Dynamic inventory rationing with mixed backorders and lost sales

Customers may react differently when stockouts occur. In this paper we investigate the rationing policy for an inventory system with a mixture of demand classes of backorder type and lost sales type. Since the penalty cost of backorders varies with time, the priorities of demand classes also alter with time. This totally changes the problem structure compared with the classic rationing models. A dynamic rationing policy is studied in this paper by considering the dynamics of demand priorities. A Markov decision model is developed to obtain the optimal dynamic rationing levels for multiple demand classes. The results indicate that between the priority switching points, rationing levels often exhibit different patterns. For lost sales demand classes, the rationing levels always decrease as the remaining time approaches to zero. For backorder demand classes, the rationing levels increase in some parts due to declining of the priorities. The rationing levels of all demand classes finally decline to zero to reduce the inventory holding cost. The application of dynamic rationing is further extended from a single period model to a multi-period (S,T) model where unit cost has to be included. The optimal ordering policy is proved to be a myopic base stock policy and the dynamic rationing policy in the single period model can still be applied with modified time-independent penalty costs for lost sales classes. To overcome the computational complexity, a heuristic dynamic rationing policy is introduced. Due to its good outcome, implementing such a heuristic dynamic rationing policy can be a practical solution for inventory system with mixed backorders and lost sales, in order to enhance the system performance.