1 Department of Economics and Business Economics, Aarhus BSS, Aarhus University2 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
Stochastic lot-sizing problems have been addressed quite extensively, but relatively few studies also consider marketing factors, such as pricing. In this paper, we address a joint stochastic lot-sizing and pricing problem with capacity constraints and backlogging for a ﬁrm that produces a single item over a ﬁnite multi-period planning horizon. Thece-dependent demands. The stochastic demand is captured by the scenario analysis approach, and this leads to a multiple-stage stochastic programming problem. Given the complexity of the stochastic programming problem, it is hard to determine optimal prices and lot sizes simultaneously. Therefore, we decompose the joint lot-sizing and pricing problem with stochastic demands and capacity constraints into a multi-phase decision process. In each phase, we solve the associated sub-problem to optimality. The decomposed decision process corresponds to a practically viable approach to decision-making. In addition to incorporating market uncertainty and pricing decisions in the traditional production and inventory planning process, our approach also accommodates the complexity of time-varying cost and capacity constraints. Finally, our numerical results show that the multi-phase heuristic algorithm solves the example problems effectively.
International Journal of Production Research, 2014, p. 1-18
Capacitated lot sizing; Pricing; Dynamic programming; Decomposition