A vendor-buyer JELS model with stock-dependent demand and consigned inventory under buyer's space constraint

In this article, we consider a single-vendor single-buyer supply chain model in which the vendor produces a single product at a constant rate and delivers to the buyer following a consignment stock policy. The customers' demand is assumed to be dependent on the on-hand stock displayed at the buyer. An integrated vendor-buyer model is developed and solved for optimal delivery batch size and number of shipments, aiming at minimizing the average cost of the system. The model is further generalized considering the space limitation at the buyer's end. As coordination mechanism, a contract which distributes the total cost between the vendor and the buyer in an arbitrary ratio is suggested. The proposed model is numerically illustrated and the effects of the buyer's space constraint on the optimal number of shipments, delivery batch size and overall cost are studied. The outcome of the proposed model is also compared with that of the model under lot-for-lot policy to conclude which of the policies should be preferred to the other and under what conditions.