Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-1 Operations Management Simulation Module F

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-2 Outline  What is Simulation?  Advantages and Disadvantages of Simulation  Monte Carlo Simulation  Simulation of a Queuing Problem  Simulation and Inventory Analysis  The Role of Computers in Simulation

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-3 Learning Objectives When you complete this chapter, you should be able to Identify or Define :  Monte Carlo simulation  Random numbers  Random number interval  Simulation software Explain or be able to use:  The advantages and disadvantages of modeling with simulation  The use of Excel spreadsheets in simulation

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-4  Numerical technique of experimentation  Attempts to duplicate a system  Features  Behavior  Requires description of system  Many application areas  Operations management  Finance & economics Simulation

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-5 Some Applications of Simulation Ambulance location and dispatchingBus scheduling Assembly-line balancingDesign of library operations Parking lot and harbor designTaxi, truck, and railroad dispatching Distribution system designProduction facility scheduling Scheduling aircraftPlant layout Labor-hiring decisionsCapital investments Personnel schedulingProduction scheduling Traffic-light timingSales forecasting Voting pattern predictionInventory planning and control

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-6 Simulation The idea behind simulation is to:  Imitate a real-world situation mathematically  Study its properties and operating characteristics  Draw conclusions and make action recommendations based on the results of the simulation

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-7 The Process of Simulation Define the Problem Introduce important variables Construct simulation model Specify values of variables to be tested Conduct the simulation Examine the results Select best course of action

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-8 Advantages of Simulation Simulation  flexible, straightforward  can analyze large, complex real-world problems for which no closed-form analytical solutions exists  can include real-world complications which most other techniques cannot  enables “time compression”  allows “what if” type questions  does not interfere with the real-world system  allows study of relationships

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-9 Simulation:  Can be expensive and time consuming  Does not yield optimal solution  Requires good managerial input  Results not generalizable to other situations © T/Maker Co. Disadvantages of Simulation

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-10 The Monte Carlo Simulation Technique  Setup probability distribution for important variables  Build cumulative distribution for each variable  Establish interval of random numbers for each variable  Generate random numbers  Simulate a series of trials

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-11 Partial Table of Random Numbers (upper left corner)

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-12 Real World Variables Which Are Probabilistic in Nature  Inventory demand  Lead time for orders to arrive  Time between machine breakdowns  Times between arrivals at a service facility  Service times  Times to complete project activities  Number of employees absent from work each day

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-13 Simulation and Inventory Analysis - the Basic Model Begin Increase current inv by qty order end inv = begin-demand # of lost sales End inv = 0 Generate Random lead time Place order Compute averages Enough Days in simulation? Order placed & not arrived? End inv < reorder point? demand > begin inv? Order arrived? random # for today's demand

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-14 Simulation – An Example Following long trips down the Mississippi River from industrial mid-western cities, fully loaded barges arrive in New Orleans. The inter-arrival times for the barges are given in Dist. 1. In the same table, the cumulative probabilities and corresponding random number intervals are also given. Dist. 2. provides similar information regarding the times taken to unload a barge.

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-15 Example: Dist. 1 – Inter-Arrival Times Time Between Arrivals (Hours) ProbabilityCumulative Probability Random - Number Interval – – – –

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-16 Example: Dist. 2 – Unloading Times Unloading Times (Hours) ProbabilityCumulative Probability Random- Number Interval – – – –

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-17 Example: Simulating RnInt Arr Time Arrival Time Unloading Starts RnUnloading Time Unloading Ends Waiting Time From Dist. 1From Dist. 2From Random Number Table

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-18 Example: Some Simple Statistics Average Time Between Arrivals (Hours) Average Time to Unload (Hours) Total Wait Time (Hours) Average Wait Time (Hours) Average Time in Port 154/9 hrs102/9 hrs38 hrs38/9 hrs hrs 17.1 hrs11.3 hrs4.2 hrs15.5 hrs