1. Reid & Sanders, Operations Management © Wiley 2002 Simulation Analysis D SUPPLEMENT

2. Reid & Sanders, Operations Management © Wiley 2002 Page 2 Learning Objectives Describe the role of simulation analysis Describe different types of simulation models Identify the steps in simulation modeling Simulate the passage of time Generate random phenomena Evaluate simulation output Describe simulation software

3. Reid & Sanders, Operations Management © Wiley 2002 Page 3 Simulation A simulation model is a set mathematical functions, probability distributions, and decision rules that mimic the way a system acts under specific conditions. The goal is description, not optimization.

4. Reid & Sanders, Operations Management © Wiley 2002 Page 4 Common Applications Evaluation of alternative designs & operating procedures: –Production & queuing systems –Capacity planning –Machine & personnel scheduling –Shop routing –Facility layout & location

5. Reid & Sanders, Operations Management © Wiley 2002 Page 5 Example: Inventory Analysis How much of a product should be ordered & when? What is the best level of safety stock to hold for crucial raw materials? In a system with multiple locations, where should inventories be held & how much at each location? How much work-in-process inventory should be held between workstations?

6. Reid & Sanders, Operations Management © Wiley 2002 Page 6 Terminology Entities: –Interrelated system components Attributes: –The system variables under observation States: –The status of the attributes at a point in time Events: –A measurable change in the system

7. Reid & Sanders, Operations Management © Wiley 2002 Page 7 Types of Models The nature of events: –Continuous event models: changes to the system (events) occur rapidly & relatively uninterrupted –Discrete event models: events occur at readily identifiable points in time Randomness of change: –Stochastic models include random (or probabilistic) changes to system attributes –Deterministic models assume no random phenomenon

8. Reid & Sanders, Operations Management © Wiley 2002 Page 8 Step-by-Step: Modeling & Analysis Understand the system Construct the system components Test the model Plan the experimental design Execute the model runs Analyze the output

9. Reid & Sanders, Operations Management © Wiley 2002 Page 9 Understand the System Questions to explore: –What is the purpose of the simulation (what do you want to learn)? –What entities & relationships are important? –What attributes describe the state of the system? –Do events occur in a random or discrete fashion? –Do attribute values change randomly? –How is system performance evaluated?

10. Reid & Sanders, Operations Management © Wiley 2002 Page 10 Construct Components Break the system into manageable pieces –Example: customer arrivals, waiting line queues, etc. Observe actual behavior (gather performance data) Identify probability distributions that estimate any random phenomena –Poisson, binominal, normal distributions, etc. –Confirm using chi-square analysis Identify the decision rules (define how system attributes change when an event occurs) –Example: first come-first served; reservations given priority Code the modules & the system links

11. Reid & Sanders, Operations Management © Wiley 2002 Page 11 Test the Model First, test each module for accuracy –Does the model estimate the actual performance observed? Second, link the components together & test the entire model: –If the system being modeled already exists, compare the computer model’s performance with the performance of the existing system (they should match) –Track down any problems & reprogram the model

12. Reid & Sanders, Operations Management © Wiley 2002 Page 12 Experimental Design Terminology: –Experiment: one configuration of the simulation model –Run: a single sampling of the experiment Design the Experiment: –Identify the alternatives to explore (often changes to decision rules) –Identify criteria to compare the relative performance of each alternative

13. Reid & Sanders, Operations Management © Wiley 2002 Page 13 Execute Model Runs & Analyze Output Use relatively short runs to narrow your focus & then longer runs of better alternatives Compare performance of various alternatives suing statistical methods –Confidence intervals, t-tests, ANOVA, etc. –Are differences statistically significant?

14. Reid & Sanders, Operations Management © Wiley 2002 Page 14 Simulating Time Quickly estimate system performance over a long period of time: –Fixed-Time Incrementing: Determine what unit of time is appropriate (e.g.: minutes, days, months) given how rapidly the system changes Each cycle through the system might represent the passage of a unit of time –Next-Event Incrementing: If events occur irregularly, jump ahead to the next time something happens (using a representative probability distribution)

15. Reid & Sanders, Operations Management © Wiley 2002 Page 15 Random Number Generators Random number generators provide a sequence of values that approximate a randomly observed value from a continuous, uniform distribution between one and zero. Often we use pseudorandom numbers (the same sequence of ‘random’ values for each experiment) to allow us to directly compare different system configurations.

16. Reid & Sanders, Operations Management © Wiley 2002 Page 16 Generating Discrete Random Values Use random generators to provide the next r (a random or pseudorandom value, uniformly distributed between one & zero) For discrete variables, identify an appropriate range to correspond with each possible value –The width of the assigned range should correspond with the probability of that discrete value occurring –For example: when modeling a coin toss, if r is greater than 0.5 then the coin equals ‘heads’, if r is less than 0.5, the coin equals ‘tails’.

17. Reid & Sanders, Operations Management © Wiley 2002 Page 17 Generating Continuous Random Values Use the random number generator to provide the next r, then convert r to an observation (x) from the appropriate probability distribution. For example: –Uniform distribution: –Poisson distribution:

18. Reid & Sanders, Operations Management © Wiley 2002 Page 18 Evaluating Output Consider using pseudorandom numbers to allow direct performance comparisons between experiments Evaluate average performance and the distribution of performance measures –Example: in some experiments you may find short average waiting times, but that a few times wait a very, very long time to be processed (this might not be acceptable – particularly if you’re modeling customers waiting in a queue).

19. Reid & Sanders, Operations Management © Wiley 2002 Page 19 Computer Software Special-purpose simulation software –E.g.: Simfactory, Map/1 –Easy to code, but lack flexibility General-purpose simulation software –E.g.: Slam, Simscript, GPSS, Siman –Still relatively easy to program, more flexibility General-purpose programming languages –E.g: Fortran, Basic, C++ –Require more programming skill, but provide maximum flexibility

20. Reid & Sanders, Operations Management © Wiley 2002 Page 20 Considerations Programming languages versus simulation packages: –The complexity of the simulation planned –The variety of simulations likely to be performed in the future –The modeling & programming skills of the user Choosing between simulation software: –Can new subroutines be added to increase flexibility? –How easy is it to compute statistics on system performance? –Is there a graphical interface or animation capability? –Are diagnostics aids and error messages provided to help debug programming errors?

21. Reid & Sanders, Operations Management © Wiley 2002 Page 21 The End Copyright © 2002 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United State Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions 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 contained herein.