Supplement
E Simulation
1. Reasons for Using Simulation Models
Simulation is useful when waiting-line models become too complex. Using simulation for
analyzing processes and supply chains may be based on other reasons.
• When the relationship between variables is nonlinear or when the situation involves too many
variables or constraints to handle with optimizing approaches, simulation models can be used
to estimate operating characteristics or objective function values and analyze a problem
• Simulation models may be used to conduct experiments without disrupting real systems
• They may also be used to obtain operating characteristic estimates in much less time (this is
called time compression)
• Simulation is useful in sharpening managerial decision-making skills through gaming
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
a. Costs
b. Productivities
c. Capacities
d. Probability distributions
e. Demonstrate with Example E.1. Specialty Steel Products
2. Random-number assignment
a. A random number is a number that has the same probability of being selected as any
other number (see Table of Random Numbers in Appendix 2)
3. Model formulation
a. Decision variables
b. Uncontrollable (or random) variables
c. Relationships among variables expressed in mathematical terms.
Demonstrate with Example E.2. Specialty Steel Products continued
d. Use Application E.1: Monte Carlo Simulation to demonstrate the construction and
execution of a simulation model.
• 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
6
0.14
13
0.03
7
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
59-70
2
01–03
9
71-80
3
04–09
10
81-87
4
10–18
11
88-92
5
19–30
12
93-96
6
31–44
13
97-99
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 minutes (i.e., :06) per car.
Random
Number
Time to
Arrival
Arrival
Time
Number in
Drive
Departure
Time
Minutes
in System
50
7
0:07
0
0:13
6
63
8
0:15
0
0:21
6
95
12
0:27
0
0:33
6
49
7
0:34
0
0:40
6
68
8
0:42
0
0:48
6
11
4
0:46
1
0:54
8
40
6
0:52
1
1:00 hr.
8
93
12
1:04
0
1:10
6
61
8
1:12
0
1:18
6
48
7
1:19
0
1:25
6
82
10
1:29
0
1:35
6
09
3
1:32
1
1:41
9
08
3
1:35
1
1:47
12
72
9
1:44
1
1:53
9
98
13
1:57
0
2:03 hrs.
6
41
6
2:03
0
2:09
6
39
6
2:09
0
2:15
6
67
8
2:17
0
2:23
6
11
4
2:21
1
2:29
8
11
4
2:25
1
2:35
10
00
1
2:26
2
2:41
15
07
3
2:29
2
2:47
18
66
8
2:37
2
2:53
16
00
1
2:38
3
2:59
21
29
5
2:43
3
3:05 hrs.
22
4. Analysis (of the above data)
3. Simulation with Excel Spreadsheets
1. Generating random numbers
a. Random numbers can be created from 0 to 1 by entering the formula =RAND() into a cell
of the Excel spreadsheet
2. Random number assignment
a. Demonstrate with Example E.3, BestCar Auto Dealer
3. Simulation with two uncontrollable variables
a. Demonstrate with Figure E.3
4. Simulation with SimQuick Software
Simulation with more advanced software
• SimQuick (use Solved Problem 2 or the Passenger Security process modeled in the
SimQuick book)
o Easy-to-use package that is simply an Excel spreadsheet with some macros.
o Models can be created for a variety of simple processes.
o A first step with SimQuick is to draw a flowchart of the process using SimQuick’s
building blocks.
o Information describing each building block is entered into SimQuick tables.