Anticipated rationing policy for inventory systems with two demand classes and backlogging costs

Abstract

This paper studies a periodic-review, infinite-horizon, backlogging inventory model with two demand classes and a constant lead time, where inventory replenishment follows a base-stock policy. We consider an anticipated rationing policy which reserves inventory for future high-priority demands with higher backlogging costs by taking the coming delivery of the next period into consideration. Due to the lack of nice properties such as convexity, both the optimal base-stock level and the optimal critical level when minimising inventory costs have to be found by an exhaustive search. Instead, we study a single-period problem truncated from the original infinite-horizon problem and derive its optimal reservation level with a closed-form expression. Surprisingly, the solution form of the single-period problem coincides exactly with the anticipated rationing policy and hence this solution serves as a good approximation for the optimal critical level of the infinite-horizon problem. An empirical study further demonstrates that our closed-form approximation is quite attractive in both solution accuracy and computation efficiency based on spare parts inventory data from a petrochemical plant in China.

Keywords:

• inventory
• backlogging
• two demand classes
• dynamic rationing
• closed-form expressions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant numbers 71771185, 71271167, 71832011]; Zhejiang Province Natural Science Foundation (grant number: LQ15G010008) and Zhejiang Province Philosophy and Social Science Program (grant number: 19NDJC052YB); and Hong Kong RGC General Research Fund [grant number CUHK-419010].