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334 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

producing on regular time or overtime. Because of other commitments and anticipated
cost increases in month 3, the production capacities in units and the production costs per
unit are as follows:

Production Capacity (units) Cost per Unit
Month 1 – Regular 275 E50
Month 1 – Overtime 100 80
Month 2 – Regular 200 50
Month 2 – Overtime 50 80
Month 3 – Regular 100 60
Month 3 – Overtime 50 100

Inventory may be carried from one month to the next, but the cost is E20 per unit per
month. For example, regular production from month 1 used to meet demand in month 2
would cost Sanders E50 + E20 ¼ E70 per unit. This same month 1 production used to
meet demand in month 3 would cost Sanders E50 + 2(E20) ¼ E90 per unit.
a. Develop a network representation of this production scheduling problem as a
transportation problem. (Hint: Use six origin nodes; the supply for origin node 1 is the
maximum that can be produced in month 1 on regular time, and so on.)
b. Develop a linear programming model that can be used to schedule regular and
overtime production for each of the three months.
c. What is the production schedule, how many units are carried in inventory each month,
and what is the total cost?
d. Is there any unused production capacity? If so, where?
Note: The remaining problems involve the use of the special purpose algorithms described in
Sections 7.2 and 7.4 for solving transportation and assignment problems.
14 Consider the following transportation tableau with four origins and four destinations.

Destination
Origin Supply
D 1 D 2 D 3 D 4

5 7 10 5

O 1 25 50 75

6 5 8 2

O 2 100 75 175

6 6 12 7
O 3 100 100

8 5 14 4

O 4 100 50 150

Demand 125 100 150 125

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