Set_7_TP_a - Dr. Maddah ENMG 500 Engineering Management I...

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1 Dr. Maddah ENMG 500 Engineering Management I 12/20/05 The Transportation Problem (1) Definition ¾ The transportation problem (TP) is concerned with shipping a commodity between a set of sources (e.g. manufacturers) and a set of destinations (e.g. retailers). ¾ Each source has a capacity dictating the amount it supplies. ¾ Each destination has a demand dictating the amount it receives. ¾ For now , we assume that the system is balanced . ¾ That is, the total amount demanded at all destinations is equal to the total supply available at all sources. ¾ The objective is to determine the amounts to be shipped between each source and destination in a way as to minimize shipping cost while meeting demand and supply constraints. ¾ The shipping cost is proportional to the amount shipped. 1 i m 1 j n . . . . . . . . x 1 j x ij x mj x i1 x i n s 1 s i s m d 1 d j d n TP Network Representation
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2 Overview ¾ The TP has many practical applications. (The one I like the most is about snow moving in Montreal.) ¾ The transportation problem can be modeled and solved as a linear program. ¾ However, this problem has a special structure , which allows for specialist solution techniques that are more efficient than the usual simplex algorithm. ¾ In particular, we will see that starting basic feasible solutions of high quality can be obtained with ease. ¾ We will then customize the simplex method to produce an efficient transportation simplex method .
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This note was uploaded on 12/23/2010 for the course ENMG 500 taught by Professor Drbacelmaddah during the Fall '09 term at American University of Beirut.

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Set_7_TP_a - Dr. Maddah ENMG 500 Engineering Management I...

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