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

Answer the following questions based on the data table and solution table shown below.

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

Houma Containers 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.

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?

(a) 250; (b) 350; (c) 0, and 50 units are back ordered; (d) 350; (e) $935,000; (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-term options, that it must utilize almost every unit available, which forces the use of the more expensive options.