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 A¡ 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.Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
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