Christian Prins’s research while affiliated with University of Technology of Troyes and other places

The Vehicle Routing Problem with Multiple Time Windows (VRPMTW) is a generalization of the Vehicle Routing Problem (VRP), where the customers have one or more time windows in which they can be visited. In this paper, we propose a Column Generation (CG) algorithm and a post optimization heuristic based on a Variable Neighborhood Search (VNS) to provide both lower and upper bounds for the cost of optimal solutions to VRPMTW. As in CG algorithms for VRP, the master problem is based on a Weighted Set Covering formulation. However, due to the multiple time windows, the pricing subproblem is an Elementary Shortest Path Problem with Multiple Time Windows and Capacity Constraints, which is more difficult to solve than the classical Elementary Shortest Path Problem with a Single Time Window and Capacity Constraints. Computational experiments were performed on 594 instances generated from classical Solomon instances with up to 17 customers. They showed that CG was able to produce lower bounds, within one hour of running time, for 66.7% of the instances. Besides, the post optimization heuristic was able to improve the solution provided by the VNS heuristic in 28.9%, finding integer optimal solutions for 39.9% of the instances. Moreover, for the instances where lower bounds are known, the average optimality gap was 6.0% on average.

This article presents a planning problem in a distribution network incorporating two levels inventory management of perishable products, lot-sizing, multi-sourcing and transport capacity with a homogeneous fleet of vehicles. This study is carried out in collaboration with a designer of an advanced planning system (APS) software. This type of network has been encountered in recent years by several customers, such as in the distribution of dairy products or beverages and with instances that can reach large sizes. A mixed integer linear programming (MILP) is developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the maximum calculation time and for other instances it takes a lot of time to solve MILP. A Lagrangian relaxation is implemented to evaluate these instances. A repair heuristic is applied to the corresponding solutions, for which the cost tends to fall during iterations.

The Vehicle Routing Problem (VRP) with Multiple Time Windows is a generalization of VRP, where the customers have one or more time windows in which they can be visited. The best heuristic in the literature is a Hybrid Variable Neighborhood Tabu Search (HVNTS) that mostly deals with infeasible solutions, because it is assumed that one may not reach some regions of the search space without passing through infeasible solutions. In this short paper, we propose a simpler Variable Neighborhood Search heuristic where all the computational effort is spent on searching for feasible solutions. Computational experiments showed that the proposed heuristic is competitive with the best heuristic in the literature.

While many children walk or cycle to and from school, buses and minibuses are major modes of travel for children. A typical journey of these pupils involves walking to and from the bus stop, waiting at bus stops, and boarding. The school bus routing problem, which consists of a set of students spread in a region who must be brought to and from their schools every school day, is considered in this paper. This paper describes the application of an efficient optimization software, Opta Scholar, to solve the school bus routing and scheduling problem. The application of this software showed major improvements in terms of the number of buses used and travelling costs. Furthermore, the embedded algorithm outperforms existing benchmark results on relaxed forms of the problem.

In this paper, a bi-objective Vehicle Routing Problem (bi-RVRP) with uncertainty in both demands and travel times is studied by means of robust optimization. Uncertain demands per customer are modeled by a discrete set of scenarios representing the deviations from an expected demand, while uncertain travel times are independent from customer demands. Then, traffic records are considered to get discrete scenarios to each arc of the transportation network. Here, the bi-RVRP aims at minimizing the worst total cost of traversed arcs and minimizing the maximum total unmet demand over all scenarios. As far as we know, this is the first study for the bi-RVRP which finds practical applications in urban transportation, e.g., serving small retail stores. To solve the problem, different variations of solution approaches, coupled with a local search procedure are proposed: the Multiobjective Evolutionary Algorithm (MOEA) and the Non-dominated Sorting Genetic Algorithm (NSGAII). Different metrics are used to measure the algorithmic performance, the convergence, as well as the diversity of solutions for the different methods.

In the aftermath of disasters such as major earthquakes, several roads may be blocked by rubble and the population tends to search refugee in certain gathering points of the city. Road network accessibility becomes an important issue for logistic operations, specially on the first days after the quake, when the relief distribution is crucial for survival. This study focused on the Road Emergency Rehabilitation Problem, divided into the Road Network Accessibility Problem (RNAP) and the Work-troops Scheduling Problem (WSP). The first one consists in finding traversable paths for relief teams to reach the population, and the later generates a repairing schedule to improve access to refugee areas. The contributions of this study are two-fold: we present the process of transcribing satellite imagery data into graphs, and mathematical formulations for the RNAP and WSP, along with heuristics to solve the WSP. The proposed methods are able to handle large-scale graphs in an acceptable running time for real scenarios. They are tested on simulated instances and on the graph of Port-au-Prince, with more than 10,000 vertices and edges. The Port-au-Prince graph was generated from satellite images obtained by the International Charter “Space and Major Disasters” a few hours after the 2010 earthquake.

The road network accessibility is an important issue for earthquake relief operations, since several roads may be damaged obstructing the access to certain areas. This work proposes a mathematical model and two heuristics for the road repairing work-troops scheduling in order to increase accessibility to the population as fast as possible after a major earthquake. Solutions for randomly generated instances given by the model are used to evaluate the heuristics' performance. The heuristics are tested on a graph with more than ten thousand vertices and edges from Port-au-Prince 2010 earthquake in Haiti.