This paper explores the fair stochastic vehicle routing problem with partial deliveries (FSVRP-PD), a variant of the traditional vehicle routing problem with uncertain customer demands. Unlike conventional approaches that mandate full customer demand satisfaction, we relax this requirement to accommodate several real-world applications, such as humanitarian logistics and food rescue operations, where total demand often exceeds available resources. Our proposed solution approach promotes fair and equitable distribution of resources across all beneficiaries by requiring that the expected fill rate for each customer meets a predefined threshold. A solution to the FSVRP-PD constitutes a set of routes with a minimal total routing cost, where the expected minimum fill rates are met for every customer. Finding such a solution requires solving two interdependent subproblems: route planning and sequential resource allocation. To this extent, we develop an exact branch-price-and-cut algorithm capable of solving instances with up to 75 customers. Resource allocation follows Rawlsian fairness criteria that maximize the minimum service level across all customers in a route. To enhance the performance of the algorithms, particularly in pricing problems, we propose several problem-specific bounding techniques. Through numerical experiments, we demonstrate that our approach outperforms traditional routing and resource allocation policies by yielding superior cost and service equity outcomes. Funding: This work was funded by the Dutch Research Council (NWO) DAta-dRiven E-Commerce Order FULfillment (DAREFUL) Project [Grant 629.002.211]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0556 .

To increase the efficiency of last-mile delivery, online retailers can adopt pickup points in their operations. The retailer may then incentivize customers to steer them from home to pickup point delivery to reduce costs. However, it is usually uncertain whether the customer accepts this incentive to switch to pickup delivery. This setup gives rise to a new last-mile delivery problem with integrated incentive and routing decisions under uncertainty. We model this problem as a two-stage stochastic program with decision-dependent uncertainty. In the first stage, a retailer decides which customers to incentivize. However, customers’ reaction to the incentive is stochastic: they may accept the offer and switch to pickup point delivery, or they may decline the offer and stick with home delivery. In the second stage, after customers’ final delivery choices are revealed, a vehicle route is planned to serve customers via the delivery option of their choice. We develop an exact branch-and-bound algorithm and propose several heuristics to improve the algorithm’s scalability. Our algorithm solves instances with up to 50 customers, realizing on average 4%–8% lower last-mile delivery costs compared with the commonly applied approaches in the industry that do not use incentives or offer incentives to all customers. We also develop a benchmark policy that gives very fast solutions with a 2% average optimality gap for small instances and up to 2% average cost increase compared with the heuristic solutions. Funding: This project received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [Grant 765395]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0287 .

In the two-echelon vehicle routing problem (2E-VRP), the distribution network is split into two echelons. Different vehicles are operated on the first and second echelon to maintain economies of scale and ad-here to any vehicle restrictions that may be present in either echelon. Intermediate facilities are located at the borders of the echelons to facilitate the consolidation and transshipment of goods between ech-elons. Examples of two-echelon distribution systems include express delivery, grocery and hypermarket products distribution, multi-modal freight transportation, city logistics, and e-commerce and home de-livery services. In recent years, the body of literature on the 2E-VRP has expanded significantly. Over 60 research papers have appeared in the scientific literature so far, which underlines both the academic and practical relevance of 2E-VRPs. In this review, we structure and revise all literature on the 2E-VRP. Math-ematical formulations, exact and heuristic solution methods, and benchmark datasets used to test and evaluate new algorithms are reviewed and discussed. This survey concludes with a selected list of open research areas on 2E-VRPs.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit within the second-echelon vehicle capacity with a high probability. We propose two efficient solution procedures based on column generation. Key to the efficiency of these procedures is the underlying labeling algorithm to generate new columns. We propose a novel labeling algorithm based on simultaneous construction of second-echelon routes and a labeling algorithm that builds second-echelon routes sequentially. To further enhance the performance of the solution procedure, we use statistical inference tests to ensure that the chance constraints are met. We reduce the number of customer combinations for which the chance constraint needs to be verified by imposing feasibility bounds on the stochastic customer demands. With these bounds, the runtimes of the labeling algorithms are reduced significantly. The novel labeling algorithm, statistical inference, and feasibility bounds can also be applied to dependent, correlated, and data-driven (scenario-based) demand distributions. Finally, we show the value of the stochastic formulation in terms of improved solution cost and guaranteed feasibility of second-echelon routes. Funding: This work was funded by the Dutch Research Council (NWO) DAREFUL project [Grant 629.002.211] and was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1162 .

This paper considers the problem of servicing a set of locations by a fleet of robots so as to minimize overall makespan. Although motivated by a specific real-world, multi-robot drilling and fastening application, the problem also arises in a range of other multi-robot domains where service start times are subject to precedence constraints and robots must be routed in space and time to avoid collisions. We formalize this general problem and analyze its complexity. We develop a heuristic local search procedure for solving it and analyze its performance on a set of synthetically generated problem instances, some of which capture the specific structure of the motivating drilling and fastening application, and others that generalize to other application settings. We provide a differential analysis of our local search procedure and a comparison to other approaches to demonstrate the efficacy of the proposed heuristic.

The Fuel Replenishment Problem (FRP) is a multi-compartment, multi-trip, split-delivery VRP in which tanker trucks transport different types of petrol, separated over multiple vehicle compartments, from an oil depot to petrol stations. Large customer demands often necessitate multiple deliveries. Throughout a single working day, a tanker truck returns several times to the oil depot to resupply. A solution to the FRP involves computing a delivery schedule of minimum duration, thereby determining for each vehicle (1) the allocation of oil products to vehicle compartments, (2) the delivery routes, and (3) the delivery patterns. To solve FRP efficiently, an Adaptive Large Neighborhood Search (ALNS) heuristic is constructed. The heuristic is evaluated on data from a Chinese petroleum transportation company and compared against exact results from a MILP model and lower bounds from a column generation approach. In addition, we perform sensitivity analysis on different problem features, including the number of vehicles, products, vehicle compartments and their capacities. Computational results show that the ALNS heuristic is capable of solving instances with up to 60 customers and 3 different products in less than 25 minutes with an average optimality gap of around 10%. On smaller instances, the heuristic finds optimal solutions in significantly less time than the exact MILP formulation. (C) 2020 Elsevier Ltd. All rights reserved.

Many cities have to cope with annual snowfall, but are struggling to manage their snow plowing activities efficiently. Despite the fact that winter road maintenance has been a popular research subject for decades, very few papers propose scalable models that can incorporate side constraints encountered in real-life applications. In this work, we propose a Constraint Programming formulation for a Snow Plow Routing Problem (SPRP). The SPRP under consideration involves finding a set of vehicle routes to service a street network in a pre-defined service area, while accounting for various vehicle constraints and traffic restrictions. The fundamental mathematical problem underlying SPRP is the well-known Capacitated Arc Routing Problem (CARP). Common Mathematical Programming (MP) approaches for CARP are typically based on: (i) a graph transformation, thereby transforming CARP into an equivalent node routing problem, or (ii) a sparse network formulation. The CP formulation in this article is based on the former graph transformation. Using geospatial data from the city of Pittsburgh, we empirically show that our CP approach outperforms existing MP formulations for SPRP. For some of the larger instances, our CP model finds 26% shorter plowing schedules than alternative Integer Programming formulations. A test pilot held with actual vehicles proves the applicability of our approach in practice: our routes are 3-156% shorter than the routes the city of Pittsburgh generated with commercial routing software.

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze, and query graphs are crucial in an era where large-scale spatial, societal, and economic network data are abundantly available. One such package is JGraphT, a programming library that contains very efficient and generic graph data structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability, and performance in mind. A distinctive feature of this library is its ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks, including transportation, social, and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism, matching and flow problems, approximation algorithms for NP-hard problems such as independent set and the traveling salesman problem, and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial products, as well as noncommercial and academic research projects. In this work, we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus several similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.

We address a stochastic variant of the Vehicle Routing Problem with Roaming Delivery Locations. In this model, direct-to-consumer deliveries can be made in the trunk of the customer’s car, while the vehicle is parked at a location along the customer’s itinerary. The stochasticity arises from the uncertainty in travel times and the problem is formulated as a two-stage stochastic model. We propose a scenario-based sample average approximation to obtain a heuristic solution. Several experiments to assess the effect of our solution approach compared to a pure deterministic solution approach using expected travel times,show that a cost savings of on average more than 30% can be obtained. Furthermore, it is shown that the flexibility provided by using alternative roaming delivery locations as a recourse to avoid missed deliveries can provide, on average, costs savings of 25% compared to a recourse staying with the locations chosen in the a priori first stage plan.

Given a weighted graph G = (V, E) , the Equitable Traveling Salesman Problem (ETSP) asks for two perfect matchings in G such that (1) the two matchings together form a Hamiltonian cycle in G and (2) the absolute difference in costs between the two matchings is minimized. The problem is shown to be NPHard, even when the graph G is complete. We present two integer programming models to solve the ETSP problem and compare the strength of these formulations. One model is solved through branch-andcut, whereas the other model is solved through a branch-and-price framework. A simple local search heuristic is also implemented. We conduct computational experiments on different types of instances, often derived from the TSPLib. It turns out that the behavior of the different approaches varies with the type of instances. For small and medium sized instances, branch-and-bound and branch-and-price produce comparable results. However, for larger instances branch-and-bound outperforms branch-andprice. © 2017 Elsevier B.V. All rights reserved.

In this paper, we introduce novel optimization methods for sequencing problems in which the setup times between a pair of tasks depend on the relative position of the tasks in the ordering. Our proposed methods rely on a hybrid approach where a constraint programming model is enhanced with two distinct relaxations: One discrete relaxation based on multivalued decision diagrams, and one continuous relaxation based on linear programming. Both relaxations are used to generate bounds and enhance constraint propagation. Experiments conducted on three variants of the time-dependent traveling salesman problem indicate that our techniques substantially outperform general-purpose methods, such as mixed integer linear programming and constraint programming models. (C)2016 Elsevier B.V. All rights reserved.

A global CP constraint is presented which improves the propagation of reservoir constraints on cumulative resources in schedules with optional tasks. The global constraint is incorporated in a CP approach to solve a Single-Commodity Pickup and Delivery Problem: the Bicycle Rebalancing Problem with Time-Windows and heterogeneous fleet. This problem was recently introduced at the 2015 ACP Summer School on Constraint Programming competition. The resulting CP approach outperforms a Branch-and-Bound approach derived from two closely related problems. In addition, the CP approach presented in this paper resulted in a first place position in the competition.

In cold weather cities, snowstorms can have a significant disruptive effect on both mobility and safety, and consequently the faster that streets can be cleared the better. Yet in most cities, plans for snowplowing are developed using simple allocation schemes that while easy to implement can also be quite inefficient. In this paper we consider the problem of optimizing the routes of a fleet of snow plowing vehicles, subject to street network topology, vehicle operating restrictions, and resource (salt, fuel) usage and replenishment constraints. We develop and analyze the performance of three different optimization models: a mixed-integer programming (MIP) model, a constraint programming (CP) model, and a constructive heuristic procedure that is amplified by an iterative improvement search. The models are evaluated on a set of snow plow routing problems of various sizes, constructed using Open Streets map data of Pittsburgh PA. Experimental results are presented that illustrate the differential strengths and weaknesses of each model, and suggest an alternative hybrid solution approach.

Scheduling projects is a difficult and time consuming process, and has far-reaching implications for any organization's operations. By generalizing various aspects of project scheduling, decision makers are enabled to capture reality and act accordingly. In the context of the MISTA 2013 conference, the first MISTA challenge, organized by the authors, introduced such a general problem model: the Multi-Mode Resource-Constrained Multi-Project Scheduling Problem (MRCMPSP). The present paper reports on the competition and provides a discussion on its results. Furthermore, it provides an analysis of the submitted algorithms, and a study of their common elements. By making all benchmark datasets and results publicly available, further research on the MRCMPSP is stimulated.

Given a weighted graph G = (V, E), the Equitable Traveling Salesman Problem (ETSP) asks for two perfect matchings in G such that (1) the two matchings together form a Hamiltonian cycle in G and (2) the absolute difference in costs between the two matchings is minimized. The problem is shown to be NP-Hard, even when the graph G is complete. We present two integer programming models to solve the ETSP problem. One model is solved through branch-and-bound-and-cut, whereas the other model is solved through a branch-and-price-and-cut framework. A simple local search heuristic is also implemented. We conduct computational experiments on different types of instances, often derived from the TSPLib. It turns out that the behavior of the different approaches varies with the type of instances; however, the branch-and-bound-and-cut approach implemented in Cplex seems to work best overall.