An integrated inventory model for single-vendor single-buyer system with freight rate discount and stochastic demand

This paper deals with joint economic lot sizing model (JELS) in the context of two stage supply chain comprising of single‐vendor and single‐buyer. The shipment from vendor to buyer is conducted in equally sized and the demand in buyer side is assumed to be normally distributed. In this paper, freight cost is explicitly incorporated in the model and formulated by all‐weight freight discount model and incremental freight discount model. We provide two procedures to find the optimal shipment size, safety factor, production batch and discount level on both models. Numerical examples are presented to illustrate the benefit of the model. The result shows that incorporating freight discount into inventory model may result in significant saving on total cost. The increase in the number of discount levels will lead to the decrease in buyer cost and total cost. Moreover, it also shows that the changes in ordering cost, purchase cost, setup cost and production rate in incremental freight discount model give significant impacts on shipment size and safety factor.