(45 points) A firm operates a docking facility for container ships in Singapore.
ID: 3367334 • Letter: #
Question
(45 points) A firm operates a docking facility for container ships in Singapore. At present, the facility consists of 2 identical docks and ships arrive during the night to be unloaded. The number of ships that arrive during a single night varies from night to night, as given in the Custom distribution below. Each dock can unload one ship during the following day; if more ships arrive than there are docks available, the ships must wait offshore until the next day (or more) when a dock is free for unloading. The cost of delaying a ship (called a demurrage charge) is $10,000 per day/per ship.
Build a simulation model for this problem to track the monthly demurrage charges incurred. Build the model to handle 30 days (hints: you need to specifically track each day; you will need to create a cell for the number of docks and reference this cell in your formulas, ensuring that you are able to perform the analysis in Part b; you will need to use some logic/comparison functions in your model – use the Excel Insert Function for help if you cannot create these functions on your own).
Assume that we are starting Day 1 of the new month with a backlog of 1 ship remaining from the last day of the previous month, plus any new ships (if any) that arrive during the night will be waiting to be unloaded on the morning of Day 1 are those.
Show the probability that the Total Demurrage Charge is less than the mean value found in your simulation, and include the statistics as well. Copy and paste your chart to your spreadsheet.
The firm is considering adding up to two additional docks. Define a Decision in Crystal Ball for the cell containing the number of docks with a range of 2 to 4 (Discrete, steps of 1.00). Create a Decision Table for the Total Demurrage Cost Forecast with 3 Test Values (and 1,000 trials for each). Copy and paste the table over to your Problem 2 worksheet in your HW2 workbook (do not keep/create a second workbook to submit).
Assume that each new dock would cost $150,000 per month to operate (including amortized construction costs). Based on the results of your Report in Part b, what would you recommend and why? (It might be helpful to make a calculation using the results to help you answer this question.)
Nightly Arrivals
.05
Nightly Arrivals
Frequency 0 .30 1 .30 2 .20 3 .10 4 .05 5.05
Explanation / Answer
Solution
Random Number Allocation
Nightly
Arrivals
Frequency
Cumulative
Frequency
Random #
Allottment
0
0.30
0.30
01 – 30
1
0.30
0.60
31 – 60
2
0.20
0.80
61 – 80
3
0.10
0.90
81 – 90
4
0.05
0.95
91 – 95
5
0.05
1.00
95 – 99, 00
Random Numbers Used
Lines 10580–10594, columns 21–40, from
RAND Corporation - RAND's A Million Random Digits
73735 45963 78134 63873 02965 58303 90708 20025 98859 23851
27965 62394 33665 63570 64775 78428 81665 26440 20422 05720
Simulation
[Q1: Number of ships in the queue at the day start; Q2: Number of ships in the queue at the day end; RN: Random Number; A: # of arriving ships; S: # of serviced ships; D: Demurrage
Charges for the day ($104) = Q2
Calculations:
Q2i = Q1i + Ai – Q1i-1 ; Di = Q2i (in $104); subscript i refers to Day #
Day # (i)
Q1
RN
A
S
Q2
D
1
1
73
2
2
1
1
2
73
2
2
1
1
3
54
1
2
0
0
4
59
1
1
0
0
5
63
2
2
0
0
6
78
2
2
0
0
7
13
0
0
0
0
8
46
1
1
0
0
9
38
1
1
0
0
10
73
2
2
0
0
11
02
0
0
0
0
12
96
5
2
3
3
13
55
1
2
2
2
14
83
3
2
3
3
15
03
0
2
1
1
16
90
3
2
2
2
17
70
2
2
2
2
18
82
3
2
3
3
19
00
5
2
6
6
20
25
0
2
4
4
21
98
5
2
7
7
22
85
3
2
8
8
23
92
4
2
10
10
24
38
1
2
9
9
25
51
1
2
8
8
26
27
0
2
6
6
27
96
5
2
9
9
28
56
1
2
8
8
29
23
0
2
6
6
30
94
4
2
8
8
Total
107
So, total demurrage cost for a month = $107 x 104 ANSWER
If one more dock is added, i.e., there are 3 docks available
The monthly demurrage cost comes down by ($84 x 104). Since added cost is only
($15 x 104), it is worthwhile adding one more dock. ANSWER 2
If one more dock is further added, i.e., there are 4 docks available
The monthly demurrage cost comes down by ($19 x 104). Since added cost is only
($15 x 104), it is worthwhile adding one more dock. ANSWER 3
Details of working are given below: [refer to last two columns of the table]
Day # (i)
Q1
RN
A
S
Q2
D
D3
D4
1
1
73
2
2
1
1
0
0
2
73
2
2
1
1
0
0
3
54
1
2
0
0
0
0
4
59
1
1
0
0
0
0
5
63
2
2
0
0
0
0
6
78
2
2
0
0
0
0
7
13
0
0
0
0
0
0
8
46
1
1
0
0
0
0
9
38
1
1
0
0
0
0
10
73
2
2
0
0
0
0
11
02
0
0
0
0
0
0
12
96
5
2
3
3
2
1
13
55
1
2
2
2
0
0
14
83
3
2
3
3
2
0
15
03
0
2
1
1
0
0
16
90
3
2
2
2
0
0
17
70
2
2
2
2
0
0
18
82
3
2
3
3
0
0
19
00
5
2
6
6
2
1
20
25
0
2
4
4
0
0
21
98
5
2
7
7
2
1
22
85
3
2
8
8
2
0
23
92
4
2
10
10
3
0
24
38
1
2
9
9
1
0
25
51
1
2
8
8
0
0
26
27
0
2
6
6
2
0
27
96
5
2
9
9
4
1
28
56
1
2
8
8
2
0
29
23
0
2
6
6
0
0
30
94
4
2
8
8
1
0
Total
107
DONE
Nightly
Arrivals
Frequency
Cumulative
Frequency
Random #
Allottment
0
0.30
0.30
01 – 30
1
0.30
0.60
31 – 60
2
0.20
0.80
61 – 80
3
0.10
0.90
81 – 90
4
0.05
0.95
91 – 95
5
0.05
1.00
95 – 99, 00
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