# Transportation Problem

## transportation problem

[‚tranz·pər′tā·shən ‚präb·ləm]
(industrial engineering)
A programming problem that is concerned with the optimal pattern of the distribution of goods from several points of origin to several different destinations, with the specified requirements at each destination.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Transportation Problem

a problem concerned with the optimal pattern of the distribution of units of a product from several points of origin to several destinations.

Suppose there are m points of origin A1, . . .,Ai, . . ., Am and n destinations B1, . . .,Bj, . . .,Bn. The point Ai(i = 1, . . .,m) can supply ai units, and the destination Bj(j = 1, . . ., n) requires bj units. It is assumed that

The cost of shipping a unit of the product from to B, is c¡¡. The problem consists in determining the optimal distribution pattern, that is, the pattern for which shipping costs are at a minimum.

Moreover, the requirements of the destinations Bj, j = 1, . . ., n, must be satisfied by the supply of units available at the points of origin Aj, i = 1, . . .,m.

If xij is the number of units shipped from Ai to Bj, then the problem consists in determining the values of the variables xij, i = 1, . . ., m and j = 1, . . ., n, that minimize the total shipping costs

under the conditions

(3) xij ≥ 0 i = 1,..., m and j = 1,..., n

Transportation problems are solved by means of special linear programming techniques.

### REFERENCE

Gol’shtein, E. G., and D. B. Iudin. Zadachi lineinogo programmirovaniia transportnogo tipa. Moscow, 1969.
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