Optimizing a production-inventory system under a cost target

Abstract

Achieving cost targets is a major concern for business managers. In this paper, we consider two risk management criteria for a production-inventory system under a cost target: Probability of Loss and Expected Loss. We study two models with stochastic demand and production: The unit stockout cost model and the backlogging cost rate model. We analyze a limited-information setting that is an excellent approximation to a full-information setting. We discover that the optimal inventory decisions for minimizing probability of loss are identical for both models, and that the optimal inventory decisions for minimizing expected loss share a similar structure for both models. In addition, we investigate inventory decisions when minimizing the expected cost subject to a probability of loss constraint. Extension to a generally-distributed unit production time is also explored. We provide comparative statics and managerial insights of value to loss-aware managers.