Optimal stochastic inventory control with deterioration and partial backlogging/service‐level constraints

A new inventory system with finite planning horizon is studied for deteriorating items. The system is under periodic review and there is a positive fixed order cost associated with any placed order. Customer demand is stochastic and a constant fraction of any positive leftover stock is deteriorated at the end of each period. This study first considers that any unsatisfied demand is partially backlogged and fulfilled immediately as a new order arrives. The optimal conditions under which a (s, S) policy holds are successfully derived. Then the effect of partial backlogging is replaced by incorporating the service‐level constraints so that the explicit order quantities are obtained by reformulating the problem as a mixed‐integer programming model.