, they used simulation to understand the behavior of the process • Today simulation is the essence of video games, of movies, and of virtual reality • In the future simulations will be conducted on Holo-decks just like in Star Trek © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -4

Three Classes of Decision Environments • Decision-making under Risk and Uncertainty – Decision tables and trees – we will not cover these— these were discussed in the Supplement to Chapter 1 that we did NOT cover • Decision Making under assumed Certainty – The optimization models we looked at. . transportation, transshipment, assignment, linear programming models • Decision Making under Change and Complexity – The simulation models we will look at today © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -5

Simulation Models…. • Characterize process behavior over time • Are usually descriptive (telling it like it is) – The optimization models we looked at were prescriptive (telling it like it should be) • Are of two basic types – Continuous-deterministic – Discrete-stochastic • i. e. , involving probabilities and randomness—monte carlo © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -6

Monte Carlo Simulation • THE COMPUTER GENERATION OF RANDOM NUMBERS—all kinds of random numbers • 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 8 e Supplement 13 -7

Major Components of Discrete Stochastic Simulation • Activities – Activities have time duration • Events – Are instants in time at which an activity begins or ends • Permanent entities • Temporary entities © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -8

Discrete Simulation Time Advance • From one time unit to the next—Time step – From one day to the next, for example – What we use in the Excel simulations • From one event to the next chronological event to occur in time © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -9

Examples of Activities, Events for an Airline Gate Turn • Activities – Unloading – Cabin cleanup – Loading – Refueling – Baggage unloading – Baggage loading – Refurbishing snacks • Events • Beginning of unloading • Ending of unloading/beginning of cabin cleanup • Ending of cabin cleanup/beginning of loading • Ending of unloading © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -10

Probability Distribution of Demand LAPTOPS DEMANDED PER WEEK, x 0 1 2 3 4 FREQUENCY OF DEMAND PROBABILITY OF DEMAND, P(x) 20 40 20 10 10 0. 20 0. 40 0. 20 0. 10 100 1. 00 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -11

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 8 e Supplement 13 -12

Computer Simulation With Excel © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -13

Simulation in Excel Enter this formula in G 6 and copy to G 7: G 20 Enter “=4300*G 6” in H 6 can copy to H 7: H 20 Generate random number for cells F 6: F 20 with the formula “=RAND()” in F 6 and copying to F 7: F 20 =AVERAGE(G 6: G 20) © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -14

Simulation in Excel Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -15

Decision Making with Simulation This formula entered in G 7 and copied to G 8: G 105 =G 6*50 entered into cell L 6 and copied to L 7: L 105 =VLOOKUP (F 6, LOOKUP, 2) in H 6 and copied to H 7: H 105 Shortages computed by entering =MIN(G 6 -H 6, 0) in I 6 and copying to I 7: I 105 © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -16

Decision Making with Simulation New formula for two laptops ordered per week. © 2014 John Wiley & Sons, Inc. - Russell and Taylor 8 e Supplement 13 -17

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 8 e Supplement 13 -18

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 8 e Supplement 13 -19

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 8 e Supplement 13 -20

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