The Generalized Consistent Vehicle Routing Problem

Abstract

T he consistent vehicle routing problem (ConVRP) takes customer satisfaction into account by assigning one driver to a customer and by bounding the variation in the arrival times over a given planning horizon. These requirements may be too restrictive in some applications. In the generalized ConVRP (GenConVRP), each customer is visited by a limited number of drivers and the variation in the arrival times is penalized in the objective function. The vehicle departure times may be adjusted to obtain stable arrival times. Additionally, customers are associated with AM/PM time windows. In contrast to previous work on the ConVRP, we do not use the template concept to generate routing plans. Our approach is based on a flexible large neighborhood search that is applied to the entire solution. Several destroy and repair heuristics have been designed to remove customers from the routes and to reinsert them at better positions. Arrival time consistency is improved by a simple 2-opt operator that reverses parts of particular routes.A computational study is performed on ConVRP benchmark instances and on new instances generated for the generalized problem. The proposed algorithm performs well on different variants of the ConVRP. It outperforms template-based approaches in terms of travel cost and time consistency. For the GenConVRP, we experiment with different input parameters and examine the trade-off between travel cost and customer satisfaction. Remarkable cost savings can be obtained by allowing more than one driver per customer.

The multi-objective generalized consistent vehicle routing problem

“…The MOGenConVRP is based on the GenConVRP (Kovacs et al, 2014a) and is modeled on a complete directed graph G = (N 0 , A). N 0 = {0, 1, .…”

“…In order to study realistic problem instances, we also devise a metaheuristic algorithm that provides an approximation of P, denoted by P approx . MDLNS integrates the large neighborhood search algorithm for the GenConVRP (Kovacs et al, 2014a) into the multi directional local search framework (Tricoire, 2012). The LNS is an advanced approach for single-objective consistent vehicle routing problems; the performance of the MDLS is comparable to the best known solution approaches for three different combinatorial optimization problems: the multi-objective multi-dimensional knapsack problem, the bi-objective set packing problem, and the bi-objective orienteering problem (Tricoire, 2012).…”

“…Each objective value in the objective vector is improved by a specialized search strategy. As mentioned above, for the MOGenConVRP, we combine the MDLS framework with the LNS algorithm proposed in Kovacs et al (2014a). The resulting algorithm is referred to as MDLNS.…”

“…The problem is based on the generalized consistent vehicle routing problem (GenConVRP, Kovacs et al, 2014a) that aggregates routing cost and arrival time consistency into a single objective function; the number of different drivers per customer is bounded. In the MOGenConVRP, routing cost, arrival time consistency, and driver consistency are independent objectives of the problem.…”

“…Optimal solutions for the MOGenConVRP are important for benchmarking tests that measure the quality of approximation methods. Our heuristic is a combination of the large neighborhood search algorithm (LNS) for the GenConVRP (Kovacs et al, 2014a) and the multi directional local search framework (MDLS, Tricoire, 2012). We refer to the heuristic algorithm as multi directional large neighborhood search (MDLNS).…”