Dispatching regular and express shipments between a supplier and manufacturer

A dispatching schedule is to be developed for a supplier providing parts to a manufacturer, given the cumulative production at the supplier and the cumulative demand at the manufacturer. This paper develops dispatching strategies that combine regular (e.g. truck of ship) and express (e.g. air) shipments, and compares these strategies as a function of the total inventory in the system (i.e. cumulative production minus cumulative demand). In most cases, one of five basic strategies should provide a cost that is close to optimal. Company A is the exclusive supplier of a part used by Company B. To satisfy all demand, the cumulative production at Company A, P(t), must always equal or exceed the cumulative demand at Company B, D(t). Parts are shipped by either of two modes: a regular mode, at a cost of A per shipment with a travel time of [tau]; or an express mode, at a cost of B + bQe (where Qe equals the shipment size) with a travel time of 0. Given P(t), D(t), A, [tau], B, and b, determine a shipment dispatch schedule that minimizes total transportation cost.