QMF QMF SimulatioSimulationn

OutlineOutline

What is SimulationWhat is Simulation Advantages and Advantages and

Disadvantages of SimulationDisadvantages of Simulation Monte Carlo SimulationMonte Carlo Simulation Simkin drillsSimkin drills

Simulate by handSimulate by handSimulate by ExcelSimulate by Excel

What is simulation?What is simulation?

Numerical technique of Numerical technique of experimentationexperimentation

Attempts to duplicate a systemAttempts to duplicate a system FeaturesFeatures BehaviorBehavior

Requires description of systemRequires description of system Many application areasMany application areas

Operations managementOperations management Finance & economicsFinance & economics EcosystemsEcosystems

SimulationSimulation

SimulationSimulation

The idea behind simulation is to:The idea behind simulation is to: Imitate a real-world situation Imitate a real-world situation

mathematicallymathematically Study its properties and Study its properties and

operating characteristicsoperating characteristics Draw conclusions and make Draw conclusions and make

action recommendations based action recommendations based on the results of the simulation on the results of the simulation studystudy

Advantages of Advantages of SimulationSimulation

is very flexible, relatively straightforwardis very flexible, relatively straightforward can be used to analyze large and complex can be used to analyze large and complex

real-world problems for which closed-form real-world problems for which closed-form analytical solutions are not possibleanalytical solutions are not possible

allows for the inclusion of real-world allows for the inclusion of real-world complications which most other techniques complications which most other techniques do not permitdo not permit

makes possible “time compression”makes possible “time compression” allows one to ask “what if” type questionsallows one to ask “what if” type questions does not interfere with the real-world systemdoes not interfere with the real-world system allows us to study the interactive effect of allows us to study the interactive effect of

individual components or variablesindividual components or variables

Can be expensive and time Can be expensive and time

consumingconsuming

Does not yield optimal solutionDoes not yield optimal solution

Requires good managerial inputRequires good managerial input

Results not generalizable to Results not generalizable to

other situationsother situations

© 1984-1994 T/Maker Co.

Disadvantages of Disadvantages of SimulationSimulation

Monte Carlo Simulation Monte Carlo Simulation TechniqueTechnique

Step A:Step A: Setup for Monte Carlo SimulationSetup for Monte Carlo Simulation

Step B: Generate values for random variablesStep B: Generate values for random variables

Step C: Perform calculationsStep C: Perform calculations

EZ Mart – Simulate EZ Mart – Simulate demanddemand

Weekly demand at a Weekly demand at a local E-Z Mart local E-Z Mart convenience store for convenience store for 1-gallon jugs of low-1-gallon jugs of low-fat milk for the last fat milk for the last 50 weeks has varied 50 weeks has varied between 60 and 65 between 60 and 65 jugs, as shown in the jugs, as shown in the following table. following table. Demand in excess of Demand in excess of stock cannot be stock cannot be backordered.backordered.

DemanDemand d

(gallon(gallons)s)

Number Number of of

weeksweeks

6060 55

6161 77

6262 1717

6363 1111

6464 66

6565 44

TotalTotal 5050

Setup for the Monte Setup for the Monte CarloCarlo

Simulation Technique Simulation Technique

Step 1:Step 1: Setup probability distribution for important Setup probability distribution for important

variablesvariables

Step 2: Build cumulative distribution for each variableStep 2: Build cumulative distribution for each variable

Step 3: Establish interval of random numbers for each Step 3: Establish interval of random numbers for each

variablevariable

EZ-MartEZ-Mart

Simulate demand for 10 weeksSimulate demand for 10 weeks

Step 1: Setup probability Step 1: Setup probability distribution for distribution for

important variables important variables

Demand (gallons)

Number of weeks

60 561 762 1763 1164 665 4

50

Demand (gallons)

Number of weeks

60 561 762 1763 1164 665 4

50

P(demand is 60)

= 5/50 = 0.10

Step 1: Setup probability distribution for important variables

Demand (jugs)

Number of weeks

60 561 762 1763 1164 665 4

50

P(demand is 61)

= 7/50 = 0.14

Step 1: Setup probability Step 1: Setup probability distribution for distribution for

important variables important variables

Demand (gallons)

Number of weeks

Probability of Occurrence

60 5 0.1061 7 0.1462 17 0.3463 11 0.2264 6 0.1265 4 0.08

50

Step 1: Setup probability Step 1: Setup probability distribution for distribution for

important variables important variables

Step 2: Build Cumulative Step 2: Build Cumulative Probability Distribution for Probability Distribution for

DemandDemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

60 5 0.10 0.1061 7 0.14 0.2462 17 0.34 0.5863 11 0.22 0.8064 6 0.12 0.9265 4 0.08 1.00

50

P(demand <= 61)

= 0.10 + 0.14 = 0.24

Step 2: Build Cumulative Step 2: Build Cumulative Probability Distribution for Probability Distribution for

DemandDemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

60 5 0.10 0.1061 7 0.14 0.2462 17 0.34 0.5863 11 0.22 0.8064 6 0.12 0.9265 4 0.08 1.00

50

P(demand <= 62)

= 0.20 + 0.34 = 0.58

Step 2: Build Cumulative Step 2: Build Cumulative Probability Distribution for Probability Distribution for

DemandDemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

60 5 0.10 0.1061 7 0.14 0.2462 17 0.34 0.5863 11 0.22 0.8064 6 0.12 0.9265 4 0.08 1.00

50

Step 3: Assign random Step 3: Assign random number intervals for number intervals for

demanddemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

Interval of Random Numbers

60 5 0.10 0.10 01-1061 7 0.14 0.2462 17 0.34 0.5863 11 0.22 0.8064 6 0.12 0.9265 4 0.08 1.00

50

Step 3: Assign random Step 3: Assign random number intervals for number intervals for

demanddemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

Interval of Random Numbers

60 5 0.10 0.10 01-1061 7 0.14 0.24 11-2462 17 0.34 0.5863 11 0.22 0.8064 6 0.12 0.9265 4 0.08 1.00

50

Step 3: Assign random Step 3: Assign random number intervals for number intervals for

demanddemand

Demand (gallons)

Number of weeks

Probability of Occurrence

Cumulative Probability

Interval of Random Numbers

60 5 0.10 0.10 01-1061 7 0.14 0.24 11-2462 17 0.34 0.58 25-5863 11 0.22 0.80 59-8064 6 0.12 0.92 81-9265 4 0.08 1.00 93-00

50

EZ Mart Cumulative EZ Mart Cumulative Distribution & Random Distribution & Random

Number AssignmentNumber Assignment

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252

22 3737

33 8282

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252

22 3737

33 8282

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

R.N. – Random number

From Table F.4 p. 854

1st column

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252

22 3737

33 8282

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252 6262

22 3737

33 8282

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252 6262

22 3737 6262

33 8282

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252 6262

22 3737 6262

33 8282 6464

44 6969

55 9898

66 9696

77 3333

88 5050

99 8888

1010 9090

EZ Mart Simulate EZ Mart Simulate DemandDemand

Demand (gallons)

Cumulative Probability

Interval of Random Numbers

60 0.10 01-1061 0.24 11-2462 0.58 25-5863 0.80 59-8064 0.92 81-9265 1.00 93-00

WeekWeek R.N.R.N. DemandDemand

11 5252 6262

22 3737 6262

33 8282 6464

44 6969 6363

55 9898 6565

66 9696 6565

77 3333 6262

88 5050 6262

99 8888 6464

1010 9090 6464

EZ Mart Simulate using EZ Mart Simulate using ExcelExcel

=rand() is an Excel function that =rand() is an Excel function that generate a random number between generate a random number between 0 and 1.00 and 1.0

=Vlookup() is an Excel function that =Vlookup() is an Excel function that looks up a value in a tablelooks up a value in a table Three parameters for vlookupThree parameters for vlookup

Cell with the value that is to be looked upCell with the value that is to be looked up Range of the table with the leftmost column Range of the table with the leftmost column

having the values that are looked uphaving the values that are looked up Column number in the table with the values Column number in the table with the values

that are to be returnedthat are to be returned

Go to Excel

Vlookup functionVlookup function

If you are given a spreadsheet and If you are given a spreadsheet and the Excel function:the Excel function:

=Vlookup(b15, c5:e18,3)=Vlookup(b15, c5:e18,3)

You should be able to determine the You should be able to determine the value that excel will place in the cell value that excel will place in the cell with the vlookup function.with the vlookup function.