Integrated production-inventory model with ordering cost reduction and variable lead time under stochastic demand

This paper proposes an integrated inventory model for single-vendor single-buyer with ordering cost reduction and variable lead time. The proposed model contributes to the current inventory literature by integrating lot size-dependent lead time, ordering cost reduction policy and raw material procurement decision into vendor-buyer system. We assume that the ordering cost of buyer can be reduced by an amount of capital investment and the lead time is comprised of production time and setup and transportation time. In this model, the vendor manages the production activity and integrates its lot-sizing decisions with the replenishments of its upstream raw material and the demand of its downstream buyer. Additionally, the shortages in buyer side are assumed to be partially backordered. The objective of the model is to minimise total cost by simultaneously determining shipment size, frequency of delivery, raw material lot size factor, safety factor and ordering cost. We develop an iterative procedure to solve the problem and illustrate the effect of key parameter’s changes on vendor cost, buyer cost and total cost. The results from numerical examples indicate that the ordering cost reduction model results in lower total cost compared to the fixed ordering cost model.