Mismatch risk allocation in a coproduct supply chain

Products such as cattles and pigs can be processed into several types of products (parts) targeting different segments of customers, which belong to the so called coproducts. Mismatch risk is a significant issue in such coproduct supply chains. Under the Stackelberg game setting, we consider a coproduct supply chain consisting of one producer acting as the leader and one retailer being the follower and establish a stylized model to study how the mismatch risk should be allocated. Two supply chain modes are considered, i.e., the P-chain mode under which the producer is responsible for the processing activity and hence holds the mismatch risk, and the R-chain under which the retailer is responsible for the processing activity. We use the unbalanced ratio to reflect the degree of mismatch between supply and demand among different parts of the coproduct and study how the tradeoff between the bargaining power and the mismatch cost, by different mismatch risk allocations, influences the optimal decisions and the performances of the two parties as well as the whole supply chain. Our main findings include: (1) P-chain dominates R-chain from the perspective of the chain performance; and (2) the upstream producer is not always better off in the P-chain under which he bears more mismatch risk. Numerical study shows the robustness of our main results and further studies the effect of demand uncertainty and the processing cost on the performance of P-chain as compared to R-chain.