A Polynomial Time Algorithm for Coordination of Pricing and Lot Sizing Model with Backlogging

In decentralized policy, lot sizing models with backlogging (LSP-B) tend to neglect the effects of market on production. In this paper, pricing is introduced into general LSP-B and by coordinating pricing and LSP-B, the rational price can be set such that the firm's profit is maximized. Demand is a deterministic function of price. It is primarily concerned that the same selling price on a product is maintained throughout horizon. An exact algorithm is developed to solve joint fixed pricing and LSP-B in polynomial time. The algorithm is based on alternate decisions on pricing and production. By restarting the alternate decisions repeatedly, the optimal pricing and corresponding production plan can be solved recursively. Results show that the joint policy may contribute more profit to the firm than the decentralized policy.