Price competition and co-operation in a duopoly closed-loop supply chain

This paper studies co-operation and competition issues in a closed-loop supply chain. The supply chain comprises of two manufacturers who compete for selling their new product as well as for collection of the used-products for remanufacturing through a common retailer. To analyze the situation, mathematical models are developed here for three different cases (i) Non-co-operative system (ii) Channel-co-operative system and (iii) Global-co-operative system. For each of the cases, we have characterized optimal wholesale price and fraction of collection of used product. To draw more managerial insights, we also examine the sensitivity of various parameters such as market size, acquisition cost and transfer price on total channel profit. A numerical study is carried out to illustrate the model, and the results reveal that global-co-operative system is the best among all the three cases considered here. Weighted Shapely Value mechanism is used for sharing of surplus generated in the system due to channel-co-operation.