Joint optimal constant pricing and lot sizing models with backlogging

Lot sizing models with backlogging (LSP-B) tend to neglect the effect of market on production. To overcome the shortcoming, pricing is here introduced into general LSP-B. Demand is a deterministic function of price. It is primarily concerned that the same selling price on a product is maintained throughout horizon. The demand unsatisfied must be backlogged and lost sales are prohibited in each period. An exact algorithm is developed to solve joint constant pricing and LSP-B in polynomial time. The algorithm transforms joint pricing and lot sizing problems into a lot of lot sizing problems previously studied. By making alternate decisions on pricing and production, the lower bound and the upper one of the optimal pricing can be obtained. Then restarting the alternate decisions repeatedly, the optimal pricing and corresponding production plan can be solved. In general, the results show that the joint policy may contribute more profit to the firm than the decentralized policy.