The stochastic dynamic product cycling problem

This paper studies the stochastic version of the dynamic, discrete period produoct cycling problem, in which several products are to be sequenced one at a time, on a single machine, to meet time-varying stochastic demands. The demand distribution for each product in each period is taken to be known, and there are variable costs incurred for holding inventory between periods, for backorders, and for production. At each changeover, fixed costs are incurred and production time is lost. All these costs can be dynamic. The problem is formulated as a multiperiod, dynamic program. A ‘restricted’ Lagranean method is used to develop three alternative decompositions. One of these is used to investigate bounds and heuristic solutions. Preliminary numerical results on small problems are presented.