Transportation problem (Minimal Cost)
There are three warehouses at different cities: Detroit, Pittsburgh and Buffalo. They
have 250, 130 and 235 tons of paper accordingly. There are four publishers in
Boston, New York, Chicago and Indianapolis. They ordered 75, 230, 240 and 70
tons of paper to publish new books.
We denote the cost of transportation from one city to another by C_ prefix, for example cost from Buffalo to Chicago is C_BF_CH.
We have to find a plan that all orders will be performed and the transportation
costs will be minimized. The decision variables are amounts of tons transported from one city to another denoted by prefix X_:
The objective function is sum of multiplications of transported tons and their costs:
The constraints are defined in terms of the transported paper amount from one warehouse or to one publisher.
The problem has been solved successfully with the following plan:
The Total Cost of Transportation is $7780
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