ABSTRACT The split delivery vehicle routing problem with time windows (SDVRPTW) extends the well‐known VRPTW by the option of satisfying individual customer demands with more than one vehicle. The SDVRPTW is relatively well studied from an exact viewpoint, but efficient heuristics that are able to provide near‐optimal solutions within short runtimes have not been proposed in the literature. In this article, we design a heuristic for the SDVRPTW, called granular tabu search with balanced customer splitting (GTS‐BCS), that is based on the principle of a priori customer splitting introduced by Chen, International Transactions in Operational Research, 24, 27–41, 2017. The main idea of this approach is to split customers into subcustomers with an a priori splitting rule and then use a solver for the unsplit counterpart of the problem to solve the resulting split‐instance. We use theoretical properties of optimal SDVRPTW solutions and numerical experiments to find well‐balanced splitting rules that find a good tradeoff between the flexibility needed to explore a large number of promising splits of the original demand and keeping the number of generated subcustomers as low as possible. We observe that starting the search from a so‐called no‐split solution, that is, a solution in which customer splits are only possible for customers whose demand exceeds the vehicle capacity, has strong positive effects on both solution quality and runtimes. The final configuration of our GTS‐BCS is able to compute near‐optimal solutions on the common SDVRPTW benchmark sets within comparatively short runtimes. We also investigate whether the proposed splitting rules can be transferred to the standard SDVRP. To this end, we use the same a priori customer splitting framework as in GTS‐BCS and integrate the hybrid genetic search of Vidal, Computers and Operations Research, 140, 105643, 2022 for solving the unsplit counterpart of the SDVRP – the CVRP. Numerical experiments show that the resulting algorithm is nearly competitive to the state‐of‐the‐art dedicated methods for the SDVRP.

Abstract To plan the postal deliveries of our industry partner DHL Group (DHL), the single truck and trailer routing problem with satellite depots (STTRPSD) is solved to optimize mail carriers routes. In this application context, instances feature a high number of customers and satellites, and they are based on real street networks. This motivates the study of the asymmetric STTRPSD (ASTTRPSD). The heuristic solution methods proposed in the literature for the STTRPSD can either solve only the symmetric problem variant, or it is unclear whether they can also be used to solve the ASTTRPSD. We introduce an iterated local search, called ILS‐ASTTRPSD, which generates different first‐level tours in the perturbation phase, and improves the second‐level tours in the local search phase. To speed up the search, granular neighborhoods are used. The computational results on instances from the literature prove the capability of ILS‐ASTTRPSD to return high‐quality solutions. On DHL instances, ILS‐ASTTRPSD significantly decreases total travel times of the mail carriers and returns solutions with a different structure compared to the ones provided by DHL. Based on these differences, we give recommendations on how DHL could design more efficient mail carrier practices. Dedicated computational experiments reveal that considering parking and loading times when solving the ASTTRPSD leads to lower travel times, and that ignoring parking times is more counterproductive than ignoring loading times. Moreover, we assess the robustness of our solutions under parking time fluctuations. Finally, we derive properties of instances for which optimal solutions contain multiple second‐level tours rooted at the same parking spot and for which the optimal solutions of the ASTTRPSD correspond to the ones of a pure traveling salesman problem.

Abstract The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterization of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: We discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight their strengths and weaknesses, and derive a set of desirable properties. Through an extensive numerical campaign, we investigate the impact of decompositions within two algorithms for the capacitated vehicle routing problem: the Adaptive Large Neighborhood Search of Pisinger and Ropke (2007 ) and the Hybrid Genetic Search of Vidal et al. (2012 ). We evaluate the quality of popular decomposition techniques from the literature and propose new strategies. We find that route-based decomposition methods, which define subproblems by means of the customers contained in selected subsets of the routes of a given solution, generally appear superior to path-based methods, which merge groups of customers to obtain smaller subproblems. The newly proposed decomposition barycenter clustering achieves the overall best performance and leads to significant gains compared with using the algorithms without decomposition. History: Erwin Pesch, Area Editor for Heuristic Search and Approximation Algorithms. Funding: This work was supported by the U.S. Air Force [Grant FA9550-17-1-0234], the Ministerio de Ciencia e Innovación (Juan de la Cierva Formación), H2020 Marie Skłodowska-Curie Actions [Grant 945380], the Ministero dell’Università e della Ricerca [Grant 2015JJLC3E_002], the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 308528/2018-2], and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grant E-26/202.790/2019]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1288 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0048 ) at ( http://dx.doi.org/10.5281/zenodo.7613129 ).

To reduce unproductive picker walking in traditional picker-to-parts warehousing systems, automated guided vehicles (AGVs) are used to support human order pickers. In an AGV-assisted order-picking system, each human order picker is accompanied by an AGV during the order-picking process. AGVs receive the picked items and, once a picking order is complete, autonomously bring the collected items to the shipping area. Meanwhile, a new AGV is requested to meet the picker at the first storage position of the next picking order. Thus, the picker does not have to return to a central depot and continuously picks order after order. This paper addresses both the routing of an AGV-assisted picker through a single-block, parallel-aisle warehouse and the sequencing of incoming orders. We present an exact polynomial time routing algorithm for the case of a given order sequence, which is an extension of the algorithm of Ratliff and Rosenthal [ Ratliff HD, Rosenthal AS (1983) Order-picking in a rectangular warehouse: A solvable case of the traveling salesman problem. Oper. Res. 1(3):507–521], and a heuristic for the case in which order sequencing is part of the problem. In addition, we investigate the use of highly effective traveling salesman problem (TSP) solvers that can be applied after a transformation of both problem types into a standard TSP. The numerical studies address the performance of these methods and study the impact of AGV usage on picker travel: by using AGVs to avoid returns to the depot and by sequencing in (near-) optimal fashion, picker walking can be reduced by about 20% compared with a traditional setting. Sharing AGVs among the picker workforce enables a pooling effect so that, in larger warehouses, only about 1.5 AGVs per picker are required to avoid picker waiting. Summary of Contribution: New technologies, such as automatic guided vehicles (AGVs) are currently considered as options to increase the efficiency of the order-picking process in warehouses, which is responsible for a large part of operational warehousing costs. In addition, picker-routing decisions are more and more often based on algorithmic decision support because of their relevance for decreasing unproductive picker walking time. This paper addresses both aspects and investigates routing algorithms for AGV-assisted order picking in parallel-aisle warehouses. We present a dynamic programming routine with polynomial runtime to solve the problem variant in which the sequence of picking orders is fixed. For the variant in which this sequence is a decision, we show that the problem becomes NP-hard, and we propose a greedy heuristic and investigate the use of state-of-the-art exact and heuristic traveling salesman problem solution methods to address the problem. The numerical studies demonstrate the effectiveness of the algorithms and indicate that AGV assistance promises strong improvements in the order-fulfillment process. Because of the practical relevance of AGV-assisted order picking and the presented algorithmic contributions, we believe that the paper is relevant for practitioners and researchers alike.

The standard single-picker routing problem (SPRP) seeks the cost-minimal tour to collect a set of given articles in a rectangular single-block warehouse with parallel picking aisles and a dedicated storage policy, that is, each stock-keeping unit is only available from one storage location in the warehouse. We present a compact formulation that forgoes classical subtour elimination constraints by directly exploiting two of the properties of an optimal picking tour used in the dynamic programming algorithm published in the seminal paper of Ratliff and Rosenthal. We extend the formulation to three important settings prevalent in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In numerical studies, our formulation outperforms existing standard SPRP formulations from the literature and proves able to solve large instances within short runtimes. Realistically sized instances of the three problem extensions can also be solved with low computational effort. For scattered storage, we note a rough tendency that runtimes increase with longer pick lists or a higher degree of duplication. In addition, we find that decoupling of picker and cart can lead to substantial cost savings depending on the speed and capacity of the picker when traveling alone, whereas additional end depots have rather limited benefits in a single-block warehouse. Summary of Contribution: Efficiently routing order pickers is of great practical interest because picking costs make up a substantial part of operational warehouse costs. For the prevalent case of a rectangular warehouse with parallel picking aisles, we present a highly effective modeling approach that covers—in addition to the standard setting—several important storage and order-picking strategies employed in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In this way, we provide practitioners as well as scientists with an easy and quick way of implementing a high-quality solution approach for routing pickers in the described settings. In addition, we shed some light on the cost benefits of the different storage and picking strategies in numerical experiments.

Abstract Driven by environmental considerations, regulations on vehicle emissions, and the offer of major subsidies, electric commercial vehicles (ECVs) are receiving ever stronger attention in logistics companies. Route planning for ECV fleets requires consideration of the special characteristics of ECVs, like limited driving range and the potential need to recharge en route at dedicated recharging stations. From a practical viewpoint, the number of recharge operations of each vehicle can very often be restricted to one recharge per route because (i) typical route distances in the most important application areas of ECVs, like small package shipping and food or beverage distribution, do not require more than one recharge given the current driving range of ECVs, and (ii) operations managers are very reluctant to plan vehicle routes with two or more recharges because recharging operations are perceived as unproductive idle times. We develop a simple hybrid of large neighborhood search and granular tabu search to solve the resulting electric vehicle‐routing problem with time windows and single recharge (EVRPTWS), considering the possibility of both full and partial recharge. The heuristic works on routes represented as customer sequences, and recharge operations are implicitly considered by determining the recharging position in the route, the recharging station to visit, and the amount to be recharged in optimal fashion. We discuss how our algorithm can be extended to handle nonlinear recharging times, different recharging times per station, and time‐dependent waiting times at stations. In numerical studies on EVRPTWS instances from the literature, the method provides optimal or near‐optimal solutions for instances with up to 100 customers within reasonable runtimes. Additional studies investigate the cost savings potential of partial recharges in comparison to full recharges in the presence of time‐window constraints, and examine the factors that influence this cost saving potential.

Abstract We study a class of vehicle‐routing problems with simultaneous pickup and delivery (VRPSPD). In VRPSPDs, each customer may require a certain quantity of goods delivered from the depot and a quantity of goods to be picked up and returned to the depot. Besides the standard VRPSPD, we address (1) the VRPSPD with time limit (VRPSPDTL), which imposes a time limit on the routes of the transportation vehicles, (2) the VRPSPD with time windows (VRPSPDTW), which takes customer time windows into account, (3) the VRP with divisible deliveries and pickups (VRPDDP), which allows for fulfilling the delivery and pickup requests of each customer in two separate visits, (4) the previously unstudied VRP with restricted mixing of divisible deliveries and pickups (VRPRMDDP), which accounts for the difficulty of rearranging the vehicle load by additionally requiring that a certain percentage of the vehicle capacity must remain unoccupied when both types of demand are simultaneously loaded, and (5) the previously unstudied VRPDDP with time windows (VRPDDPTW). We develop a hybrid heuristic solution method which combines an adaptive large neighborhood search algorithm with a path relinking approach, called ALNS‐PR, and we demonstrate the competitiveness of our algorithm on benchmark instances proposed in the literature. Especially on VRPSPDTL, VRPSPDTW, and VRPDDP instances, our ALNS‐PR proves to be superior to the majority of comparison algorithms and is able to obtain numerous new best solutions.

Motivated by an industry project with a small package shipping company in France, we study a vehicle routing problem with stochastic travel and service times that considers the influence of driver familiarity with routes and customers on routing efficiency. Our approach forgoes any fixing of delivery areas thus maintaining routing flexibility. Driver specific travel and service times give drivers incentives to stay in familiar areas. Following common practice, we consider delivery deadlines instead of time windows. To solve the routing problem, we develop an Ant Colony Optimization (ACO) method due to its robustness when dealing with stochastic problem parameters. Our ACO approach includes a new indicator value to deal with customers that are hard to integrate into tours because of delivery restrictions. Numerical studies show that our algorithm is able to trade off between driver learning and routing flexibility and performs strongly for most types of test instances.

In recent years, the leasing concept has become increasingly popular in the field of distributed systems; main examples are JINI and the introduction of leasing to the CORBA context. Nevertheless, no detailed analysis of leasing variants and their fields of application has been done yet. In this paper, we give a systematic classification of possible leasing variants, discuss their advantages and disadvantages and point out their possible uses. In this context, we dispose of the restriction that resource claimants are not capable of waiting for a resource; an assumption made in hitherto literature for simplicity reasons. Furthermore, we consider possible mechanisms on which to base lease renewal decisions that go beyond the simple rules examined in previous works. In the process, we hint at how existing leasing approaches have to be enhanced to accomplish these relaxations