A decomposable transshipment algorithm for a multiperiod transportation problem

Abstract

AbstractA dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t2 can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t1 < t2 (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks.Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables.Storage requirements are proportional to T2 for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.