Simulation Part 2

1
Chapter 13

• Simulation Part 2

2
Brew-Thru Example
Service entrance
Service lane
Exit
Car 2
Car 3
Car 1
Waiting area
Note Customers balk if more than 4 cars in line
3
Monte Carlo Simulation

• Set up probability distributions for the
  exogenous variables
• Build cumulative probability distributions
• Establish an interval of random numbers for each
  exogenous variable
• Generate a set of random numbers
• Simulate the situation for many trials

4
Brew-Thru Example
Number of customers arriving every 3 min.
Probability
0 1 2 3 4
0.19 0.39 0.19 0.15 0.08 1.00
5
Brew-Thru Example
Average time to fill order
Average profit
Order size
Probability
Small Medium Large
0.39 0.50 0.11 1.00
3 min. 6 min. 9 min.
.75 1.50 3.00
6
Monte Carlo Simulation

• Set up probability distributions for the
  exogenous variables
• Build cumulative probability distributions
• Establish an interval of random numbers for each
  exogenous variable
• Generate a set of random numbers
• Simulate the situation for many trials

7
Brew-Thru Example
of customers arriving every 3 min.
Cumulative Prob.
Prob.
Interval
0.19 0.39 0.19 0.15 0.08 1.00
0.19 0.58 0.77 0.92 1.00
0ltRNlt0.19 0.19ltRNlt0.58 0.58ltRNlt0.77 0.77ltRNlt0.
92 0.92ltRNlt1.00
0 1 2 3 4
8
Brew-Thru Example
Order size
Cumulative probability
Interval
Prob.
Small Medium Large
0.39 0.50 0.11 1.00
0.39 0.89 1.00
0ltRNlt0.39 0.39ltRNlt0.89 0.89ltRNlt1.00
9
Monte Carlo Simulation

• Set up probability distributions for the
  exogenous variables
• Build cumulative probability distributions
• Establish an interval of random numbers for each
  exogenous variable
• Generate a set of random numbers
• Simulate the situation for many trials

10
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
1 2 3 4 5 6 7
11
Brew-Thru Example
Service completed?
Profit
Period
1 2 3 4 5 6 7 8
12
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
1 2 3 4 5 6 7
13
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
1 2 3 4 5 6 7
14
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
1 2 3 4 5 6 7
15
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
1 2 3 4 5 6 7
16
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
1 2 3 4 5 6 7
17
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1 2 3 4 5 6 7
18
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
19
Brew-Thru Example
Service completed?
Profit
Period
No
1 2 3 4 5 6 7
20
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
21
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
.32
22
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
1
.32
23
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
no
1
.32
24
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
--
--
--
no
1
.32
25
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
--
0
--
--
no
1
.32
26
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
27
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
28
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
.15
29
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
0
.15
30
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
yes
0
.15
31
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
.73
yes
0
.15
32
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
.73
1
yes
Small
0
.15
33
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
.73
1
0
yes
Small
0
.15
34
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
35
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
36
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
.95
37
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
.95
4
38
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
yes
.95
4
39
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
.50
yes
.95
4
40
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
.50
Med
yes
.95
4
41
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
0
2
.50
Med
yes
.95
4
42
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
43
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
No
44
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
---
No
45
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
.68
46
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
2
.68
47
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
no
2
.68
48
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
--
--
--
no
2
.68
49
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
--
2
--
--
no
2
.68
50
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
51
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
---
No
Yes(3)
52
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
---
No
1.50
Yes(3)
53
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
.23
54
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
.23
1
55
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
yes
.23
1
56
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
.89
yes
.23
1
57
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
.89
Large
yes
.23
1
58
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
3
.89
Large
yes
.23
1
59
Brew-Thru Example
of Lost Cust.
of New Cust.
Service avail?
Order Size
Service Periods
Number waiting
Period
RN
RN
.63
2
yes
.41
Med
2
0
1
1 2 3 4 5 6 7
2
--
0
--
--
no
1
.32
1
.73
1
0
yes
Small
0
.15
4
0
2
.50
Med
yes
.95
4
4
--
2
--
--
no
2
.68
4
0
3
.89
Large
yes
.23
1
60
Brew-Thru Example
Service completed?
Profit
Period
No
---
1 2 3 4 5 6 7
Yes(1)
1.50
Yes(2)
.75
---
No
1.50
Yes(3)
---
No
61
Brew-Thru Example
Total revenue
8.25
Average revenue per period 8.25/6 1.38
Average profit per customer 8.25/6 1.38
Opportunity cost due to balking
0 (1.25) 0
Total profit 8.25 0 8.25