Houma Containers, Inc., makes industrial fiberglass tanks that are used on offsh
ID: 379470 • Letter: H
Question
Houma Containers, Inc., makes industrial fiberglass tanks that are used on offshore oil platforms. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $400. Overtime cost is 150% of regular time cost. Subcontracting is available in substantial quantity but at a very high cost, $1100 per unit. Holding costs are $200 per tank per month; back orders cost the firm $1000 per unit per month. Houma's management believes that the transportation algorithm can be used to optimize this scheduling problem. The firm has no beginning inventory and anticipates no ending inventory.
March
April
May
June
Demand
300
500
300
350
Regular capacity
200
200
250
250
Overtime capacity
50
50
50
50
Subcontract cap.
150
100
100
150
a. How many units will be produced on regular time in June?
b. How many units will be produced by subcontracting over the four-month period?
c. What will be the inventory at the end of April?
d. What will be total production from all sources in April?
e. What will be the total cost of the optimum solution?
f. Does the firm utilize the expensive options of subcontracting and back ordering? When; why?
March
April
May
June
Demand
300
500
300
350
Regular capacity
200
200
250
250
Overtime capacity
50
50
50
50
Subcontract cap.
150
100
100
150
Explanation / Answer
Houma Containers
March
April
May
June
SUPPLY
March regular time
400
600
800
1,000
200
March overtime
600
800
1,000
1,200
50
March subcontracting
1,100
1,300
1,500
1,700
150
April regular time
1,400
400
600
800
200
April overtime
1,600
600
800
1,000
50
April subcontracting
2,100
1,100
1,300
1,500
100
May regular time
2,400
1,400
400
600
250
May overtime
2,600
1,600
600
800
50
May subcontracting
3,100
2,100
1,100
1,300
100
June regular time
3,400
2,400
1,400
400
250
June overtime
3,600
2,600
1,600
600
50
June subcontracting
4,100
3,100
2,100
1,100
150
DEMAND
300
500
300
350
Solution
Optimal Cost =
$935,00
March
April
May
June
DUMMY
March regular time
100.
100.
March overtime
50.
March subcontracting
150.
April regular time
200.
April overtime
50.
April subcontracting
100.
May regular time
250.
May overtime
50.
May subcontracting
50.
0.
50.
June regular time
250.
June overtime
50.
June subcontracting
50.
100.
Hence, from the above table answers are:
a.250 units will be produced on regular time in June
b. 350 units will be produced by subcontracting over the four-month period
c. 0, and 50 units are back ordered
d. 350 units will be total production from all sources in April
e. $935,000 (the total cost of optimum solution)
f. They use subcontracting every month; there are back orders in April filled with May production. The firm has so little excess capacity, even with the short-termoptions, that it must utilize almost every unit available, which forces the use of the more expensive options.
March
April
May
June
SUPPLY
March regular time
400
600
800
1,000
200
March overtime
600
800
1,000
1,200
50
March subcontracting
1,100
1,300
1,500
1,700
150
April regular time
1,400
400
600
800
200
April overtime
1,600
600
800
1,000
50
April subcontracting
2,100
1,100
1,300
1,500
100
May regular time
2,400
1,400
400
600
250
May overtime
2,600
1,600
600
800
50
May subcontracting
3,100
2,100
1,100
1,300
100
June regular time
3,400
2,400
1,400
400
250
June overtime
3,600
2,600
1,600
600
50
June subcontracting
4,100
3,100
2,100
1,100
150
DEMAND
300
500
300
350
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