Cost optimization in the $$(S-1, S)$$ ( S - 1 , S ) backorder inventory model with two demand classes and rationing

Within the framework of continuous-review $$(S-1, S)$$ ( S - 1 , S ) inventory systems with rationing and backorders, there are two streams of studies in the literature that involve optimization models. In the first stream, service level optimizations are studied for which exact optimization routines are provided. The second stream of studies involves cost optimization models, which relies on optimizing approximate cost models rather than the original cost model. Our main contribution in this study is to fill this research gap by providing a computationally efficient and exact optimization algorithm for determining the optimal policy parameters which minimizes the expected cost rate per unit time. One important aspect of our method is that, as the base-stock level is increased by 1 as the iteration continues, the steady-state probabilities need to be calculated only once in our optimization routine (for which the rationing level equals to zero). For the given base-stock level, the cost measures of all other policy parameters can be computed immediately through the knowledge of the probabilities computed in previous iterations. This result significantly reduces the computational complexity of the optimization routine. In the numerical study section, we show the efficiency of the proposed optimization routine under varying system parameters. We also compare the performance of our approach with the existing heuristic in the literature and show that savings up to $$34.75 \%$$ 34.75 % can be achieved.