You are here

Inventory Routing

This work is done is collaboration with Martin Josef Geiger, at the Institute of Logistics and Organization, Helmut Schmidt Universität. Mirror web site can be reached here.


Many logistic activities are concerned with linking material flows among companies and processes. In such applications, we find a combination of quantity decisions, e. g. the amount of goods shipped (Inventory Management), and routing decisions as tackled in the area of Vehicle Routing. Clearly, both areas intersect to a considerable degree, complicating the solution of such problems. Recently, intensive research has been conducted in this context which is commonly refereed to as Inventory Routing Problems (IRP). Several variants of the IRP can be found, ranging from deterministic demand cases to stochastic models.

From the practical point of view of the companies, reality is much more complex than a know demand and much more uncertain than a stochastic law. In fact, companies often have a partial knowledge of the demand over the planning horizon. Our observation of this phenomenon can be transformed in a new type of data, which we propose for further experimental investigations. We here assume that demand of the current period is known at the beginning of the period. Besides, we have an approximate overview of the demand over the 5 next periods, the 20 next periods and the 60 next periods. This overview is rather good (e.g. it does not differ from reality by more that ±10%) but of course, we cannot predict with certainty what will happen the next periods.

The global objective of this work is to provide practical optimization methods to companies involved in inventory routing problems, taking into account this new type of data. Also, companies are sometimes not able to deal with changing plans every period and would like to adopt regular structures for serving customers.

As our work is a long term project, we are gradually going to develop our solution approach. In a first phase, we will focus on the Inventory Routing problem with a single product, deterministic known demand over a finite horizon. We assume that the routing costs and the inventory costs are not comparable and therefore should be handled as two different objectives. To our knowledge, this is the first time that a bi-objective approach is considered for this problem.

Problem definition

We consider a distribution network (usually a complete graph or a distance matrix) where a single product is shipped from a depot (denoted by 0) of unlimited capacity to a set C={1,...,n} of customers over a time finite horizon H of p periods. A homogeneous fleet of trucks of capacity K serves the customers (the number of trucks that can be used at every time period is not limited). Alternatively, a single truck can be used to do several tours over the same period. Each customer i has a maximum capacity Ui and an initial inventory level Ii0. The goal is to minimize two cost functions, namely the total routing costs (the sum of routing costs in each period) and the total inventory costs (the sum of the inventory levels at the end of each period for all customers).

Proposed benchmark instances

Preview of the IRP Solver software


IRP Solver screenshot

Related presentations

Marc Sevaux presented his work at INOC 2011

The 5th international conference on network optimization was held in Hamburg, Germany. Marc Sevaux has presented part of tis work done in collaboration with Martin Josef Geiger during tis sabbatical year at Helmut Schmidt Universität.

This work presents a study on a biobjective generalization of the inventory routing problem, an important optimization problem found in logistical networks in which aspects of inventory management and vehicle routing intersect. A compact solution representation and a heuristic optimization approach are presented, and experimental investigations involving novel benchmark instances are carried out. As the investigated problem is computationally very demanding, only a small subset of solutions can be computed within reasonable time. Decision support is nevertheless obtained by means of a set of reference points, which guide the search towards the Pareto-front.

Research Seminar at the University of Magdeburg

During its sabbatical year in Germany, Prof. Marc Sevaux was invited by Prof. Gerhard Wascher at the University of Magdeburg to give a research seminar on its latest research conducted. The presentation that was given introduced the Inventory Routing Problem and the On-line Inventory Routing problem. The presentation can be downloaded here.

Dies Academicus

On February 24th, the Helmut-Schmidt-University celebrated its annual Dies Academicus. In this context, research talks were given, and advances in science were shown and reported to interested visitors from industry, public administration and other governmental organizations. Marc Sevaux contributed by giving a short presentation on "Inventory Routing: a central problem in logistics".