Coordination of pricing and multi-item capacitated lot sizing problems

The effects of pricing on production decisions were studied. The dynamic prices as the decision variables were introduced into multi-item capacitated lot sizing problem with backlogging. The problem was formulated as a mixed-integer program. Lagrangean relaxation was used to decompose the capacitated problem into a set of simple uncapacitated sub-problems. A heuristic method based on Lagrangean smoothing multipliers was proposed to solve the original problem. Although multi-item capacitated lot sizing problem (MCLSP) is an NP-hard problem, the model appears to be easier to solve than MCLSP from a numerical point of view. The model also improves the firm's profit in comparison with the decentralized policy.