Robust optimization for the hierarchical mixed capacitated general routing problem applied to winter road maintenance

Abstract

This paper studies the Mixed Capacitated General Routing Problem (MCGRP) under demand uncertainty and service hierarchy using a robust optimization approach. The problem is motivated by an industrial problem: the winter road salt spreading with street hierarchy and demand variation due to the weather or traffic conditions. The street hierarchy or the street priority is modeled with time-dependent cost. We present a robust counterpart formulation with graph transformation to node routing in order to optimize the worst-case realization of the demands from the uncertainty set. We use CPLEX to solve small instances and we developed a variant of the Slack Induction by String Removals metaheuristic for large-scale instances called the Robust SISRs. In the computational analysis we used a Monte carlo simulation to study the robust approach on real-life case studies.