A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

We study the rationing policy in an inventory system with two demand classes and different service criteria for backorders. Due to the difference of customer values, system performance sometimes has to be measured with a mixture of penalty cost and service level in managing inventory. With a continuous review (r,Q) system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the complexity of the problem, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.