### G-2016-08

# Minimizing the logistic ratio in the inventory routing problem

## Claudia Archetti, Guy Desaulniers, and Maria Grazia Speranza

Inventory routing problems aim at minimizing the cost of the total distance traveled over a time horizon discretized in periods, while guaranteeing that the customers do not incur a stock-out event. In an optimal solution of an inventory routing problem the customers in general have no inventory at the end of the horizon. Some inventory may remain only if this does not increase the cost of the distance traveled. To avoid this ending drawback, we consider in this paper an objective function, the so-called logistic ratio, which is the ratio between the total routing cost and the total quantity distributed. The logistic ratio is a measure commonly used in practice to assess the efficiency of the distribution. The mathematical programming formulation of the problem becomes non linear. The solutions of the problem are compared with the solutions of a classical inventory routing problem, both from the worst-case point of view and computationally.

Published **February 2016**
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16 pages