Integrated inventory system with freight costs and two types of quantity discounts

In this paper, we investigate an integrated inventory model for single supplier-buyer considering stochastic demand. We consider two quantity discounts with freight environment. The objective is to minimise the integrated total cost incurred by the supplier and buyer. Freight costs are the function of shipping weight and distance with two transportation modes: truckload (TL) and less-than-truckload (LTL) shipments. We develop two optimal models considering all-units quantity discount and incremental quantity discount. The study shows how freight costs and the two discount policies affect the total cost of the supplier and the buyer. Numerical examples are used to illustrate of two models.