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Transportation Problem


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Transportation Problem

  1. 1. TRANSPORTATION PROBLEM Transportation problem is one of the subclasses of LPP’s in which the objective is to transport various quantities of a single homogeneous commodity, that are initially stored at various origins to different destinations in such a way that the total transportation cost is minimum. To achieve this objective we must know the amount and location of available supplies and the quantities demanded. In addition, we must know the costs that result from transporting one unit of commodity from various origins to various destinations.
  2. 2. Mathematical Formulation of the Transportation Problem <ul><li>A transportation problem can be stated mathematically as a Linear Programming Problem as below: </li></ul><ul><li>Minimize Z = </li></ul><ul><li>subject to the constraints </li></ul><ul><li> = a i , i = 1, 2,…..,m </li></ul><ul><li> = b j , j = 1, 2,…..,m </li></ul><ul><li>x ij ≥ 0 for all i and j </li></ul><ul><li>Where, a i = quantity of commodity available at origin i </li></ul><ul><li>b j = quantity of commodity demanded at destination j </li></ul><ul><li>c ij = cost of transporting one unit of commodity from i th origin to j th </li></ul><ul><li>destination </li></ul><ul><li>x ij = quantity transported from i th origin to j th destination </li></ul><ul><li> </li></ul>
  3. 3. Tabular form of the Transportation Problem x 11 x 12 x 1n x 21 x 22 x 2n x m1 x m2 x mn b n …… . b 2 b 1 Demand a m c mn …… . c m2 c m1 O m . . . . . . …… . . . . . . . . . . a 2 c 2n …… . c 22 c 21 O 2 a 1 c 1n …… . c 12 c 11 O 1 Supply D n …… . D 2 D 1 To From