Supplement
E Simulation
1. Reasons for Using Simulation Models
• What is simulation?
• What are the reasons for using simulation?
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2. The Monte Carlo Simulation Process
This process is known as Monte Carlo simulation, after the European gambling capital, because
of the random numbers used to generate the simulation events.
1. Data collection for Example E.1
Specialty Steel Products
2. Random-number assignment
a. Random number defined
b. Random number assignment: Specialty Steel Products
3. Model formulation
a. Decision variables
b. Uncontrollable (or random) variables
c. Relationships among variables. Example E.2, Specialty Steel Products continued
• To simulate a particular capacity level, we proceed as follows:
• Step 1: Draw a random number from the first two rows of the table. Start with the
first number in the first row, then go to the second number in the first row, and so on.
• Step 2: Find the random-number interval for production requirements associated with
the random number.
• Step 3: Record the production hours (PROD) required for the current week.
• Step 4: Draw another random number from row 3 or 4 of the table. Start with the first
number in row 3, then go to the second number in row 3, and so on.
• Step 5: Find the random-number interval for capacity (CAP) associated with the
random number.
• Step 6: Record the capacity hours available for the current week.
• Step 7: If CAP ≥ PROD, then IDLE HR = CAP – PROD.
• Step 8: If CAP < PROD, then SHORT = PROD – CAP.
If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0.
If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR =
SHORT – 100.
• Step 9: Repeat steps 1–8 until you have simulated 20 weeks.
• Analysis
Results from 20-week simulation
Results from 1,000-week simulation
d. Application E.1: Monte Carlo Simulation
• Car Arrival Distribution (time between arrivals)
Famous Chamois is an automated car wash that advertises that your car can be finished in
just 15 minutes. The time until the next car arrival is described by the following
distribution.
Minutes
Probability
Minutes
Probability
1
0.01
8
0.12
2
0.03
9
0.10
3
0.06
10
0.07
4
0.09
11
0.05
5
0.12
12
0.04
0.14
13
0.03
0.14
1.00
• Random Number Assignment
Assign a range of random numbers to each event so that the demand pattern can be
simulated.
Minutes
Random Numbers
Minutes
Random Numbers
1
00–00
8
2
01–03
9
3
04–09
10
4
10–18
11
5
19–30
12
6
31–44
13
7
45–58
• Simulation of Famous Chamois Operation
Simulate the operation for 3 hours, using the following random numbers, assuming that the
service time is constant at 6, (:06), minutes per car.
Random
Number
Time to
Arrival
Arrival
Time
Number in
Drive
Service
Begins
Departure
Time
Minutes in
System
50
7
0:07
0
0:07
0:13
6
63
8
0:15
0
0:15
0:21
6
95
12
0:27
49
68
11
40
93
61
48
82
09
08
72
98
41
39
67
11
11
00
07
66
00
29
4. Analysis
a. Average time a car is in the system:
b. Percentage of cars that take more than 15 minutes:
/25 x 100 = %
3. Simulation with Excel Spreadsheets
• Steady State
1. Generating random numbers with the formula = RAND()
2. Random number assignment with the VLOOKUP() function
a. Simulation model for Example E.3: BestCar Auto Dealer
3. Simulation with two uncontrollable variables
a. Figure E.3 shows an Excel simulation model with both weekly demand and lead time
being uncontrollable variables. There are two decision variables, the order size and
the reorder point.
b. Dependent variables are average holding costs, average holding cost, and average
stockout cost.
c. When problems get any more complex than this, it is best to turn to more advanced
simulation software such as SimQuick.
4. Simulation with SimQuick Software
• Simulation with SimQuick: Passenger Security process (Solved Problem 2)
o Flowchart
o Entering data
o Simulation results