Supply chain coordination by contracts under binomial production yield

Supply chain coordination is enabled by adequately designed contracts so that decision making by multiple actors avoids efficiency losses in the supply chain. From the literature it is known that in newsvendor-type settings with random demand and deterministic supply the activities in supply chains can be coordinated by sophisticated contracts while the simple wholesale price contract fails to achieve coordination due to the double marginalization effect. Advanced contracts are typically characterized by risk sharing mechanisms between the actors, which have the potential to coordinate the supply chain. Regarding the opposite setting with random supply and deterministic demand, literature offers a considerably smaller spectrum of solution schemes. While contract types for the well-known stochastically proportional yield have been analyzed under different settings, other yield distributions have not received much attention in the literature so far. However, practice shows that yield types strongly depend on the industry and the production process that is considered. As consequence, they can deviate very much from the specific case of a stochastically proportional yield. This paper analyzes a buyer-supplier supply chain in a random yield, deterministic demand setting with production yield of a binomial type. It is shown how under binomially distributed yields risk sharing contracts can be used to coordinate buyer's ordering and supplier's production decision. Both parties are exposed to risks of overproduction and under-delivery. In contrast to settings with stochastically proportional yield, however, the impact of yield uncertainty can be quite different in the binomial yield case. Under binomial yield, the output uncertainty decreases with larger production quantities while it is independent from lot sizes under stochastically proportional yield. Consequently, the results from previous contract analyses on other yield types may not hold any longer. The current analytical study reveals that, like under stochastically proportional yield, coordination is impeded by double marginalization if a simple wholesale price contract is applied. However, more sophisticated contracts which penalize or reward the supplier can change the risk distribution so that supply chain coordination is possible also under binomial yield. In this context, many contract properties from planning under stochastically proportional yield carry over. Nevertheless, numerical examples reveal that a misspecification of the yield type can considerably downgrade the extent of supply chain coordination.