A branch and cut algorithm for the inventory routing problem

The inventory routing problem arises in vendor managed systems where products are distributed from a supplier to a set of retailers by a homogeneous eet of capacitated vehicles. The routes of the vehicles and the quantities of products sent to each retailer in each time period are determined in such a way that no stockouts occur and total costs arising from inventory holding and transportation are minimized. Different inventory replenishment policies can be used while managing the inventories at retailers. We consider the problem with the maximum level inventory replenishment policy. We present a mixed integer linear programming model and derive valid inequalities using several structured relaxations. We relate our valid inequalities to those in the previous studies. We also propose new valid inequalities, implement a branch and cut algorithm and present computational results on benchmark instances from the literature as well as new randomly generated instances.