On the validity of aggregate models in designing supply chain contracts

The vast majority of the existing papers on supply chain contracts analyse these contracts based on a highly aggregate model description of the supply chain. Recognizing the high complexity of real (supply chain) systems, such models can naturally only be rough approximations of reality. Out of the many possible ways for aggregating a planning model our study focuses on item aggregation. Here, due to computational, informational, or organizational reasons, a multi-product reality is approximated by a model representation with fewer products. We explore the aggregation error made when using an aggregate model in order to optimize a supply chain contract, which is subsequently applied to a more detailed (real) system. Based on a numerical analysis it is shown that the design of supply chain contracts by means of an aggregate planning model may lead to significant suboptimalities.