THE EFFECT OF SPACE-TIME DEMAND PROCESSES ON THE SOLUTION OF TRANSPORTATION PROBLEMS

Using a formulation of the transportation problem with a stochastic demand represented by a space-time autoregressive moving average (STARMA) model, a simulation study is presented whereby the consequences of ignoring space and/or time dependencies in the demand process are evaluated. It is found that the percentage change in total deliveries, x(PCT), when space-time dependency is ignored varies linearly with space-time autoregressive (STAR) parameters. Furthermore, x(PCT) is larger when we ignore spatial dependency than temporal dependency. When both dependencies are ignored, x(PCT) may be larger than that for both spatial and temporal cases depending upon the signs of STAR parameters. Results for space-time moving average (STMA) are similar to that of STAR. However, for STARMA, when both the temporal and spatial dependencies in demand are ignored, x(PCT) is piecewise linear. The improvement in percentage change in total cost, PCT, is found to vary between 1-55% as the ratio of unit holding cost to unit product cost, H/P, varies from its minimum to its maximum, and 1-95% for the ratio of unit shortage cost to unit product cost, SH/P, when space-time dependencies are taken into account, depending upon the values of various parameters.