Vendor managed inventory models for single-vendor multi-retailer supply chains with quality consideration

In this paper, efficient algorithms are devised to solve two VMI models for a single-vendor multi-retailer supply chain. The first model is for a decentralised supply chain where the vendor's expected profit is maximised. The other model, however, is for a centralised supply chain where the expected system profit is maximised. It is assumed that the lot received by vendor contains a random number of non-conforming items and, thus, inspection is performed on the incoming lot before it is delivered the retailers. In addition, we assume that non-conforming items are sold as a single batch to a secondary market at a reduced price. We also assume that the inspection process is perfect and is performed at a finite rate. In the proposed models, we incorporate a VMI contract which includes an upper limit on retailer's inventory level. In order to encourage cooperation between vendor and retailers, we propose a scheme that distributes the extra profit obtained by the integrated solution between the vendor and retailers.