The manager of a regional warehouse must decide on the number of loading docks t
ID: 343684 • Letter: T
Question
The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver-truck costs. The manager has learned that each driver-truck combination represents a cost of $202 per day and that each dock plus loading crew represents a cost of $1,163 per day. Use Table 1 and Table 2.
b. An employee has proposed adding new equipment that would speed up the loading rate to 5.71 trucks per day. The equipment would cost an additional $100 per day for each dock. Should the manager invest in the new equipment?
Yes, because the daily total cost with the new equipment is $______________ which is lower than without the new equipment.
Explanation / Answer
Qa.
Arrival rate (trucks/day)
= 4 trucks per day
Service rate (trucks/day)
µ = 5 trucks per day
Individual dock Utilization
= /µ
= /µ = 4/5 = 0.80
= 0.80
From table, for /µ = 0.80, three dock options are available – 1, 2, and 3 docks
Number of docks
M
Dock cost
Lq (from table)
Ls = Lq + /µ
Driver-truck waiting cost
Cw = Ls x $202
Total cost
= Dock cost + Waiting cost
1
1163
3.2
3.2+0.8
= 4
4*202
= $808
1163+808
= $1971
2
1163*2
= 2326
0.152
0.952
$192.304
$2518.304
3
1163*3
= 3489
0.019
0.819
$165.438
$3654.438
Lowest system cost is $1971 per day for single dock.
Thus, to minimize the cost single dock is required.
Qb.
Arrival rate (trucks/day)
= 4 trucks per day
Service rate (trucks/day)
µ = 5.71 trucks per day
Individual dock Utilization
= /µ
= /µ = 4/5.71 = 0.70
= 0.70
From table, for /µ = 0.70, three dock options are available – 1, 2, and 3 docks
Number of docks
M
Dock cost
Lq (from table)
Ls = Lq + /µ
Driver-truck waiting cost
Cw = Ls x $202
Total cost
= Dock cost + Waiting cost
1
1163+100
= $1263
1.633
2.333525
471.3721296
1734.372
2
2*(1163+100)= 2726
0.098
0.798525
161.3021296
2887.302
3
4089
0.011
0.711525
143.7281296
4232.728
Lowest system cost is $1734.372 per day for single dock, which is less than above option.
Total cost with new equipment = $1734.37
Thus, to minimize the cost new equipment should be used.
Arrival rate (trucks/day)
= 4 trucks per day
Service rate (trucks/day)
µ = 5 trucks per day
Individual dock Utilization
= /µ
= /µ = 4/5 = 0.80
= 0.80
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