In this paper, considering the amount invested in preservation technology and the replenishment schedule as decision variables, we formulate an inventory model with a time-varying rate of deterioration and partial backlogging. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, under given replenishment schedule, we show that the total profit per unit time is a concave function of preservation technology cost. We then provide a simple algorithm to figure out the optimal preservation technology cost and replenishment schedule for the proposed model. We use numerical examples to illustrate the model.
European Journal of Operational Research 218(1), pp.106–112