The Optimal Pricing and Multi-Item Capacitated Lot Sizing Problem

The multi-item capacitated lot sizing problems (MCLSP) extensively studied paid little attention to the product prices and neglected the effects of market on production. However, pricing and production are coordinated here, and the dynamic product prices are introduced into our model as the decision variables. The product demand is a function of the product price. An item-by-item heuristic algorithm is developed, which transforms the J-item problem into J single-item problems. The algorithm also includes a Lagrangean upper bound problem and a Lagrangean lower bound problem. A special case with linear demand function of price concludes that although MCLSP is an NP-hard problem, our model seems to be easier to solve from a numerical point of view than MCLSP. The algorithm may improve the firm's profit in comparison with the decentralized policy and the coordination policy with constant price over time.