A vendor-purchaser economic lot size problem with remanufacturing and deposit

An economic lot size problem is studied in which a single vendor supplies a single purchaser with a homogeneous product and takes a certain fraction of the used items back for remanufacturing, in exchange for a deposit transferred to the purchaser. For the given demand, productivity, fixed ordering and setup costs, amount of the deposit, unit disposal, production and remanufacturing costs, and unit holding costs at the vendor and the purchaser, the cost-minimal order/lot sizes and remanufacturing rates are determined for the purchaser, the vendor, the whole system assuming partners' cooperation, and for a bargaining scheme in which the vendor offers an amount of the deposit and a remanufacturing rate, and the purchaser responds by setting an order size.