Optimal pricing and lot-sizing under conditions of perishability and partial backordering

We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good. We assume that when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered. When the good is highly perishable, the reseller may need to backlog demand in order to market the good at a reasonable price. We present a simple solution procedure for solving the optimization problem. The procedure entails solving first a single nonlinear equation and then, if required, two nonlinear equations.