Stability Analysis of Cost Allocation Methods for Inventory Routing

Abstract

This paper considers the Inventory Routing Problem under two different inventory replenishment policies, namely the Maximum Level replenishment policy and the Order-up-to Level policy. The distribution cost under both replenishment policies is determined and allocated over the retailers that are served by the supplier. The distribution cost is obtained through an exact solution algorithm by Archetti et al. (2004). Various allocation methods, like proportional rules, methods based on separable and non-separable cost and game theoretic allocation concepts (Shapley value, nucleolus, pre-nucleolus), are used to allocate the cost over the retailers. Once the distribution cost and the cost allocations are obtained, the objective is to quantify and analyze the stability or instability of the cost allocation resulting from the various allocation methods.