1. F - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall F F Simulation PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl

2. F - 2 © 2011 Pearson Education, Inc. publishing as Prentice Hall Outline  What Is Simulation?  Advantages and Disadvantages of Simulation  Monte Carlo Simulation  Simulation of A Queuing Problem  Simulation and Inventory Analysis

3. F - 3 © 2011 Pearson Education, Inc. publishing as Prentice Hall Learning Objectives When you complete this module you should be able to: 1.List the advantages and disadvantages of modeling with simulation 2.Perform the five steps in a Monte Carlo simulation 3.Simulate a queuing problem 4.Simulate an inventory problem 5.Use Excel spreadsheets to create a simulation

4. F - 4 © 2011 Pearson Education, Inc. publishing as Prentice Hall Computer Analysis

5. F - 5 © 2011 Pearson Education, Inc. publishing as Prentice Hall What is Simulation?  An attempt to duplicate the features, appearance, and characteristics of a real system 1.To imitate a real-world situation mathematically 2.To study its properties and operating characteristics 3.To draw conclusions and make action decisions based on the results of the simulation

6. F - 6 © 2011 Pearson Education, Inc. publishing as Prentice Hall Simulation Applications Ambulance location and dispatching Assembly-line balancing Parking lot and harbor design Distribution system design Scheduling aircraft Labor-hiring decisions Personnel scheduling Traffic-light timing Voting pattern prediction Bus scheduling Design of library operations Taxi, truck, and railroad dispatching Production facility scheduling Plant layout Capital investments Production scheduling Sales forecasting Inventory planning and control Table F.1

7. F - 7 © 2011 Pearson Education, Inc. publishing as Prentice Hall What Is Simulation? 1.Define the problem 2.Introduce the important variables associated with the problem 3.Construct a numerical model 4.Set up possible courses of action for testing by specifying values of variables 5.Run the experiment 6.Consider the results (possibly modifying the model or changing data inputs) 7.Decide what course of action to take

8. F - 8 © 2011 Pearson Education, Inc. publishing as Prentice Hall Select best course Examine results Conduct simulation Specify values of variables Construct model Introduce variables The Process of Simulation Figure F.1 Define problem

9. F - 9 © 2011 Pearson Education, Inc. publishing as Prentice Hall Advantages of Simulation 1.Relatively straightforward and flexible 2.Can be used to analyze large and complex real-world situations that cannot be solved by conventional models 3.Real-world complications can be included that most OM models cannot permit 4.“Time compression” is possible

10. F - 10 © 2011 Pearson Education, Inc. publishing as Prentice Hall Advantages of Simulation 5.Allows “what-if” types of questions 6.Does not interfere with real-world systems 7.Can study the interactive effects of individual components or variables in order to determine which ones are important

11. F - 11 © 2011 Pearson Education, Inc. publishing as Prentice Hall Disadvantages of Simulation 1.Can be very expensive and may take months to develop 2.It is a trial-and-error approach that may produce different solutions in repeated runs 3.Managers must generate all of the conditions and constraints for solutions they want to examine 4.Each simulation model is unique

12. F - 12 © 2011 Pearson Education, Inc. publishing as Prentice Hall Monte Carlo Simulation The Monte Carlo method may be used when the model contains elements that exhibit chance in their behavior 1.Set up probability distributions for important variables 2.Build a cumulative probability distribution for each variable 3.Establish an interval of random numbers for each variable 4.Generate random numbers 5.Simulate a series of trials

13. F - 13 © 2011 Pearson Education, Inc. publishing as Prentice Hall Probability of Demand (1)(2)(3)(4) Demand for TiresFrequency Probability of Occurrence Cumulative Probability 01010/200 =.05.05 12020/200 =.10.15 24040/200 =.20.35 36060/200 =.30.65 44040/200 =.20.85 53030/ 200 =.151.00 200 days200/200 = 1.00 Table F.2

14. F - 14 © 2011 Pearson Education, Inc. publishing as Prentice Hall Assignment of Random Numbers Daily DemandProbability Cumulative Probability Interval of Random Numbers 0.05 01 through 05 1.10.1506 through 15 2.20.3516 through 35 3.30.6536 through 65 4.20.8566 through 85 5.151.0086 through 00 Table F.3

15. F - 15 © 2011 Pearson Education, Inc. publishing as Prentice Hall Table of Random Numbers 5250605205 3727806934 8245533355 6981693209 9866373077 9674064808 3330638845 5059571484 886702 84 9060948377 Table F.4

16. F - 16 © 2011 Pearson Education, Inc. publishing as Prentice Hall Simulation Example 1 Select random numbers from Table F.3 Day Number Random Number Simulated Daily Demand 1523 2373 3824 4694 5985 6965 7332 8503 9885 10905 39Total 3.9 Average

17. F - 17 © 2011 Pearson Education, Inc. publishing as Prentice Hall Simulation Example 1 Day Number Random Number Simulated Daily Demand 1523 2373 3824 4694 5985 6965 7332 8503 9885 10905 39Total 3.9 Average Expected demand = ∑ (probability of i units) x (demand of i units) =(.05)(0) + (.10)(1) + (.20)(2) + (.30)(3) + (.20)(4) + (.15)(5) =0 +.1 +.4 +.9 +.8 +.75 =2.95 tires 5 i =1

18. F - 18 © 2011 Pearson Education, Inc. publishing as Prentice Hall Queuing Simulation Number of ArrivalsProbability Cumulative Probability Random-Number Interval 0.13 01 through 13 1.17.3014 through 30 2.15.4531 through 45 3.25.7046 through 70 4.20.9071 through 90 5.101.0091 through 00 1.00 Overnight barge arrival rates Table F.5

19. F - 19 © 2011 Pearson Education, Inc. publishing as Prentice Hall Queuing Simulation Daily Unloading RatesProbability Cumulative Probability Random-Number Interval 1.05 01 through 05 2.15.2006 through 20 3.50.7021 through 70 4.20.9071 through 90 5.101.0091 through 00 1.00 Barge unloading rates Table F.6

20. F - 20 © 2011 Pearson Education, Inc. publishing as Prentice Hall Queuing Simulation (1) Day (2) Number Delayed from Previous Day (3) Random Number (4) Number of Nightly Arrivals (5) Total to Be Unloaded (6) Random Number (7) Number Unloaded 105233373 200600630 305033283 408844021 535336744 623013353 701000240 804733031 929957293 1043726603 1136636744 1229157854 1333525904 1413223733 1500055593 204139

21. F - 21 © 2011 Pearson Education, Inc. publishing as Prentice Hall Queuing Simulation Average number of barges delayed to the next day = = 1.33 barges delayed per day 20 delays 15 days Average number of nightly arrivals = = 2.73 arrivals per night 41 arrivals 15 days Average number of barges unloaded each day = = 2.60 unloadings per day 39 unloadings 15 days

22. F - 22 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation (1) Demand for Ace Drill (2) Frequency (3) Probability (4) Cumulative Probability (5) Interval of Random Numbers 015.05 01 through 05 130.10.1506 through 15 260.20.3516 through 35 3120.40.7536 through 75 445.15.9076 through 90 530.101.0091 through 00 3001.00 Table F.8 Daily demand for Ace Drill

23. F - 23 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation (1) Demand for Ace Drill (2) Frequency (3) Probability (4) Cumulative Probability (5) Interval of Random Numbers 110.20 01 through 20 225.50.7021 through 70 315.301.0071 through 00 501.00 Table F.9 Reorder lead time

24. F - 24 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation 1.Begin each simulation day by checking to see if ordered inventory has arrived. If it has, increase current inventory by the quantity ordered. 2.Generate daily demand using probability distribution and random numbers. 3.Compute ending inventory. If on-hand is insufficient to meet demand, satisfy as much as possible and note lost sales. 4.Determine whether the day's ending inventory has reached the reorder point. If it has, and there are no outstanding orders, place an order. Choose lead time using probability distribution and random numbers.

25. F - 25 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation (1) Day (2) Units Received (3) Beginning Inventory (4) Random Number (5) Demand (6) Ending Inventory (7) Lost Sales (8) Order? (9) Random Number (10) Lead Time 11006190No 20963360No 30657330Yes021 40394502No 510 52370No 60769340Yes332 70432220No 80230200No 910 48370No 100788430Yes141 412 Table F.10 Order quantity = 10 units Reorder point = 5 units

26. F - 26 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation Average ending inventory = = 4.1 units/day 41 total units 10 days Average lost sales = =.2 unit/day 2 sales lost 10 days = =.3 order/day 3 orders 10 days Average number of orders placed

27. F - 27 © 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Simulation Daily order cost=(cost of placing 1 order) x (number of orders placed per day) =$10 per order x.3 order per day = $3 Daily holding cost=(cost of holding 1 unit for 1 day) x (average ending inventory) =50¢ per unit per day x 4.1 units per day =$2.05 Daily stockout cost=(cost per lost sale) x (average number of lost sales per day) =$8 per lost sale x.2 lost sales per day =$1.60 Total daily inventory cost=Daily order cost + Daily holding cost + Daily stockout cost =$6.65

28. F - 28 © 2011 Pearson Education, Inc. publishing as Prentice Hall Using Software in Simulation  Computers are critical in simulating complex tasks  General-purpose languages - BASIC, C++  Special-purpose simulation languages - GPSS, SIMSCRIPT 1.Require less programming time for large simulations 2.Usually more efficient and easier to check for errors 3.Random-number generators are built in

29. F - 29 © 2011 Pearson Education, Inc. publishing as Prentice Hall Using Software in Simulation  Commercial simulation programs are available for many applications - Extend, Modsim, Witness, MAP/1, Enterprise Dynamics, Simfactory, ProModel, Micro Saint, ARENA  Spreadsheets such as Excel can be used to develop some simulations

30. F - 30 © 2011 Pearson Education, Inc. publishing as Prentice Hall Using Software in Simulation

31. F - 31 © 2011 Pearson Education, Inc. publishing as Prentice Hall All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.