Cost Sharing for the Economic Lot-Sizing Problem with Remanufacturing Options

We consider a new class of cooperative cost sharing games, associated with the economic lot-sizing problem with remanufacturing options (ELSR). As a preliminary step, we investigate the relative strength and integrality gaps of various mathematical optimization formulations of ELSR. Using insights from these results, we study the core of the associated cost sharing game. We show that the cost sharing game has an empty core in general. On the other hand, for two special cases—zero setup costs, and large initial quantity of low cost returns—we show that the cost sharing game has a non-empty core, and that a cost allocation in the core can be computed in polynomial time.