Mathematical formulations for a two-echelon inventory routing problem

Abstract

Integrated supply chain management is a current practice in the search for overall cost minimization. The vendor management inventory is one of those practices, in which the supplier is responsible for managing the inventory of the customers in accordance with pre-determined management policies. The problem that considers transportation decisions in addition to inventory management is referred to as the Inventory Routing Problem (IRP). The classic IRP considers a system with one supplier that manages the inventory level of a set of customers aiming at defining when and how much products to supply and how to combine customers in routes while minimizing storage and transportation costs. We present an extension of this problem that considers a two-echelon system with indirect deliveries and route decisions at both levels. In this variant, the customers demands have to be met by deliveries through distribution centers with minimum total cost. We propose two mathematical formulations for the two-echelon IRP under different inventory policies. Computational experiments on a set of randomly generated instances evaluate the proposed formulations. The obtained results show that both formulations are able to solve to the proven optimality small-scale instances and one of the models found feasible solutions for almost all instances under all considered inventory policies.