Strategies for online inventory routing problem under real-time information

The inventory routing problem (IRP) under real-time information studied in this paper involves repeated delivery of products from a depot to a set of retailers that face stochastic demands over a long period. This system is controlled by a central decision maker who operates with realtime information about the complete state of the system. To address this online IRP under real-time information, rolling horizon approaches are proposed: plans are updated and solve a mixed integer programming formulation for the off-line version of the problem. In this mixed integer programming formulation, an incremental inventory cost (IIC) function is introduced to combine inventory and transportation costs in the same objective function. This IIC function takes into account additional inventory costs associated with serving a customer at a different time and refilling an amount different from that prescribed by the best inventory policy with fixed transportation costs. Three rolling horizon strategies for the real-time version are compared. These policies are based on repeated reoptimization of different instances of the offline IRP and differ in the number of steps that are implemented for current solutions and the events that trigger plan updates. These policies are compared with a benchmark policy of operating the system in a decentralized manner. The comparison is conducted with a general simulation framework. New replanning policies are shown to outperform systematically the benchmark policy under all scenarios considered.