Question

SealCo is an automobile manufacturer and at the beginning of April, SealCo wants to come up with a production plan to meet the following demands for a car: April, 30 units; May, 30 units; June, 20 units. When SealCo cannot meet the demand for a specific month, it may be backlogged at a cost of $5/unit/month. All the backlogged demand must be met at most during June (at the end of the 3-months planning horizon), then a backlogging cost of 5(2) = $10 is incurred. SealCo’s monthly production capacity and unit production cost during each month are given in table below. A holding cost of $20/unit is charged due to the inventory at the end of each month. Month Production Capacity (units) Unit Production Cost April 30 $100 May 30 $120 June 30 $110 (a) Construct a transportation tableau for the problem. Is this a balanced TP? Why or why not? Explain. Also show the cost calculations on the transportation tableau. (b) Formulate a balanced transportation problem that could be used to determine how to minimize the total cost (including backlogging, holding, and production costs) of meeting demand. (c) Solve the problem by using IBM ILOG CPLEX Optimization Studio. Write down the optimal solution and make comments. Submit also your OPL output with your homework.

Answer 1

(a) Transportation tableau is as follows

Parameter Table
	April	May	June	Capacity
April	100	120	140	30
May	125	120	140	30
June	120	115	110	30
Demand	30	30	20

This is not a balanced TP, because total demand (30+30+20 = 80) is less than total capacity (30+30+30=90)

(b) Balanced TP is created by adding a dummy demand node having a demand of 10 and cost of 0

Parameter Table
	April	May	June	dummy	Capacity
April	100	120	140	0	30
May	125	120	140	0	30
June	120	115	110	0	30
Demand	30	30	20	10

(c) Solution is as follows

Formula:

E11 =SUM(B11:D11) copy to E11:E13

B14 =SUM(B11:B13) copy to B14:D14

B17 =SUMPRODUCT(B3:D5,B11:D13)

The optimal solution is:

Produce 30 units in April, 20 in May and 30 in June. 10 units of demand of May will be backordered.

Total cost = $ 8750