Forward and backward stocking policies for a two-level supply chain with consignment stock agreement and stock-dependent demand

We consider a vendor-managed inventory with consignment stock agreement applied to the integrated vendor-buyer system, in which the vendor manufactures a single product in batches and delivers it in equal-sized transfer lots to the buyer. Some of the delivered items are presented to the end customers in the buyer's display area, while the rest of the items are kept in the buyer's backroom warehouse. Demand is assumed to be positively dependent on the amount of stock displayed. We propose a new joint economic lot sizing (JELS) model, taking into account the vendor's stocking policy, to maximize the total profit for the coordinated system. This paper first proves that, for any stock-dependent demand, a minimum restocking level at the buyer's sales floor is a more profitable strategy than the traditional run-out replenishment policy. It then shows that when the unit inventory holding cost decreases as stock moves downstream the supply chain, the vendor ought to adopt the forward stocking policy, in which product is pushed forward to the buyer's warehouse as soon as possible. Finally, it derives the analytical formulations for the maximum inventory levels at different stocking points, while the vendor adopts either forward or backward stocking policy. Numerical examples are also provided for illustration.