Integrated production inventory routing planning for vendor-buyers coordination supply chain with probabilistic demand, unstable lead time, setup cost reduction, service level consideration

Abstract

This paper introduces a single-vendor multi-buyer system in a divergent supply chain associated with the inventory, production, and transportation or vehicle routing problem (VRP). The demand is distributed normally. The vendor is concerned with lowering setup costs through investments, while buyers are concerned with reducing lead time. Buyers' lead time, except transportation time, can be shortened by adding crashing expense. The vendor produces goods and transports them to buyers in various locations using a fleet of vehicles with similar capability. The related VRP's goal is to reduce the overall distance travelled by all vehicles. The aim of this study is to develop an integrated system considering production, inventory, and transportation; and to minimise the total expected cost by determining the optimal solution of lead time, order quantity, safety factor, routing decision and shipment frequency, which has been demonstrated numerically. The optimum output, inventory, and distribution for the vendor and buyers can be obtained by designing an integrated-inventory algorithm and employing the Clark-Wright algorithm.