On the performance of sparse process structures in partial postponement production systems

Abstract

Production postponement, the strategy to hold reserved production capacity that can be deployed based on actual demand signals, is often used to mitigate supply-demand mismatch risk. The effectiveness of this strategy depends crucially on the ease, or flexibility, in deploying the reserved capacity to meet product demands. Existing literature assumes that the reserved capacity is fully flexible, i.e., capable of being deployed to meet the demand of any item in a multiproduct system. Little is known if reserved capacity is held at many different locations, with each location having only a limited range of flexibility on production options. This paper examines how effective the production postponement strategy is in this environment.

When the amount of reserved capacity is small (i.e., postponement level near 0%), no amount of flexibility can reap significant benefits. When the reserved capacity is high (i.e., postponement level near 100%), it is well known that a sparse structure such as a 2-chain can perform nearly as well as a fully flexible structure. Hence, process flexibility beyond 2-chain has little impact on the effectiveness of production postponement strategy in these two extreme environments. Interestingly, in a symmetric system, we prove that the performance of 2-chain, vis-à-vis the full flexibility structure, has a wider gap when postponement level (i.e., amount of reserved capacity) is moderate, and thus process flexibility beyond 2-chain matters and affects appreciably the performance of the production postponement strategy. Fortunately, adding a little more flexibility, say turning a 2-chain into a 3-chain, the system can perform almost as well as a full flexibility structure for all postponement levels. This is important as first stage production capacity can be allocated as if the reserve capacity is fully flexible. Our analysis hinges on an exact analytical expression for the performance of d-chain, obtained from solving a related class of random walk problems. To the best of our knowledge, this is the first paper with analytical results on the performance of d-chain for d > 2.