A supply chain of deteriorating items with variable demand

Here two-level supply chain model is considered for a deteriorating item where the retailer's warehouse in the market place has a limited capacity. Therefore the retailer can rent a warehouse (RW) if needed with a higher cost compared to own warehouse (OW). This model includes one wholesaler and one retailer and our aim is to maximize the total profit. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. Retailer also introduces some promotional cost to boost the base demand of the item. It is established that if the wholesaler shares a part of promotional cost then channel profit as well as individual profit increase. The supply chain model is also considered for imprecise environment when different inventory parameters are fuzzy/rough in nature. In this case individual profits as well as channel profit become fuzzy/rough in nature. As optimization of fuzzy/rough objective is not well defined, following credibility/trust measure of fuzzy/rough event, an approach is proposed for comparison of fuzzy/rough objectives and a Particle Swarm Optimization (PSO) algorithm is used to find marketing decisions. Models are illustrated with numerical examples.