Supply Chain Coordination with Pooling Contracts

In designing coordination contracts, the conflict between theory and practice often appears in the form of a trade-off between the complexity of theoretically optimal solutions and their ease of implementation in the real world. In this study, we explicitly consider complexity as a design factor and evaluate the performance of simpler contracts versus theoretically optimal but arbitrary complex ones. Our setting is a two-tier supply chain consisting of a single supplier serving a single retailer who possesses private information about a cost parameter. Assuming a discrete type space for the retailer’s private information, we formulate the supplier’s problem of designing optimal "pooling" contract menus. In a pooling (as opposed to a "separating") menu, each contract is intended to appeal to multiple retailer types, and as such, the design is simplified in terms of the number of contracts in the menu. We propose a simple, intuitive design for the pooling contract menu in which inefficient retailer (i.e., higher costs) types are offered customized contracts tailored for their own cost type, and the remaining more efficient types are pooled together and offered a common contract. We numerically show that the cost of our design is, on average, only 1% larger than its theoretically optimal but more complicated counterpart. Our results demonstrate the value of simple contract designs for real-world settings where decision-makers usually rely on straightforward decision rules