A Stochastic Dynamic Multimode Transportation Model

A mathematical model and two solution techniques for selecting preferred combinations of different transportation modes over consecutive periods in the face of uncertainty. Some acquaintance with control theory, dynamic programming, and nonlinear programming is assumed. The model is formulated as a problem of optimal stochastic control theory. It assigns individual commodity classes to various carriers, determines which supply points serve which destinations, and reroutes carriers where they will be most effective. It takes account of differential transit times and costs, availabilities, and costs of storage, oversupply, and shortages. Generally, the carrier for a given commodity class will vary over time and place. The system dynamics consist of inventory balance equations relating end-of-period stocks at each point to inflows and outflows. An alternative method is also presented for cases in which the assumptions required for the dynamic programming algorithm are not valid.