The coordination of planning decisions in the lot-sizing problem

A classical supply chain is composed of independent entities that take their decisions independently from the others and have their own objectives. However, some of them may have the market power within this supply chain. The market power allows them to take decisions such that their objectives are optimized and to impose their decisions on the others. In particular, we are interested in the planning decisions within a two-level supply chain composed of one supplier and one retailer where the supplier has the market power. In this supply chain, the planning decisions imposed by the supplier may lead to a poor performance for the retailer. The planning decisions can be modeled by a lot-sizing problem. This problem aims at satisfying demand over a discrete time horizon such that the total cost (ordering and holding cost) is minimized. In order to coordinate the planning decisions, we consider contracts with a side payment between the supplier and the retailer to minimize the retailer's cost. The main aim of our work is to evaluate the impact of contracts within this supply chain. We investigate the reservation capacity contract in which the supplier reserves an amount of units, called capacity, for the retailer at each period and allows him to order more than this capacity at a higher cost. This contract leads us to study a lot-sizing problem with subcontracting for which we propose a polynomial dynamic programming algorithm. An experimental analysis shows that the proposed contracts improve the retailer's performance within this supply chain.