The cumulative vehicle routing problem with arc time windows

In this paper, we introduce a new variant of the cumulative Vehicle Routing Problem (cum-VRP), where certain arcs of the undirected complete graph can only be utilized within specified time constraints. The problem is referred to as the Cumulative Vehicle Routing Problem with Arc Time Windows (Cum-VRPATW) and emerges in routing situations with flow disruptions across road segments, which generally emerges from military and civilian transportation. We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. To effectively address this problem, an effective algorithm is designed. It is a hybrid algorithm that combines principles of the Greedy Randomized Adaptive Search Procedure (GRASP) and decomposition strategies reducing computational complexity. Also, we propose two indexes, the RatioIn and the RatioTWL index that can identify difficult problems. Furthermore, we compare the CPLEX results vis-a-vis the new hybrid heuristic we have developed. Computational tests on converted Solomon (1987) data sets show that the new hybrid heuristic provides extremely good performance results for the cum-VRPATW large size test problems, justifying its effectiveness and robustness.