Single supplier scheduling for multiple deliveries

The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied. The orders fulfilled by the supplier are delivered to the manufacturers in batches of the same size. The supplier's production line has to be set up whenever it switches from processing an order of one manufacturer to an order of another manufacturer. The objective is to minimize the total setup cost, subject to maintaining continuous production for all manufacturers. The problem is proved to be NP-hard. It is reduced to a single machine scheduling problem with deadlines and jobs belonging to F part types. An O(N log F) algorithm, where N is the number of delivery batches, is presented to find a feasible schedule. A dynamic programming algorithm with O(N-F/FF-2) running time is presented to find an optimal schedule. If F = 2 and setup costs are unit, an O(N) time algorithm is derived.