An exact algorithm for the inventory routing problem with logistic ratio

Abstract

The Inventory Routing Problem with Logistic Ratio (IRPLR) is a variant of the classical IRP where, instead of the total distribution cost, the ratio between the total distribution cost and the total delivered quantity is minimized, giving rise to a fractional objective function. An exact algorithm is known, solving instances with up to 15 customers. We propose an iterative exact algorithm where, at each iteration, an IRP with a linear objective function is solved. Experiments show that the proposed algorithm is faster when the number of vehicles is small, solving instances with more customers and a longer planning horizon.