Modeling load-dependent lead time constraints for efficient supply chain coordination: convexity issues

The lead time at each component of a supply chain contains information which is critical for effective coordination. Lead times vary non-linearly with load, production mix, detailed scheduling and other operational practices within each component of the supply chain. Widely used material requirements planning (MRP) systems employ constant lead time values to avoid the task of generating and accessing variable lead time information. We investigate the value of variable lead time information in the coordination of the supply chain and in particular the potential contribution of this information towards decreasing inventory and backlog costs. We also investigate the computational burden associated with generating the requisite information through calculations distributed to the various components of the supply chain and communicated to a master-problem solving coordinator. More specifically, we study master-problem solving requirements and performance for non-linear lead time relationships that are concave and relatively easy to model, as well as non-concave and harder to deal with. Computational experience is provided to elaborate the value of variable lead time information and the effectiveness of the proposed master-problem solving algorithms.