Workload equity in vehicle routing with a medium-term perspective
Maxime Agius  1, 2, 3@  , Nabil Absi  4, 5@  , Dominique Feillet  6@  , Thierry Garaix  6@  
1 : Ecole des Mines de Saint Etienne
Ecole des Mines de Saint Etienne, Ecole des Mines de Saint-Etienne
2 : Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS)
CNRS : UMR6158
3 : Laboratoire de Conception, Optimisation et Modélisation des Systèmes
Université de Lorraine : EA7306
4 : Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes  (LIMOS)
CNRS : UMR6158
F-13541 Gardanne -  France
5 : Ecole des Mines de Saint-Etienne  (EMSE)
Ecole des Mines de Saint-Etienne
Campus Georges Charpak Provence, F-13451 Gardanne, France -  France
6 : Mines Saint-Etienne and LIMOS
Mines Saint-Etienne, Univ Clermont Auvergne, INP Clermont Auvergne, CNRS, UMR 6158 LIMOS, F - 42023 Saint-Etienne France

In the vehicle routing literature, equity for drivers is mostly considered on a daily basis. In this work, we extend the literature by addressing equity on a longer term. We consider a time horizon of a few weeks and a test-bed routing problem motivated by healthcare logistics, with customer demand progressively revealed. Having unbalanced routes at some periods (days) is accepted, but some degree of equity is imposed on the complete horizon. We propose five solution frameworks with different levels of control on equity. A dedicated branch-and-price algorithm is used to solve the daily routing problem and is adapted for the different solution frameworks. Numerical experiments are conducted on a benchmark of realistic instances to evaluate how addressing equity this way impacts the routing cost, equity and feasibility.


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