Simulation. Introduction What is Simulation? –Try to duplicate features, appearance, and characteristics of real system. Idea behind Simulation –Imitate

Simulation

Introduction

• What is Simulation?

– Try to duplicate features, appearance, and

characteristics of real system.

• Idea behind Simulation

– Imitate real-world situation mathematically.

– Study its properties and operating characteristics.

– Draw conclusions and make action decisions based

on results of simulation.

Process of a Simulation

Advantages And Disadvantages Of Simulation

Advantages• Relatively straightforward and flexible. • Used to analyze large and complex real-world

situations.• Allows “what-if ? ” types of questions. • Does not interfere with real-world system. • Allows study of interactive effects of individual

components or variables to determine which ones are important.

• Time compression.• Allows for inclusion of real-world complications.

Advantages And Disadvantages Of Simulation

Disadvantages

• Good models can be very expensive.

• Often it is a long, complicated process to develop

model.

• Does not generate optimal solutions to problems.

• Managers must generate all of conditions and

constraints for solutions to be examined.

• Each simulation model is unique and not easily

transferable.

Monte Carlo Simulation

• Applicable when system contains elements that

exhibit chance behavior.

• Experimentation based on chance elements through

random sampling.

• Steps of Monte Carlo Simulation -

– Set up probability distribution for each variable in

model subject to chance.

– Use random numbers to simulate values from

probability distribution for each variable in Step 1.

– Repeat process for series of replications or trials.

Auto Tire Shop Example• Monthly demand for radial tires over past 60 months. • Assume past demand rates will hold in future.• Convert data to probability distribution. • Divide each demand frequency by total number of months 60. • Distributions can either be empirical or known such as normal,

binomial, Poisson, or exponential patterns.

Step 2 - Simulate Values From the Probability Distributions

• Simulate demand for a specific month? • Actual demand value is 300, 320, 340, 360, 380, or

400.• There is 5% chance monthly demand is 300,

– 10% chance that it is 320. – 20% chance that it is 340. – 30% chance that it is 360. – 25% chance that it is 380. – 10% chance that it is 400.

Harry’s Auto Tire Shop

Step 2 - Simulate Values From the Probability Distributions

• For long run -

Expected monthly demand= (demand Di) x

(probability of Di)

= (300)(0.05) + (320)(0.10) + (340)(0.20) +

+ (360)(0.30) + (380)(0.25) + (400)(0.10)

= 358 tires

• In short term, occurrence of demand may be quite

different from these probability values.

Auto Tire Shop

Random Numbers• In simulation, use random numbers to achieve

preceding objectives. • Random number is number that has been selected by

totally random process. • Assume generate an integer valued random number

from set 0, 1, 2, …, 97, 98, 99. • One way to do this would be:

1. Take 100 identical balls and mark each one with

unique number between 00 and 99.

2. Put all balls in large bowl and mix thoroughly.

3. Select one ball from bowl and write down number.

4. Replace ball in bowl and mix again. Go to step 2.

Random Numbers

• Instead of balls in bowl, one could have used spin of

roulette wheel that has 100 slots to accomplish this

task.

• Another commonly used means is to choose numbers

from table of random digits such as table of random

numbers.

• Table of random numbers appears on next slide.

Table of Random Numbers

Using Random Numbers to Simulate Demand

Auto Tire Shop

Using Simulation To Compute Expected Profit

• Using this information, simulate and calculate average profit per month from of auto tires.

Harry’s Auto Tire Shop

Simulation ProcessSimulation Process

WeeklyProduction Relative

Requirements (hr) Frequency

200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Average weekly production requirements =




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Average weekly production requirements = 200(0.05)




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Average weekly production requirements = 200(0.05) + 250(0.06)




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Average weekly production requirements = 200(0.05) + 250(0.06) + 300(0.17) + … + 600(0.02) = 400 hours




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Average weekly production requirements = 400 hours




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00

Regular RelativeCapacity (hr) Frequency

320 (8 machines) 0.30360 (9 machines) 0.40

400 (10 machines) 0.30





200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours =




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours = 320(0.30)




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours = 320(0.30) + 360(0.40) +




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours = 320(0.30) + 360(0.40) + 400(0.30)




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours = 320(0.30) + 360(0.40) + 400(0.30) = 360 hours




200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30


Average weekly operating machine hours = 360 hours

Simulation ProcessSimulation ProcessWeekly

Production RelativeRequirements (hr) Frequency

200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02

Total 1.00



400 (10 machines) 0.30




360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30



320 (8 machines) 0.30360 (9 machines) 0.40400 (10 machines) 0.30





Event Weekly

Demand (hr) Probability








Event Weekly

Demand (hr) Probability

200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02








Event Weekly Random Weekly Random

Demand (hr) Probability Numbers Capacity (hr) Probability Numbers

200 0.05250 0.06300 0.17350 0.05400 0.30450 0.15500 0.06550 0.14600 0.02










200 0.05 00–04250 0.06 05–10300 0.17 11–27350 0.05 28–32400 0.30 33–62450 0.15 63–77500 0.06 78–83550 0.14 84–97600 0.02 98–99










200 0.05 00–04 320 0.30250 0.06 05–10 360 0.40300 0.17 11–27 400 0.30350 0.05 28–32400 0.30 33–62450 0.15 63–77500 0.06 78–83550 0.14 84–97600 0.02 98–99










200 0.05 00–04 320 0.30 00–29250 0.06 05–10 360 0.40 30–69300 0.17 11–27 400 0.30 70–99350 0.05 28–32400 0.30 33–62450 0.15 63–77500 0.06 78–83550 0.14 84–97600 0.02 98–99










200 0.05 00-04 320 0.30 00-29250 0.06 05-10 360 0.40 30-69300 0.17 11-27 400 0.30 70-99350 0.05 28-32400 0.30 33-62450 0.15 63-77500 0.06 78-83550 0.14 84-97600 0.02 98-99

Simulation Process

1. Draw a random number.2. Find the random number interval for production.3. Record the production hours.4. Draw another random number.5. Find the random number interval for capacity.6. Record the capacity hours.7. If CAP ≥ PROD, then IDLE HR = CAP - PROD.8. If CAP < PROD, then SHORT = PROD - CAP.

If SHORT ≤ 100, then OVERTIME HR = SHORTand SUBCONTRACT HR = 0.If SHORT > 100, then OVERTIME HR = 100and SUBCONTRACT HR = SHORT - 100.

9. Repeat steps 1-8 to simulate 20 weeks.

10 Machines

ExistingDemand Weekly Capacity Weekly Sub-Random Production Random Capacity Idle Overtime contract

Week Number (hr) Number (hr) Hours Hours Hours










200 0.05 00-04 320 0.30 00-29250 0.06 05-10 360 0.40 30-69300 0.17 11-27 400 0.30 70-99350 0.05 28-32400 0.30 33-62450 0.15 63-77500 0.06 78-83550 0.14 84-97600 0.02 98-99

Simulation Process




10 Machines



1 71 450 50 360 902 68 450 54 360 903 48 400 11 320 804 99 600 36 360 100 1405 64 450 82 400 506 13 300 87 400 1007 36 400 41 360 408 58 400 71 4009 13 300 00 320 20

10 93 550 60 360 100 90

Total 490 830 360 Weekly average 24.5 41.5 18.0










200 0.05 00-04 320 0.30 00-29250 0.06 05-10 360 0.40 30-69300 0.17 11-27 400 0.30 70-99350 0.05 28-32400 0.30 33-62450 0.15 63-77500 0.06 78-83550 0.14 84-97600 0.02 98-99

Simulation Process




10 Machines



1 71 450 50 360 902 68 450 54 360 903 48 400 11 320 804 99 600 36 360 100 1405 64 450 82 400 506 13 300 87 400 1007 36 400 41 360 408 58 400 71 4009 13 300 00 320 20

10 93 550 60 360 100 90


Comparison of 1000-week Simulations

10 Machines 11 Machines










200 0.05 00-04 320 0.30 00-29250 0.06 05-10 360 0.40 30-69300 0.17 11-27 400 0.30 70-99350 0.05 28-32400 0.30 33-62450 0.15 63-77500 0.06 78-83550 0.14 84-97600 0.02 98-99

Simulation Process




10 Machines



1 71 450 50 360 902 68 450 54 360 903 48 400 11 320 804 99 600 36 360 100 1405 64 450 82 400 506 13 300 87 400 1007 36 400 41 360 408 58 400 71 4009 13 300 00 320 20

10 93 550 60 360 100 90


Comparison of 1000-week Simulations

10 Machines 11 Machines

Idle hours 26.0 42.2Overtime hours 48.3 34.2Subcontract hours 18.4 8.7Cost $1,851.50 $1,159.50

Documents

Simulation. Introduction What is Simulation? –Try to duplicate features, appearance, and characteristics of real system. Idea behind Simulation –Imitate