1. 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. 07458 F-1 Operations Management Simulation Module F

2. 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. 07458 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

3. 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. 07458 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

4. 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. 07458 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

5. 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. 07458 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

6. 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. 07458 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

7. 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. 07458 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

8. 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. 07458 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

9. 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. 07458 F-9 Simulation:  Can be expensive and time consuming  Does not yield optimal solution  Requires good managerial input  Results not generalizable to other situations © 1984-1994 T/Maker Co. Disadvantages of Simulation

10. 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. 07458 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

11. 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. 07458 F-11 Partial Table of Random Numbers (upper left corner) 52065088533010479937669135 37632802743524032960748590 82576828059403112779908792 69023649719932107521959094 98949036067823678985292125 96526287495649237871729057 33692721116095896848178934 50335095134434626339552930 88321850625734566231154090 303624608251743035368501 50486118852308541712806924 27882162696448311273026800 45144632134966627441869892

12. 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. 07458 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

13. 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. 07458 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

14. 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. 07458 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.

15. 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. 07458 F-15 Example: Dist. 1 – Inter-Arrival Times Time Between Arrivals (Hours) ProbabilityCumulative Probability Random - Number Interval 360.13 01 – 13 240.170.3014 – 30 120.150.4531 – 45 80.250.7045 – 70 60.200.9071 - 90 40.101.0091 - 00

16. 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. 07458 F-16 Example: Dist. 2 – Unloading Times Unloading Times (Hours) ProbabilityCumulative Probability Random- Number Interval 240.05 01 – 05 120.150.2006 – 20 80.500.7021 – 70 60.200.9071 – 90 40.101.0091 - 00

17. 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. 07458 F-17 Example: Simulating RnInt Arr Time Arrival Time Unloading Starts RnUnloading Time Unloading Ends Waiting Time 52888378160 063644 638520 502468 288760 88674760224982 538829874610416 3024106 3581140 1036142 2481500 478150 03241740 99415417429818220 From Dist. 1From Dist. 2From Random Number Table

18. 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. 07458 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 hrs11.3 + 4.2 hrs 17.1 hrs11.3 hrs4.2 hrs15.5 hrs