Joint optimization of procurement, production and shipping quantities under consignment stock partnership

This paper seeks to jointly optimize the operational decisions associated with raw material procurement, production lot sizing as well as finished product dispatching for a two layer supply chain comprised of a single-vendor and a single-buyer. A more general raw material replenishment schedule is considered wherein multiple raw material shipments may take place within one cycle, referred to as multi-to-one (MTO) policy, or alternatively a single shipment that covers the production for multiple cycles, referred to as one-to-multi (OTM) policy, may rather be adopted depending on whichever is optimal. The aforementioned decisions are simultaneously optimized through mathematical models that embrace the integer multiplier of the cycle time policy. A numerical example that illustrates the performance of the developed models is also presented.