A single-vendor, multiple-buyer coordinated supply chain model with unequal-sized batch shipments and cycle-dependent safety stocks

This paper investigates a single-vendor, multiple-buyer coordinated supply chain under stochastic demand. Each buyer implements a continuous review policy, and the shortage quantity is fully back-ordered. The lead time for the first shipment includes setup, production, and transportation times, while the lead time for the remaining shipments includes only transportation time. The production time is a function of production lot and production rate, which are both decision variables, and the setup and transportation times are controllable as well. For each buyer, the safety stock in the first replenishment cycle is not necessarily identical to that in the remaining cycles. Two successive shipments from the vendor to a buyer may have different sizes, and their ratio is a decision variable. The problem is finding the production and inventory replenishment policy, production rate, and lead times that minimise the long-run expected total cost per time unit. We demonstrate properties satisfied by the cost function and develop an optimisation algorithm, whose performance is compared to a benchmark algorithm based on a commercial solver in a numerical experiment. The experiments also investigate the benefits stemming from the proposed model when compared to models reproducing situations that leverage some or any of the controlled factors.