Optimal stopping and restarting production times for an economic order quantity model with deteriorating items and time-dependent partial backlogging

Yan and Cheng presented a general production–inventory model with production rate, product demand rate and deterioration rate, all considered as functions of the time. Their model allows for shortages and partial backlogging of the unsatisfied demand at a constant rate. In this paper, we extend the results of Yan and Cheng to cover the case where the backlogging rate is a time-dependent function and we propose an algorithm for the solution of this problem. We also propose some conditions which we believe to be necessary for the validity for some of Yan's and Cheng's statements. The paper closes with numerical examples which cover each one of the cases considered in the paper.