© 2008 Prentice Hall, Inc.F – 1 Operations Management Module F – Simulation PowerPoint presentation to accompany Heizer/Render Principles of Operations

© 2008 Prentice Hall, Inc. F – 1

Operations ManagementOperations ManagementModule F – Module F – SimulationSimulation

PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer/Render Heizer/Render Principles of Operations Management, 7ePrinciples of Operations Management, 7eOperations Management, 9e Operations Management, 9e


OutlineOutline

What Is Simulation?What Is Simulation?

Advantages and Disadvantages of Advantages and Disadvantages of SimulationSimulation

Monte Carlo SimulationMonte Carlo Simulation

Simulation of A Queuing ProblemSimulation of A Queuing Problem

Simulation and Inventory AnalysisSimulation and Inventory Analysis


Learning ObjectivesLearning Objectives

When you complete this module you When you complete this module you should be able to:should be able to:

List the advantages and disadvantages List the advantages and disadvantages of modeling with simulationof modeling with simulation

Perform the five steps in a Monte Carlo Perform the five steps in a Monte Carlo simulationsimulation

Simulate a queuing problemSimulate a queuing problem

Simulate an inventory problemSimulate an inventory problem

Use Excel spreadsheets to create a Use Excel spreadsheets to create a simulationsimulation


What is Simulation?What is Simulation?

An attempt to duplicate the An attempt to duplicate the features, appearance, and features, appearance, and characteristics of a real systemcharacteristics of a real system

1.1. To imitate a real-world situation To imitate a real-world situation mathematicallymathematically

2.2. To study its properties and To study its properties and operating characteristicsoperating characteristics

3.3. To draw conclusions and make To draw conclusions and make action decisions based on the action decisions based on the results of the simulationresults of the simulation


Computer AnalysisComputer Analysis


Simulation ApplicationsSimulation Applications

Ambulance location and Ambulance location and dispatchingdispatching

Assembly-line balancingAssembly-line balancing

Parking lot and harbor designParking lot and harbor design

Distribution system designDistribution system design

Scheduling aircraftScheduling aircraft

Labor-hiring decisionsLabor-hiring decisions

Personnel schedulingPersonnel scheduling

Traffic-light timingTraffic-light timing

Voting pattern predictionVoting pattern prediction

Bus schedulingBus scheduling

Design of library operationsDesign of library operations

Taxi, truck, and railroad Taxi, truck, and railroad dispatchingdispatching

Production facility schedulingProduction facility scheduling

Plant layoutPlant layout

Capital investmentsCapital investments

Production schedulingProduction scheduling

Sales forecastingSales forecasting

Inventory planning and controlInventory planning and control

Table F.1Table F.1


Select best course

Examine results

Conduct simulation

Specify valuesof variables

Construct model

Introduce variables

The The Process of Process of SimulationSimulation

Figure F.1Figure F.1

Define problem


Advantages of SimulationAdvantages of Simulation

1.1. Relatively straightforward and flexibleRelatively straightforward and flexible

2.2. Can be used to analyze large and Can be used to analyze large and complex real-world situations that complex real-world situations that cannot be solved by conventional cannot be solved by conventional modelsmodels

3.3. Real-world complications can be Real-world complications can be included that most OM models cannot included that most OM models cannot permitpermit

4.4. ““Time compression” is possibleTime compression” is possible


Advantages of SimulationAdvantages of Simulation

5.5. Allows “what-if” types of questionsAllows “what-if” types of questions

6.6. Does not interfere with real-world Does not interfere with real-world systemssystems

7.7. Can study the interactive effects of Can study the interactive effects of individual components or variables in individual components or variables in order to determine which ones are order to determine which ones are importantimportant


Disadvantages of SimulationDisadvantages of Simulation

1.1. Can be very expensive and may take Can be very expensive and may take months to developmonths to develop

2.2. It is a trial-and-error approach that may It is a trial-and-error approach that may produce different solutions in repeated produce different solutions in repeated runsruns

3.3. Managers must generate all of the Managers must generate all of the conditions and constraints for conditions and constraints for solutions they want to examinesolutions they want to examine

4.4. Each simulation model is uniqueEach simulation model is unique


Monte Carlo SimulationMonte Carlo Simulation

The Monte Carlo method may be used The Monte Carlo method may be used when the model contains elements thatwhen the model contains elements thatexhibit chance in their behaviorexhibit chance in their behavior

1.1. Set up probability distributions for important Set up probability distributions for important variablesvariables

2.2. Build a cumulative probability distribution for Build a cumulative probability distribution for each variableeach variable

3.3. Establish an interval of random numbers for Establish an interval of random numbers for each variableeach variable

4.4. Generate random numbersGenerate random numbers

5.5. Simulate a series of trialsSimulate a series of trials


Probability of DemandProbability of Demand(1)(1) (2)(2) (3)(3) (4)(4)

Demand Demand for Tiresfor Tires FrequencyFrequency

Probability of Probability of OccurrenceOccurrence

Cumulative Cumulative ProbabilityProbability

00 1010 10/200 = .0510/200 = .05 .05.05

11 2020 20/200 = .1020/200 = .10 .15.15

22 4040 40/200 = .2040/200 = .20 .35.35

33 6060 60/200 = .3060/200 = .30 .65.65

44 4040 40/200 = .2040/200 = .20 .85.85

55 3030 30/ 200 = .1530/ 200 = .15 1.001.00

200 days200 days 200/200 = 1.00200/200 = 1.00

Table F.2Table F.2


Assignment of Random Assignment of Random NumbersNumbers

Daily Daily DemandDemand ProbabilityProbability


Interval of Interval of Random Random NumbersNumbers

00 .05.05 .05.05 01 01 throughthrough 05 05

11 .10.10 .15.15 06 06 throughthrough 15 15

22 .20.20 .35.35 16 16 throughthrough 35 35

33 .30.30 .65.65 36 36 throughthrough 65 65

44 .20.20 .85.85 66 66 throughthrough 85 85

55 .15.15 1.001.00 86 86 throughthrough 00 00

Table F.3Table F.3


Table of Random NumbersTable of Random Numbers

5252 5050 6060 5252 0505

3737 2727 8080 6969 3434

8282 4545 5353 3333 5555

6969 8181 6969 3232 0909

9898 6666 3737 3030 7777

9696 7474 0606 4848 0808

3333 3030 6363 8888 4545

5050 5959 5757 1414 8484

8888 6767 0202 0202 8484

9090 6060 9494 8383 7777

Table F.4Table F.4


Simulation Example 1Simulation Example 1

Select random numbers from

Table F.3

DayDayNumberNumber

RandomRandomNumberNumber

Simulated Simulated Daily DemandDaily Demand

11 5252 33

22 3737 33

33 8282 44

44 6969 44

55 9898 55

66 9696 55

77 3333 22

88 5050 33

99 8888 55

1010 9090 55

3939 TotalTotal

3.93.9 Average Average


Simulation Example 1Simulation Example 1

DayDayNumberNumber

RandomRandomNumberNumber

Simulated Simulated Daily DemandDaily Demand

11 5252 33

22 3737 33

33 8282 44

44 6969 44

55 9898 55

66 9696 55

77 3333 22

88 5050 33

99 8888 55

1010 9090 55

3939 TotalTotal

3.93.9 Average Average

Expecteddemand = ∑ (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


Queuing SimulationQueuing Simulation

Number Number of Arrivalsof Arrivals ProbabilityProbability


Random-NumberRandom-NumberIntervalInterval

00 .13.13 .13.13 01 01 throughthrough 13 13

11 .17.17 .30.30 14 14 throughthrough 30 30

22 .15.15 .45.45 31 31 throughthrough 45 45

33 .25.25 .70.70 46 46 throughthrough 70 70

44 .20.20 .90.90 71 71 throughthrough 90 90

55 .10.10 1.001.00 91 91 throughthrough 00 00

1.001.00

Overnight barge arrival rates Overnight barge arrival rates Table F.5Table F.5



Daily Daily Unloading Unloading

RatesRates ProbabilityProbabilityCumulative Cumulative ProbabilityProbability

Random-NumberRandom-NumberIntervalInterval

11 .05.05 .05.05 01 01 throughthrough 05 05

22 .15.15 .20.20 06 06 throughthrough 20 20

33 .50.50 .70.70 21 21 throughthrough 70 70

44 .20.20 .90.90 71 71 throughthrough 90 90

55 .10.10 1.001.00 91 91 throughthrough 00 00

1.001.00

Barge unloading rates Barge unloading rates Table F.6Table F.6


Queuing SimulationQueuing Simulation(1)(1)

DayDay

(2)(2)NumberNumber

Delayed fromDelayed fromPrevious DayPrevious Day

(3)(3)

Random Random NumberNumber

(4)(4)NumberNumber

of Nightlyof NightlyArrivalsArrivals

(5)(5)TotalTotalto Beto Be

UnloadedUnloaded

(6)(6)

Random Random NumberNumber

(7)(7)

Number Number UnloadedUnloaded

11 00 5252 33 33 3737 33

22 00 0606 00 00 6363 00

33 00 5050 33 33 2828 33

44 00 8888 44 44 0202 11

55 33 5353 33 66 7474 44

66 22 3030 11 33 3535 33

77 00 1010 00 00 2424 00

88 00 4747 33 33 0303 11

99 22 9999 55 77 2929 33

1010 44 3737 22 66 6060 33

1111 33 6666 33 66 7474 44

1212 22 9191 55 77 8585 44

1313 33 3535 22 55 9090 44

1414 11 3232 22 33 7373 33

1515 00 0000 55 55 5959 33

2020 4141 3939



Average number of bargesAverage number of bargesdelayed to the next daydelayed to the next day ==

= 1.33= 1.33 barges delayed per day barges delayed per day

20 20 delaysdelays1515 days days

Average number of Average number of nightly arrivalsnightly arrivals ==

= 2.73= 2.73 arrivals per night arrivals per night

41 41 arrivalsarrivals1515 days days

Average number of bargesAverage number of bargesunloaded each dayunloaded each day ==

= 2.60= 2.60 unloadings per day unloadings per day

39 39 unloadingsunloadings1515 days days


Inventory SimulationInventory Simulation

(1)(1)Demand forDemand for

Ace DrillAce Drill

(2)(2)

FrequencyFrequency

(3)(3)

ProbabilityProbability

(4)(4)CumulativeCumulativeProbabilityProbability

(5)(5)Interval ofInterval of

Random NumbersRandom Numbers

00 1515 .05.05 .05.05 01 01 throughthrough 05 05

11 3030 .10.10 .15.15 06 06 throughthrough 15 15

22 6060 .20.20 .35.35 16 16 throughthrough 35 35

33 120120 .40.40 .75.75 36 36 throughthrough 75 75

44 4545 .15.15 .90.90 76 76 throughthrough 90 90

55 3030 .10.10 1.001.00 91 91 throughthrough 00 00

300300 1.001.00

Table F.8Table F.8

Daily demand for Ace DrillDaily demand for Ace Drill



(1)(1)Demand forDemand for

Ace DrillAce Drill

(2)(2)

FrequencyFrequency

(3)(3)

ProbabilityProbability

(4)(4)CumulativeCumulativeProbabilityProbability

(5)(5)Interval ofInterval of

Random NumbersRandom Numbers

11 1010 .20.20 .20.20 01 01 throughthrough 20 20

22 2525 .50.50 .70.70 21 21 throughthrough 70 70

33 1515 .30.30 1.001.00 71 71 throughthrough 00 00

5050 1.001.00

Table F.9Table F.9

Reorder lead timeReorder lead time



1.1. Begin each simulation day by checking to see if Begin each simulation day by checking to see if ordered inventory has arrived. If if has, increase ordered inventory has arrived. If if has, increase current inventory by the quantity ordered.current inventory by the quantity ordered.

2.2. Generate daily demand using probability Generate daily demand using probability distribution and random numbers.distribution and random numbers.

3.3. Compute ending inventory. If on-hand is Compute ending inventory. If on-hand is insufficient to meet demand, satisfy as much as insufficient to meet demand, satisfy as much as possible and note lost sales.possible and note lost sales.

4.4. Determine whether the day's ending inventory has Determine whether the day's ending inventory has reached the reorder point. If it has, and there are reached the reorder point. If it has, and there are no outstanding orders, place an order. Choose no outstanding orders, place an order. Choose lead time using probability distribution and lead time using probability distribution and random numbers.random numbers.



(1)(1)

DayDay

(2)(2)UnitsUnits

ReceivedReceived

(3)(3)Beginning Beginning InventoryInventory

(4)(4)Random Random NumberNumber

(5)(5)

DemandDemand

(6)(6)Ending Ending

InventoryInventory

(7)(7)LostLostSalesSales

(8)(8)

Order?Order?

(9)(9)RandomRandomNumberNumber

(10)(10)LeadLeadTimeTime

11 1010 0606 11 99 00 NoNo

22 00 99 6363 33 66 00 NoNo

33 00 66 5757 33 33 00 YesYes 0202 11

44 00 33 9494 55 00 22 NoNo

55 1010 1010 5252 33 77 00 NoNo

66 00 77 6969 33 44 00 YesYes 3333 22

77 00 44 3232 22 22 00 NoNo

88 00 22 3030 22 00 00 NoNo

99 1010 1010 4848 33 77 00 NoNo

1010 00 77 8888 44 33 00 YesYes 1414 11

4141 22

Table F.10Table F.10Order quantity = Order quantity = 10 10 units Reorder point = units Reorder point = 55 units units



Average ending inventory Average ending inventory = = 4.1= = 4.1 units/day units/day4141 total units total units1010 days days

Average lost sales Average lost sales = = .2= = .2 unit/day unit/day22 sales lost sales lost1010 days days

= = .3= = .3 order/day order/day3 3 ordersorders1010 days days

Average number Average number of orders placedof orders placed


Inventory SimulationInventory SimulationDaily order costDaily order cost == ((cost of placingcost of placing 1 1 orderorder) x ) x ((number of orders placed per daynumber of orders placed per day))

== $10 $10 per orderper order xx .3 .3 order per dayorder per day = $3 = $3Daily holding costDaily holding cost == ((cost of holdingcost of holding 1 1 unit forunit for 1 1 dayday) x ) x ((average ending inventoryaverage ending inventory))

== 50¢ 50¢ per unit per per unit per dayday xx 4.1 units 4.1 units per day per day

== $2.05$2.05Daily stockout costDaily stockout cost== ((cost per lost cost per lost salesale) x ) x ((averageaverage number of lost sales per daynumber of lost sales per day))

== $8 $8 per lost saleper lost sale xx .2 .2 lost sales per daylost sales per day

== $1.60$1.60Total daily inventory costTotal daily inventory cost== DailyDaily order costorder cost + D + Daily holding cost + aily holding cost + Daily stockout costDaily stockout cost

==$6.65$6.65


Using Software in SimulationUsing Software in Simulation

Computers are critical in simulating Computers are critical in simulating complex taskscomplex tasks

General-purpose languages - BASIC, C++General-purpose languages - BASIC, C++

Special-purpose simulation languages - Special-purpose simulation languages - GPSS, SIMSCRIPTGPSS, SIMSCRIPT

1.1. Require less programming time for large Require less programming time for large simulationssimulations

2.2. Usually more efficient and easier to check Usually more efficient and easier to check for errorsfor errors

3.3. Random-number generators are built inRandom-number generators are built in



Commercial simulation programs are Commercial simulation programs are available for many applications - Extend, available for many applications - Extend, Modsim, Witness, MAP/1, Enterprise Modsim, Witness, MAP/1, Enterprise Dynamics, Simfactory, ProModel, Micro Dynamics, Simfactory, ProModel, Micro Saint, ARENASaint, ARENA

Spreadsheets such as Excel can be used Spreadsheets such as Excel can be used to develop some simulationsto develop some simulations



Documents

© 2008 Prentice Hall, Inc.F – 1 Operations Management Module F – Simulation PowerPoint presentation to accompany Heizer/Render Principles of Operations