Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs

In this paper, we consider the pricing and lot-sizing problem for a product subject to general rate of deterioration and partial backordering. We use impatience functions to model backlogging of demand. We show that even when lost sale and backorder costs are present, the problem is well posed in the reduced space. We provide an iterative procedure for solving the overall problem. We describe structural properties of the solution for the new model and comment on the recent work incorporating backorder cost. We illustrate the solution procedure for the new model with examples.