Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still be allowed. For some of the most common vehicle-routing problems, we show how this issue can be overcome by modifying the route-generation labeling algorithm in order to remove indirectly these sequences from the network. The proposed acceleration strategy is tested on benchmark instances of the vehicle-routing problem with time windows (VRPTW) and four variants of the electric VRPTW. The computational results show that it yields a significant speedup, especially for the most difficult instances.

Freight distribution with electric vehicles (EVs) is a promising alternative to reduce the carbon footprint associated with city logistics. Algorithms for planning routes for EVs should take into account their relatively short driving range and the effects of traffic congestion on the battery consumption. This paper proposes new methodology and illustrates how it can be applied to solve an electric vehicle routing problem with stochastic and time-dependent travel times where battery recharging along routes is not allowed. First, a new method for generating network-consistent (correlated in time and space) and time-dependent speed scenarios is introduced. Second, a new technique for applying branch and price on instances defined on real street networks is developed. Computational experiments demonstrate the effectiveness of the approach for finding optimal or near-optimal solutions in instances with up to 133 customers and almost 1,500 road links. With a high probability, the routes in the obtained solutions can be performed by EVs without requiring intermediate recharging stops. An execution time control policy to further reduce the chances of stranded EVs is also presented. In addition, we measure the cost of independence, which is the impact on solution feasibility when travel times are assumed statistically independent. Last, we give directions on how to extend the proposed framework to handle recourse actions.

Motivated by urban freight transportation practices in China, we study an optimal truck loading problem in which a fixed cost and an additional cost that depends on the number of unloading points are associated with each truck used. The truck loading problem is modeled as a one-dimensional bin packing problem, where the cost of each bin is a convex fixed-plus-linear function of the number of items in the bin. The objective is to minimize the total cost of bins used. We develop an asymptotic polynomial time approximation scheme and an efficient approximation algorithm with an asymptotic worst-case performance ratio of 1.5 to tackle the problem. Our computational experiments indicate that the approximation algorithm performs well for certain order patterns, and also reveal several important insights on using the freight charge scheme.

We introduce the electric vehicle routing problem with public-private recharging strategy in which vehicles may recharge en route at public charging infrastructure as well as at a privately-owned depot. To hedge against uncertain demand at public charging stations, we design routing policies that anticipate station queue dynamics. We leverage a decomposition to identify good routing policies, including the optimal static policy and fixed-route-based rollout policies that dynamically respond to observed queues. The decomposition also enables us to establish dual bounds, providing a measure of goodness for our routing policies. In computational experiments using real instances from industry, we show the value of our policies to be within 10% of a dual bound. Furthermore, we demonstrate that our policies significantly outperform the industry-standard routing strategy in which vehicle recharging generally occurs at a central depot. Our methods stand to reduce the operating costs associated with electric vehicles, facilitating the transition from internal-combustion engine vehicles.

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

We introduce a mission planning concept for routing unmanned aerial vehicles (UAVs) through a set of sampling locations in the immediate aftermath of an incident such as a fire or chemical accident. Using interpolation methods that account for the spatial interdependencies inherent in the surveyed phenomenon, these samples allow predicting the distribution of hazardous substances across the affected area. We define the generalized correlated team orienteering problem (GCorTOP) for selecting informative samples considering spatial correlations between observed and unobserved locations, as well as priorities in the surveyed area. To quickly provide high-quality solutions in time-sensitive situations, we propose a two-phase multistart adaptive large neighborhood search (2MLS). We show the competitiveness of the solution approach using benchmark instances for the team orienteering problem and investigate the performance of the proposed models and solution approach in an extensive study based on newly introduced benchmark instances for the mission planning problem.

In global liner shipping networks, a large share of transported cargo is transshipped at least once between container vessels, and the total transportation time of these containers depends on how well the corresponding services are synchronized. We propose a problem formulation that integrates service scheduling into the liner shipping network design problem. Furthermore, the model incorporates many industry-relevant modeling aspects: it allows for leg-based sailing speed optimization, it is not limited to simple or butterfly-type services, and it accounts for service-level requirements such as cargo transit time limits. The classic liner shipping network design problem is already a hard problem, and to solve the extended version, we propose a column-generation matheuristic that uses advanced linear programming techniques. The proposed method solves LINER-LIB instances of up to 114 ports and, if applied to the classic liner shipping network design problem, finds new best solutions to all instances, outperforming existing methods reported in the literature. Additionally, we analyze the relevance of scheduling for liner shipping network design. The results indicate that neglecting scheduling and approximating transshipments instead may result in the design of liner shipping networks that underestimate cargo transit times and their implications.

Unmanned aerial vehicles, commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large retailers and courier delivery companies. We introduce a novel way to exploit drones in same-day home delivery settings: drone resupply. We consider a home delivery system in which delivery trucks are regularly resupplied by drones. Resupply can take place whenever a delivery truck is stationary and a drone can land on the truck’s roof. We introduce the vehicle routing problem with drone resupply to capture and investigate this setting. We develop different algorithms and compare their performance. Finally, we quantify the potential benefits of drone resupply and generate valuable insights for advancing this concept.

Freight forwarding companies commonly encounter difficulties in handling uncertainties, especially demand uncertainty under the circumstances of no sufficient historical data or accurate forecasting approach. A two-stage robust optimization method is proposed for service network design under demand uncertainty. We employ probability-free uncertainty sets to illuminate the potential scenarios and develop a column-and-constraint generation approach as the solution method to solve the introduced robust models exactly. As indicated by the numerical results, the algorithm we proposed herein performs better than the Benders decomposition approach in terms of computing speed and quality of the solution. Comparative results demonstrate the robustness of the proposed models. We also analyze the structural properties of robust solutions, which provide operational flexibility against uncertainty.

Planning maritime surveillance activities in military operations and long-term defense planning is a huge task that is done manually today. Because maritime surveillance resources are extremely expensive, the potential cost savings of using optimization models to do such planning are large. In this paper, we developed a methodology for making maritime surveillance planning more efficient. The purpose of our tool is to find routes for the force elements involved in maritime surveillance operations, where the goal is to keep a maritime picture sufficiently updated. Our problem may be viewed as a variant of the classical periodic vehicle routing problem, but it differs from this problem in some major aspects. To cope with the specific issues of our problem, we introduce a novel time-indexed formulation, where each variable is associated with a set of contiguous time periods. We defined and implemented a branch-and-price procedure to solve this formulation to exact optimality. Moreover, to tackle instances of practical size, we defined and applied efficient and effective heuristic techniques for solving the pricing problem. We show how our approach can plan up to 72-hour realistic missions with routing ships.