Stochastic lot‐sizing model for deteriorating items under partial backlogging

A finite horizon deteriorating inventory model is studied. 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. Any unsatisfied demand is partially backlogged and fulfilled immediately as a new order arrives. This research is distinguished from most literature by considering the effects of deterioration and partial backlogging under stochastic customer demand. The optimal conditions under which a (s, S) policy holds are successfully derived and the explicit order quantities are obtained by reformulating the problem as a stochastic programming model.