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# Transportation, Assignment, and Transhipment Problem

Sounds Electronics, Inc produces a battery-operated tape recorder at plants located in Martinsville, NC, Plymouth, Ny and Franklin, Missouri. The unit transportation cost for shipments from the three plants to distribution centers in Chicago, Dallas, and New York are as follows

To
From Chicago Dallas New York
Martinsville 1.45 1.60 1.40
Plymouth 1.10 2.25 0.60
Franklin 1.20 1.20 1.80

After considering transportation costs, management has decided that under no circumstances will it use Plymouth-Dallas route. The plant capacities and distributor orders for the next month are as follows:

Plant Capacity
(units)

Martinsville 400
Plymouth 600
Franklin 300

Distributor Order (units)
Chicago 400
Dallas 400
New York 400

Because of different wage scales at the three plants, the unit production cost varies from plant to plant. Assuming the costs are \$29.50 per unit at Martinsville, \$31.20 per unit at Plymouth, and \$30.35 per unit at Franklin, find the production and distribution plan that minimizes production and transportation costs.

#### Solution Preview

Hello

This problem is tackled with as a linear program. Let us look at decision variables first
Let us denote the three plants as 1, 2, and 3
Martinsville - 1
Plymouth - 2
Franklin - 3
Similarly we denote three destinations
Chicago -1
Dallas - 2
New York - 3
Now decision variables are
x11 - quantity of tape recorders shipped from plant 1 i.e. Martinsville to destination 1 i.e. Chicago. Similarly we define x12, x13, x21, x22, x23, x31, x32, x33 where first subscript denotes plant and second subscript denotes destination
Objective is to minimize transportation and production cost
Minimize: 1.45x11+1.60x12+1.40x13+1.10x21+2.25x22+0.60x23+1.20x31+1.20x32+1.80x33
+29.50(x11+x12+x13)+31.20(x21+x22+x23)+30.35(x31+x32+x33)
In the above function terms 1 to 9 are ...

#### Solution Summary

The transportation problem is solved by using LINDO.

\$2.19