Column Generation based heuristic for the Vehicle Routing Problem with Time-Dependent Demand

This paper presents a novel Capacitated Vehicle Routing Problem with Time-Dependent Demand (CVRP-TDD) applied to humanitarian logistics. This is a problem where the demand is time dependent and the objective is to maximize the total satisfied demand. When a disaster strikes a territory, the people go directly to shelters. If they do not receive the first aid, water, food, etc. They tend to flee out of the shelters looking for the aid outside of the affected area. This mobilization of people generates an increase in the chaos already caused by the disaster. The aid must arrive at shelters as quickly as possible to stop this mobilization. We developed a mixed integer linear program (MILP) and a column generation (CG) algorithm where the promising columns are generated using dynamic programming (DP). In CG algorithm, two dominance rules and one heuristic are proposed to solve the problem. The algorithm is tested on small and medium instances. CG gives good bounds and find more optimal solutions than those reported by MILP in less than one hour. Also, we show that the heuristic improves significantly the solution time.