Exact solution of the evasive flow capturing problem

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally

Charge scheduling for electric freight vehicles

We consider a fleet of electric freight vehicles (EFVs) that must deliver goods to a set of customers over the course of multiple days. In an urban environment, EFVs are typically charged at a central depot and rarely use public charging stations during delivery routes. Therefore, the charging schedule at the depot must be planned ahead of time so as to allow the vehicles to complete their routes at minimal cost. Vehicle fleet operators are subject to commercial electricity rate plans, which should be accounted for in order to provide an accurate estimation of the energy-related costs and restrictions. In addition, high vehicle utilization rates can accelerate battery aging, thereby requiring degradation mitigation considerations. We develop and solve a comprehensive mathematical model that incorporates a large variety of features associated with the use of EFVs. These include a realistic charging process, time-dependent energy costs, battery degradation, grid restrictions, and facility-related demand charges. Extensive numerical experiments are conducted in order to draw managerial insights regarding the impact of such features on the charging schedules of EFVs

The electric vehicle routing problem with energy consumption uncertainty

Compared with conventional freight vehicles, electric freight vehicles create less local pollution and are thus generally perceived as a more sustainable means of goods distribution. In urban areas, such vehicles must often perform the entirety of their delivery routes without recharging. However, their energy consumption is subject to a fair amount of uncertainty, which is due to exogenous factors such as the weather and road conditions, endogenous factors such as driver behaviour, and several energy consumption parameters that are difficult to measure precisely. Hence we propose a robust optimization framework to take into account these energy consumption uncertainties in the context of an electric vehicle routing problem. The objective is to determine minimum cost delivery routes capable of providing strong guarantees that a given vehicle will not run out of charge during its route. We formulate the problem as a robust mixed integer linear program and solve small instances to optimality using robust optimization techniques. Furthermore, we develop a two-phase heuristic method based on large neighbourhood search to solve larger instances of the problem, and we conduct several numerical tests to assess the quality of the methodology. The computational experiments illustrate the trade-off between cost and risk, and demonstrate the influence of several parameters on best found solutions. Furthermore, our heuristic identifies 42 new best solutions when tested on instances of the closely related robust capacitated vehicle routing problem

A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints

Given a graph, a set of origin-destination (OD) pairs with communication requirements, and an integer k >= 2, the network design problem with vulnerability constraints (NDPVC) is to identify a subgraph with the minimum total edge costs such that, between each OD pair, there exist a hop-constrained primary path and a hop-constrained backup path after any k - 1 edges of the graph fail. Formulations exist for single-edge failures (i.e., k = 2). To solve the NDPVC for an arbitrary number of edge failures, we develop two natural formulations based on the notion of length-bounded cuts. We compare their strengths and flexibilities in solving the problem for k >= 3. We study different methods to separate infeasible solutions by computing length-bounded cuts of a given size. Experimental results show that, for single-edge failures, our formulation increases the number of solved benchmark instances from 61% (obtained within a two-hour limit by the best published algorithm) to more than 95%, thus increasing the number of solved instances by 1,065. Our formulation also accelerates the solution process for larger hop limits and efficiently solves the NDPVC for general k. We test our best algorithm for two to five simultaneous edge failures and investigate the impact of multiple failures on the network design

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

The electric bus fleet transition problem

The use of electric bus fleets has become a topical issue in recent years. Several companies and municipalities, either voluntarily or to comply with legal requirements, will transition to greener bus fleets in the next decades. Such transitions are often established by fleet electrification targets, which dictate the number of electric buses that should be in the fleet by a given time period. In this paper we introduce a comprehensive optimization-based decision making tool to support such transitions. More precisely, we present a fleet replacement problem which allows organizations to determine bus replacement plans that will meet their fleet electrification targets in a cost-effective way, namely considering purchase costs, salvage revenues, operating costs, charging infrastructure investments, and demand charges. We account for several charging infrastructure options, such as slow and fast plug-in stations, overhead pantograph chargers, and inductive (wireless) chargers. We refer to this problem as the electric bus fleet transition problem, and we model it as an integer linear program. We apply our model to conduct computational experiments based on several scenarios. We use real data provided by a public transit agency in order to draw insights into optimal transition plans

An Enhanced Path Planner for Electric Vehicles Considering User-Defined Time Windows and Preferences

A number of decision support tools facilitating the use of Electric Vehicles (EVs) have been recently developed. Due to the EVs’ limited autonomy, routing and path planning are the main challenges treated in such tools. Specifically, determining at which Charging Stations (CSs) to stop, and how much the EV should charge at them is complex. This complexity is further compounded by the fact that charging times depend on the CS technology, the EV characteristics, and follow a nonlinear function. Considering these factors, we propose a path-planning methodology for EVs with user preferences, where charging is performed at public CSs. To achieve this, we introduce the Electric Vehicle Shortest Path Problem with time windows and user preferences (EVSPPWP) and propose an efficient heuristic algorithm for it. Given an origin and a destination, the algorithm prioritizes CSs close to Points of Interest (POIs) that match user inputted preferences, and user-defined time windows are considered for activities such as lunch and spending the night at hotels. The algorithm produces flexible solutions by considering clusters of charging points (CPs) as separate CSs. Furthermore, the algorithm yields resilient paths by ensuring that recommended paths have a minimum number of CSs in their vicinity. The main contributions of our methodology are the following: modeling user-defined time windows, including user-defined weights for different POI categories, creating CSs based on clusters of CPs with sufficient proximity, using resilient paths, and proposing an efficient algorithm for solving the EVSPPWP. To facilitate the use of our methodology, the algorithm was integrated into a web interface. We demonstrate the use of the web interface, giving usage examples and comparing different settings

Locating and Sizing Electric Vehicle Chargers Considering Multiple Technologies

In order to foster electric vehicle (EV) adoption rates, the availability of a pervasive and efficient charging network is a crucial requirement. In this paper, we provide a decision support tool for helping policymakers to locate and size EV charging stations. We consider a multi-year planning horizon, taking into account different charging technologies and different time periods (day and night). Accounting for these features, we propose an optimization model that minimizes total investment costs while ensuring a predetermined adequate level of demand coverage. In particular, the setup of charging stations is optimized every year, allowing for an increase in the number of chargers installed at charging stations set up in previous years. We have developed a tailored heuristic algorithm for the resulting problem. We validated our algorithm using case study instances based on the village of Gardone Val Trompia (Italy), the city of Barcelona (Spain), and the country of Luxembourg. Despite the variability in the sizes of the considered instances, our algorithm consistently provided high-quality results in short computational times, when compared to a commercial MILP solver. Produced solutions achieved optimality gaps within 7.5% in less than 90 s, often achieving computational times of less than 5 s

The Bi-objective Long-haul Transportation Problem on a Road Network

In this paper we study a long-haul truck scheduling problem where a path has to be determined for a vehicle traveling from a specified origin to a specified destination. We consider refueling decisions along the path, while accounting for heterogeneous fuel prices in a road network. Furthermore, the path has to comply with Hours of Service (HoS) regulations. Therefore, a path is defined by the actual road trajectory traveled by the vehicle, as well as the locations where the vehicle stops due to refueling, compliance with HoS regulations, or a combination of the two. This setting is cast in a bi-objective optimization problem, considering the minimization of fuel cost and the minimization of path duration. An algorithm is proposed to solve the problem on a road network. The algorithm builds a set of non-dominated paths with respect to the two objectives. Given the enormous theoretical size of the road network, the algorithm follows an interactive path construction mechanism. Specifically, the algorithm dynamically interacts with a geographic information system to identify the relevant potential paths and stop locations. Computational tests are made on real-sized instances where the distance covered ranges from 500 to 1500 km. The algorithm is compared with solutions obtained from a policy mimicking the current practice of a logistics company. The results show that the non-dominated solutions produced by the algorithm significantly dominate the ones generated by the current practice, in terms of fuel costs, while achieving similar path durations. The average number of non-dominated paths is 2.7, which allows decision makers to ultimately visually inspect the proposed alternatives

Stochastic vehicle routing with random time dependent travel times subject to perturbations

Assigning and scheduling vehicle routes in a stochastic time dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic, resulting in a planning gap (i.e. difference in performance between planned route and actual route). Our methodology introduces the traffic congestion component based on queueing theory, thereby introducing an analytical expression for the expected travel. In real life travel times are subject to uncertainty, we solve a time dependent vehicle routing problem to find robust solutions, that can potentially absorb such uncertainties. We model uncertainty as perturbations that are randomly inserted on the routes, we optimize the perturbed solutions via Tabu Search. We conduct experiments on a set of 32 cities, and found that the perturbed solutions generally cope better with the uncertainty than the non-perturbed solutions, with a small increase in expected travel times