The electric vehicle routing problem with capacitated charging stations

Much of the existing research on electric vehicle routing problems (E-VRPs) assumes that the charging stations (CSs) can simultaneously charge an unlimited number of electric vehicles, but this is not the case. In this research, we investigate how to model and solve E-VRPs taking into account these capacity restrictions. In particular, we study an E-VRP with non-linear charging functions, multiple charging technologies, en route charging, and variable charging quantities, while explicitly accounting for the capacity of CSs expressed in the number of chargers. We refer to this problem as the E-VRP with non-linear charging functions and capacitated stations (E-VRP-NL-C). This problem advances the E-VRP literature by considering the scheduling of charging operations at each CS. We first introduce two mixed integer linear programming formulations showing how CS capacity constraints can be incorporated into E-VRP models. We then introduce an algorithmic framework to the E-VRP-NL-C, that iterates between two main components: a route generator and a solution assembler. The route generator uses an iterated local search algorithm to build a pool of high-quality routes. The solution assembler applies a branch-and-cut algorithm to select a subset of routes from the pool. We report on computational experiments comparing four different assembly strategies on a large and diverse set of instances. Our results show that our algorithm deals with the CS capacity constraints effectively. Furthermore, considering the well-known uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 out of 120 instances

New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

We study the prize-collecting job sequencing problem with one common and multiple secondary resources. In this problem, a set of jobs is given, each with a profit, multiple time windows for its execution, and a duration during which it requires the main resource. Each job also requires one of the secondary resources before, during, and after its use of the main resource. The goal is to select and schedule the subset of jobs that maximize the total profit. We present a new mixed integer linear programming formulation of the problem and a branch-cut-and-price algorithm as exact solution methods. We also introduce a heuristic algorithm to tackle larger instances. Extensive numerical experiments show that our exact algorithms can solve to optimality literature instances with up to 500 jobs for a particular dataset and up to 250 jobs for another dataset with different characteristics. Our heuristic builds high-quality solutions in a small computational time. It computes new best-known solutions for most of the larger instances

The Electric Vehicle Routing Problem with Capacitated Charging Stations

Electric vehicle routing problems (E-VRPs) deal with routing a fleet of electric vehicles (EVs) to serve a set of customers while minimizing an operational criterion, for example, cost or time. The feasibility of the routes is constrained by the autonomy of the EVs, which may be recharged along the route. Much of the E-VRP research neglects the capacity of charging stations (CSs) and thus implicitly assumes that an unlimited number of EVs can be simultaneously charged at a CS. In this paper, we model and solve E-VRPs considering these capacity restrictions. In particular, we study an E-VRP with nonlinear charging functions, multiple charging technologies, en route charging, and variable charging quantities while explicitly accounting for the number of chargers available at privately managed CSs. We refer to this problem as the E-VRP with nonlinear charging functions and capacitated stations (E-VRP-NL-C). We introduce a continuous-time model formulation for the problem. We then introduce an algorithmic framework that iterates between two main components: (1) the route generator, which uses an iterated local search algorithm to build a pool of high-quality routes, and (2) the solution assembler, which applies a branch-and cut algorithm to combine a subset of routes from the pool into a solution satisfying the capacity constraints. We compare four assembly strategies on a set of instances. We show that our algorithm effectively deals with the E-VRP-NL-C. Furthermore, considering the uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 of 120 instances

Mathematical models based on decision hypergraphs for designing a storage cabinet

We study the problem of designing a cabinet made up of a set of shelves that contain compartments whose contents slide forward on opening. Considering a set of items candidate to be stored in the cabinet over a given time horizon, the problem is to design a set of shelves, a set of compartments in each shelf and to select the items to be inserted into the compartments. The objective is to maximize the sum of the profits of the selected items. We call our problem the Storage Cabinet Physical Design (SCPD) problem. The SCPD problem combines a two-dimensional guillotine cutting problem for the design of the shelves and compartments with a set of temporal knapsack problems for the selection and assignment of items to compartments. We formalize the SCPD problem and formulate it as a maximum cost flow problem in a decision hypergraph with additional linear constraints. To reduce the size of this model, we break symmetries, generalize graph compression techniques and exploit dominance rules for precomputing subproblem solutions. We also present a set of valid inequalities to improve the linear relaxation of the model. We empirically show that solving the arc flow model with all our enhancements outperforms solving a compact mixed integer linear programming formulation of the SCPD problem

A set packing approach for scheduling passenger train drivers: the French experience

International audienceIn this paper, we describe a method to solve the passenger crew scheduling problem for SNCF (the French national railway company). From rolling-stock rosters, the primary objective of the problem we address is to build shifts to maximize the number of trains that are assigned to drivers. Other objectives are mainly concerned with limiting the number of times where drivers have to rest away from their home, and with minimizing taxi trips. The problem is solved with a day-by-day approach, while guaranteeing a consistent chaining on consecutive days for shifts which include an external rest for drivers. Each day, a set of shifts is first generated according to regulation and business rules using a depth-first search algorithm. Then an iterative procedure based on a Lagrangian heuristic is used to solve the resulting set packing model. This procedure relies on a three-step algorithm: a subgradi-ent method, a constructive heuristic and a fixation technique for selecting efficient shifts. The algorithm has been implemented in a proprietary software module: PLAISANCE. Numerical experiments have been performed on several real-life instances with up to 2,300 passenger trains to schedule. The results correspond to the business requirements and prove the effectiveness of the described method

PLAISANCE : A tool for scheduling trains drivers for French railways

International audienceIn this paper, we describe a method to solve the passenger crew scheduling problem for SNCF (the French national railway company). From rolling-stock rosters and a limited number of train drivers in several depots, the objective of the problem we address is to build duties to minimize a total certain cost in the week. Several models for the cost function are proposed in this article. We first generate a set of shifts according to regulation rules using a depth-first search algorithm. Then an iterative procedure based on a Lagrangian relaxation is used to solve the resulting set covering problem. This procedure relies on a three-step algorithm based on a method developed by Caprara et al. : a subgradient method, a constructive heuristic and a fixation technique to select efficient shifts. The algorithm has been implemented in a proprietary software module named PLAISANCE. Numerical experiments have been performed on several real-life instances with up to 2,900 passenger trains to schedule in a week. The results correspond to the business requirements and prove the effectiveness of the described method

frvcpy: An Open-Source Solver for the Fixed Route Vehicle Charging Problem

Electric vehicles offer a pathway to more sustainable transportation, but their adoption entails new challenges not faced by their petroleum-based counterparts. One of the most challenging tasks in vehicle routing problems addressing these challenges is determining how to make good charging decisions for an electric vehicle traveling a given route. This is known as the fixed route vehicle charging problem. An exact and efficient algorithm for this task exists, but its implementation is sufficiently complex to deter researchers from adopting it. In this work we introduce frvcpy, an open-source Python package implementing this algorithm. Our aim with the package is to make it easier for researchers to solve electric vehicle routing problems, facilitating the development of optimization tools that may ultimately enable the mass adoption of electric vehicles.Electric Vehicle Routing Optimizatio

Modeling and solving a stochastic generation and transmission expansion planning problem with a “Loss Of Load Expectation” reliability criterion

In this paper, we study how a regulatory constraint limiting a measure of unserved demand, called Loss Of Load Expectation (LOLE), can be incorporated into a strategic version of a stochastic generation and transmission expansion planning problem. This problem is tackled by the French Transmission System Operator RTE for producing prospective reports on the evolution of the electricity network. We show that a direct inclusion of the constraint into the extensive form of the two-stage stochastic problem leads to a formulation that violates the time-consistency principle. To obtain a valid model, we use bilevel programming and introduce a formulation of the problem in which the leader and follower have the same objective function. To solve this formulation, we propose a matheuristic that embeds a Benders decomposition algorithm in a binary search on the total investment cost. We performed computational experiments to study the practical difficulty of the problem and validate the proposed solution method. Our experiments show that solving the single-level reformulation of the problem obtained using the KKT complementary conditions is intractable in practice, even for small size instances, and that a simple heuristic procedure is not sufficient to compute feasible solutions for all test cases. This is not the case for our matheuristic, which finds a feasible solutions for all instances of our test bed