H. Murat Afsar

Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem

This paper addresses the multitrip Cumulative Capacitated Single-Vehicle Routing Problem (mt-CCSVRP). In this problem inspired by disaster logistics, a single vehicle can perform successive trips to serve a set of affected sites and minimize an emergency criterion, the sum of arrival times. Two mixed integer linear programs, a flow-based model and a set partitioning model, are proposed for small instances with 20 sites. An exact algorithm for larger cases transforms the mt-CCSVRP into a resource-constrained shortest path problem where each node corresponds to one trip and the sites to visit become resources. The resulting problem can be solved via an adaptation of Bellman–Ford algorithm to a directed acyclic graph with resource constraints and a cumulative objective function. Seven dominance rules, two upper bounds and five lower bounds speed up the procedure. Computational results on instances derived from classical benchmark problems for the capacitated VRP indicate that the exact algorithm outperforms a commercial MIP solver on small instances and can solve cases with 40 sites to optimality.

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

The multitrip cumulative capacitated vehicle routing problem (mt-CCVRP) is a non-trivial extension of the classical CVRP: the goal is to minimize the sum of arrival times at demand nodes and each vehicle may perform several trips. Applications of this NP-hard problem can be found in disaster logistics and maintenance operations. Contrary to the CVRP, the cost of a solution varies if a trip is reversed or if its rank in a multitrip is changed. Moreover, evaluating local search moves in constant time is not obvious. This article presents a mixed integer linear program (MILP), a dominance rule, and a hybrid metaheuristic: a multi-start iterated local search (MS-ILS) calling a variable neighborhood descent with

Team Orienteering Problem with Decreasing Profits

O(1)

A Branch-and-Price Algorithm for Capacitated Arc Routing Problem with Flexible Time Windows

O(1) move evaluations. On three sets of instances, MS-ILS obtains good solutions, not only on the mt-CCVRP, but also on the cumulative CVRP where it competes with four existing algorithms. Moreover, the metaheuristic retrieves the optimal solutions of the MILP, which can be computed for small instances using a commercial solver.

Vehicle Routing Problem with Time-Dependent Demand in humanitarian logistics

The generalized vehicle routing problem with flexible fleet size (GVRP-flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.

Metaheuristic Framework for a Disaster Logistics Problem with Time-Dependent Demands.

Team Orienteering with Decreasing Profits (DP-TOP) extends the classical Team Orienteering problem (TOP) by considering the profit of each client as a decreasing function of time. It consists of maximizing the sum of collected profit by a fixed number K of vehicles, visiting each client at most once. In this work, we present lower bounds based on a Dantzig-Wolfe decomposition and column generation as well as upper bounds obtained by an evolutionary local search approach (ELS).

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

This paper studies the multitrip cumulative capacitated vehicle routing problem (mt-CCVRP), a variant of the classical capacitated vehicle routing problem (CVRP). In the mt-CCVRP the objective function becomes the minimization of the sum of arrival times at required nodes and each vehicle may perform more than one trip. Applications of this NP-Hard problem can be found in disaster logistics. This article presents a Multistart Evolutionary Local Search (MS-ELS) that alternates between giant tour and mt-CCVRP solutions, and uses an adapted split procedure and a variable neighborhood descent (VND). The results on two sets of instances show that this approach finds very good results in relatively short computing time compared with a multistart iterated local search which works directly on the mt-CCVRP solution space.

A Hybrid Iterative Local Search Algorithm for The Electric Fleet Size and Mix Vehicle Routing Problem with Time Windows and Recharging Stations

Abstract In this paper we study Capacitated Arc Routing Problem with Flexible Time Windows where violating a time windows implies some extra cost. We propose a branch-and-price algorithm due to the Dantzig-Wolfe decomposition. The subproblem is a non-elementary capacitated shortest path problem. Experimental results are presented on the instances up to 40 nodes and 69 required edges.