Design of contract parameters in a closed-loop supply chain

We study an extended joint economic lot size problem which incorporates the return flow of remanufacturable used products. The supply chain under consideration consists of a single supplier and a single buyer. The buyer orders a single product from the supplier, uses it for her own needs, and collects the remanufacturable items after use. The ordered items are shipped from the supplier to the buyer in the lot-for-lot fashion by a vehicle which also returns the collected used items from the buyer to the supplier for remanufacturing and subsequent service of the buyer's demand in the next order cycle. For satisfying the total demand, the supplier manufactures new items or remanufactures used ones received from the buyer. For given demand, productivity, collection rate, disposal cost, setup cost, order cost, holding cost for serviceable and nonserviceable products at the supplier as well as the buyer the lot size (order size) for the supplier (buyer) has to be found which minimizes the total cost. Furthermore, we address a decentralised decision making of the parties under a two-part tariff and determine their equilibrium strategies within the Nash framework.