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# Heizer om10 mod_f

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### Heizer om10 mod_f

1. 1. F - 1© 2011 Pearson Education, Inc. publishing as Prentice HallF SimulationPowerPoint presentation to accompanyHeizer and RenderOperations Management, 10ePrinciples of Operations Management, 8ePowerPoint slides by Jeff Heyl
2. 2. F - 2© 2011 Pearson Education, Inc. publishing as Prentice HallOutline What Is Simulation? Advantages and Disadvantages ofSimulation Monte Carlo Simulation Simulation of A Queuing Problem Simulation and Inventory Analysis
3. 3. F - 3© 2011 Pearson Education, Inc. publishing as Prentice HallLearning ObjectivesWhen you complete this module youshould be able to:1. List the advantages and disadvantagesof modeling with simulation2. Perform the five steps in a Monte Carlosimulation3. Simulate a queuing problem4. Simulate an inventory problem5. Use Excel spreadsheets to create asimulation
4. 4. F - 4© 2011 Pearson Education, Inc. publishing as Prentice HallComputer Analysis
5. 5. F - 5© 2011 Pearson Education, Inc. publishing as Prentice HallWhat is Simulation? An attempt to duplicate the features,appearance, and characteristics of areal system1. To imitate a real-world situationmathematically2. To study its properties and operatingcharacteristics3. To draw conclusions and make actiondecisions based on the results of thesimulation
6. 6. F - 6© 2011 Pearson Education, Inc. publishing as Prentice HallSimulation ApplicationsAmbulance location anddispatchingAssembly-line balancingParking lot and harbor designDistribution system designScheduling aircraftLabor-hiring decisionsPersonnel schedulingTraffic-light timingVoting pattern predictionBus schedulingDesign of library operationsTaxi, truck, and railroaddispatchingProduction facility schedulingPlant layoutCapital investmentsProduction schedulingSales forecastingInventory planning and controlTable F.1
7. 7. F - 7© 2011 Pearson Education, Inc. publishing as Prentice HallWhat Is Simulation?1. Define the problem2. Introduce the important variables associatedwith the problem3. Construct a numerical model4. Set up possible courses of action for testing byspecifying values of variables5. Run the experiment6. Consider the results (possibly modifying themodel or changing data inputs)7. Decide what course of action to take
8. 8. F - 8© 2011 Pearson Education, Inc. publishing as Prentice HallSelect best courseExamine resultsConduct simulationSpecify valuesof variablesConstruct modelIntroduce variablesTheProcess ofSimulationFigure F.1Define problem
9. 9. F - 9© 2011 Pearson Education, Inc. publishing as Prentice HallAdvantages of Simulation1. Relatively straightforward and flexible2. Can be used to analyze large andcomplex real-world situations thatcannot be solved by conventionalmodels3. Real-world complications can beincluded that most OM models cannotpermit4. “Time compression” is possible
10. 10. F - 10© 2011 Pearson Education, Inc. publishing as Prentice HallAdvantages of Simulation5. Allows “what-if” types of questions6. Does not interfere with real-worldsystems7. Can study the interactive effects ofindividual components or variables inorder to determine which ones areimportant
11. 11. F - 11© 2011 Pearson Education, Inc. publishing as Prentice HallDisadvantages of Simulation1. Can be very expensive and may takemonths to develop2. It is a trial-and-error approach that mayproduce different solutions in repeatedruns3. Managers must generate all of theconditions and constraints forsolutions they want to examine4. Each simulation model is unique
12. 12. F - 12© 2011 Pearson Education, Inc. publishing as Prentice HallMonte Carlo SimulationThe Monte Carlo method may be usedwhen the model contains elements thatexhibit chance in their behavior1. Set up probability distributions for importantvariables2. Build a cumulative probability distribution foreach variable3. Establish an interval of random numbers foreach variable4. Generate random numbers5. Simulate a series of trials
13. 13. F - 13© 2011 Pearson Education, Inc. publishing as Prentice HallProbability of Demand(1) (2) (3) (4)Demandfor Tires FrequencyProbability ofOccurrenceCumulativeProbability0 10 10/200 = .05 .051 20 20/200 = .10 .152 40 40/200 = .20 .353 60 60/200 = .30 .654 40 40/200 = .20 .855 30 30/ 200 = .15 1.00200 days 200/200 = 1.00Table F.2
14. 14. F - 14© 2011 Pearson Education, Inc. publishing as Prentice HallAssignment of RandomNumbersDailyDemand ProbabilityCumulativeProbabilityInterval ofRandomNumbers0 .05 .05 01 through 051 .10 .15 06 through 152 .20 .35 16 through 353 .30 .65 36 through 654 .20 .85 66 through 855 .15 1.00 86 through 00Table F.3
15. 15. F - 15© 2011 Pearson Education, Inc. publishing as Prentice HallTable of Random Numbers52 50 60 52 0537 27 80 69 3482 45 53 33 5569 81 69 32 0998 66 37 30 7796 74 06 48 0833 30 63 88 4550 59 57 14 8488 67 02 02 8490 60 94 83 77Table F.4
16. 16. F - 16© 2011 Pearson Education, Inc. publishing as Prentice HallSimulation Example 1Select randomnumbers fromTable F.3DayNumberRandomNumberSimulatedDaily Demand1 52 32 37 33 82 44 69 45 98 56 96 57 33 28 50 39 88 510 90 539 Total3.9 Average
17. 17. F - 17© 2011 Pearson Education, Inc. publishing as Prentice HallSimulation Example 1DayNumberRandomNumberSimulatedDaily Demand1 52 32 37 33 82 44 69 45 98 56 96 57 33 28 50 39 88 510 90 539 Total3.9 AverageExpecteddemand = ∑ (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 tires5i =1
18. 18. F - 18© 2011 Pearson Education, Inc. publishing as Prentice HallQueuing SimulationNumberof Arrivals ProbabilityCumulativeProbabilityRandom-NumberInterval0 .13 .13 01 through 131 .17 .30 14 through 302 .15 .45 31 through 453 .25 .70 46 through 704 .20 .90 71 through 905 .10 1.00 91 through 001.00Overnight barge arrival ratesTable F.5
19. 19. F - 19© 2011 Pearson Education, Inc. publishing as Prentice HallQueuing SimulationDailyUnloadingRates ProbabilityCumulativeProbabilityRandom-NumberInterval1 .05 .05 01 through 052 .15 .20 06 through 203 .50 .70 21 through 704 .20 .90 71 through 905 .10 1.00 91 through 001.00Barge unloading ratesTable F.6
20. 20. F - 20© 2011 Pearson Education, Inc. publishing as Prentice HallQueuing Simulation(1)Day(2)NumberDelayed fromPrevious Day(3)RandomNumber(4)Numberof NightlyArrivals(5)Totalto BeUnloaded(6)RandomNumber(7)NumberUnloaded1 0 52 3 3 37 32 0 06 0 0 63 03 0 50 3 3 28 34 0 88 4 4 02 15 3 53 3 6 74 46 2 30 1 3 35 37 0 10 0 0 24 08 0 47 3 3 03 19 2 99 5 7 29 310 4 37 2 6 60 311 3 66 3 6 74 412 2 91 5 7 85 413 3 35 2 5 90 414 1 32 2 3 73 315 0 00 5 5 59 320 41 39
21. 21. F - 21© 2011 Pearson Education, Inc. publishing as Prentice HallQueuing SimulationAverage number of bargesdelayed to the next day== 1.33 barges delayed per day20 delays15 daysAverage number ofnightly arrivals== 2.73 arrivals per night41 arrivals15 daysAverage number of bargesunloaded each day== 2.60 unloadings per day39 unloadings15 days
22. 22. F - 22© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Simulation(1)Demand forAce Drill(2)Frequency(3)Probability(4)CumulativeProbability(5)Interval ofRandom Numbers0 15 .05 .05 01 through 051 30 .10 .15 06 through 152 60 .20 .35 16 through 353 120 .40 .75 36 through 754 45 .15 .90 76 through 905 30 .10 1.00 91 through 00300 1.00Table F.8Daily demand for Ace Drill
23. 23. F - 23© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Simulation(1)Demand forAce Drill(2)Frequency(3)Probability(4)CumulativeProbability(5)Interval ofRandom Numbers1 10 .20 .20 01 through 202 25 .50 .70 21 through 703 15 .30 1.00 71 through 0050 1.00Table F.9Reorder lead time
24. 24. F - 24© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Simulation1. Begin each simulation day by checking to see ifordered inventory has arrived. If it has, increasecurrent inventory by the quantity ordered.2. Generate daily demand using probabilitydistribution and random numbers.3. Compute ending inventory. If on-hand isinsufficient to meet demand, satisfy as much aspossible and note lost sales.4. Determine whether the days ending inventory hasreached the reorder point. If it has, and there areno outstanding orders, place an order. Chooselead time using probability distribution andrandom numbers.
25. 25. F - 25© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Simulation(1)Day(2)UnitsReceived(3)BeginningInventory(4)RandomNumber(5)Demand(6)EndingInventory(7)LostSales(8)Order?(9)RandomNumber(10)LeadTime1 10 06 1 9 0 No2 0 9 63 3 6 0 No3 0 6 57 3 3 0 Yes 02 14 0 3 94 5 0 2 No5 10 10 52 3 7 0 No6 0 7 69 3 4 0 Yes 33 27 0 4 32 2 2 0 No8 0 2 30 2 0 0 No9 10 10 48 3 7 0 No10 0 7 88 4 3 0 Yes 14 141 2Table F.10Order quantity = 10 units Reorder point = 5 units
26. 26. F - 26© 2011 Pearson Education, Inc. publishing as Prentice HallInventory SimulationAverage ending inventory = = 4.1 units/day41 total units10 daysAverage lost sales = = .2 unit/day2 sales lost10 days= = .3 order/day3 orders10 daysAverage numberof orders placed
27. 27. F - 27© 2011 Pearson Education, Inc. publishing as Prentice HallInventory SimulationDaily order cost = (cost of placing 1 order) x(number of orders placed per day)= \$10 per order x .3 order per day = \$3Daily 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= \$2.05Daily stockout cost = (cost per lost sale) x(average number of lost sales per day)= \$8 per lost sale x .2 lost sales per day= \$1.60Total daily inventory cost = Daily order cost + Daily holdingcost + Daily stockout cost= \$6.65
28. 28. F - 28© 2011 Pearson Education, Inc. publishing as Prentice HallUsing Software in Simulation Computers are critical in simulatingcomplex tasks General-purpose languages - BASIC, C++ Special-purpose simulation languages -GPSS, SIMSCRIPT1. Require less programming time for largesimulations2. Usually more efficient and easier to checkfor errors3. Random-number generators are built in
29. 29. F - 29© 2011 Pearson Education, Inc. publishing as Prentice HallUsing Software in Simulation Commercial simulation programs areavailable for many applications - Extend,Modsim, Witness, MAP/1, EnterpriseDynamics, Simfactory, ProModel, MicroSaint, ARENA Spreadsheets such as Excel can be usedto develop some simulations
30. 30. F - 30© 2011 Pearson Education, Inc. publishing as Prentice HallUsing Software in Simulation
31. 31. F - 31© 2011 Pearson Education, Inc. publishing as Prentice HallAll rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, 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.