ISyE SEMINAR SERIES - PERIODIC-REVIEW INVENTORY SYSTEMS UNDER SUPPLY CAPACITY CONTRACT
Motivated by the practice of transportation contracts in the modern era, we study periodic-review inventory control models with ordering cost c(x)=cx +K 1[x>R], i.e. the ordering is cx if the ordering quantity is below its quota R, and K+cx if the ordering quantity is over its quota, where K is a setup cost for working out additional contract terms such as additional truck and processing fees, etc. This ordering cost function is neither convex nor concave, and the classical periodic-review inventory model with setup cost is a special case with R=0. We show that the optimal policy is a refined (s,S) policy. We apply this result to a production control problem under energy crisis where the supplier provides an incentive for the manufacturer to not exceed a certain quota.