Vehicle Routing Problem with Time-Dependent Demand in humanitarian logistics

The Cumulative Capacitated Vehicle Routing Problem with Time-Dependent Demand(CCVRP-TDD) is a novel problem in humanitarian logistics where the demand is dynamic and the objective is to minimize the sum of arrival times at critical nodes due to the emergency of the situation. Critical nodes are the nodes closest to the source, from which people try to flee to seek first aid, food, etc. This mobilization of people through the affected territory generates an increase in the chaos already caused by the disaster. The vehicles must arrive at these nodes as soon as possible and after they must supply at farthest ones (non critical/safe points). This article presents a mixed integer linear program (MILP) and a two-phase heuristic method (TPHM) based on multi-start iterated local search (MS-ILS). The moves are evaluated in constant time. Both solutions methods are tested in small and medium instances. We show that the heuristic method finds the optimal solution on small instances.