Approaches for periodic inventory control under random production yield and fixed setup cost

Abstract

In this paper, we study a multi-period inventory control problem with random demand and stochastically proportional production yield. The model includes nonzero processing lead time as well as fixed setup cost for a replenishment order. From prior research, it is evident that the optimal control rule must have a highly complex structure so that only simple policies are reasonable candidates for practical problem solving. In this paper, we propose a periodic review (s, S) policy with simple order inflation and compare different heuristic approaches for determining the two policy parameters. Two of these approaches are taken from the literature and, partly, adjusted to fit into the periodic-review planning context. A comprehensive numerical study reveals that both methods perform insufficiently, mainly because they do not take into account the yield risk from open orders during lead time. Therefore, three new approaches for parameter determination are developed, which consider this risk but follow very different concepts in their design. Two of these approaches follow simple-to-implement ideas for parameter adjustment to demand and yield risks and can be applied as spreadsheet applications, while the third one is based on an approximation of the objective value as function of the parameters s and S, which then must be computed numerically. From the experimental study, it turns out that all three approaches have a similarly high performance, not only concerning their average but also their worst-case behavior. The numerical study also provides insights into how yield randomness affects the policy parameters and elements of total expected cost.