Split Delivery Vehicle Routing Problem Research Articles

An exact method for the two-echelon split-delivery vehicle routing problem for liquefied natural gas delivery with the boil-off phenomenon

In this paper we investigate a two-echelon vehicle routing problem for liquefied natural gas (LNG) delivery to determine how to transport LNG from an overseas production terminal to a set of import terminals by vessels, and transport the LNG from the import terminals to a set of filling stations either by tanker trucks or bunker barges. Some important features of this problem are that part of LNG will be evaporated during delivery and split deliveries are allowed at both import terminals and filling stations, which render the problem more intractable than those considered in most of the existing two-echelon vehicle routing studies. The objective is to find the optimal first-echelon and second-echelon delivery schemes to minimize the sum of the routing cost and boil-off cost. To solve the problem, we develop a customized branch-and-price-and-cut (BPC) algorithm incorporating a specialized labeling algorithm tailored to address the issues of LNG evaporation and split deliveries in solving the challenging pricing subproblems. To speed up the solution algorithm, we introduce some heuristic pricing strategies to quickly solve the pricing subproblems, and explore the (strong) k-path inequalities and subset-row inequalities to tighten the lower bound obtained by column generation. We conduct extensive numerical studies on simulation instances and a case study of LNG delivery in region along the Yangtze river, China to verify the effectiveness of the model and proposed algorithm. The numerical results demonstrate that our algorithm significantly outperforms CPLEX and the existing BPC algorithm on related topic, confirm the superiority of our integrated two-echelon solution method over its sequential solution counterpart, and illustrate that the locations of the production terminal and import terminals are highly related to the solution performance.

A heuristic with a performance guarantee for the commodity constrained split delivery vehicle routing problem

A heuristic with a performance guarantee for the commodity constrained split delivery vehicle routing problem

Partial dominance in branch-price-and-cut algorithms for vehicle routing and scheduling problems with a single-segment tradeoff

For many variants of vehicle routing and scheduling problems solved by a branch-price-and-cut (BPC) algorithm, the pricing subproblem is an elementary shortest-path problem with resource constraints (SPPRC) typically solved by a dynamic-programming labeling algorithm. Solving the SPPRC subproblems consumes most of the total BPC computation time. Critical to the performance of the labeling algorithms and thus the BPC algorithm as a whole is the use of effective dominance rules. Classical dominance rules rely on a pairwise comparison of labels and have been used in many labeling algorithms. In contrast, partial dominance describes situations where several labels together are needed to dominate another label, which can then be safely discarded. In this work, we consider SPPRCs, where a linear tradeoff describes the relationship between two resources. We derive a unified partial dominance rule to be used in ad hoc labeling algorithms for solving such SPPRCs as well as insights into its practical implementation. We introduce partial dominance for two important variants of the vehicle routing problem, namely the electric vehicle routing problem with time windows with a partial recharge policy and the split-delivery vehicle routing problem with time windows (SDVRPTW). Computational experiments show the effectiveness of the approach, in particular for the SDVRPTW, leading to an average reduction of 20% of the total BPC computation time, with savings of 30% for the more difficult instances requiring more than 600 s of computation time.

Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem

The split delivery vehicle routing problem (SDVRP) is a classic combinatorial optimization problem, which is usually solved using a heuristic algorithm. The ant colony optimization algorithm is an excellent heuristic algorithm that has been successfully applied to solve various practical problems, and it has achieved good results. However, in the existing ant colony optimization algorithms, there are issues with weak targeting of different customer selection strategies, difficulty in balancing convergence speed and global search ability, and a predisposition to become trapped in local optima. To solve these problems, this paper proposes an improved ant colony algorithm (IACA). First, in terms of customer point selection, the initial customer and noninitial customer selection strategies are proposed for different customers, and the adaptive selection threshold is designed. Second, in terms of pheromone processing, an initial pheromone distribution method based on a greedy strategy, a pheromone backtracking mechanism, and an adaptive pheromone volatile factor are proposed. Finally, based on the 2-opt local search method, vehicle path self-search and intervehicle path search are proposed to further improve the quality of the solution. This paper tests the performance of the IACA on datasets of different scales. The experimental results show that compared with the clustering algorithm, artificial bee colony algorithm, particle swarm optimization algorithm, traditional ant colony algorithm, and other algorithms, the IACA can achieve more competitive results. Specifically, compared to the path length calculated by other algorithms, the path length calculated by IACA decreased by an average of 1.58%, 4.28%, and 3.64% in small, medium, and large-scale tests, respectively.

Estimating optimal split delivery vehicle routing problem solution values

This paper explores the application of linear regression models to estimate the optimal solution value (i.e., the sum of tour lengths) for the Split Delivery Vehicle Routing Problem (SDVRP). We present novel models that integrate topological features along with the mean and standard deviation of feasible solution values, achieving an impressive accuracy with an error margin of approximately 3%. To obtain random feasible solutions for the SDVRP quickly, we propose a modified Clarke & Wright algorithm with split delivery (MCWSD). Our results demonstrate the potential of extending our earlier work to more complex routing problems, highlighting the importance of incorporating diverse features to obtain accurate approximations.

Penyelesaian Split Delivery VRP dengan Ant Colony Optimization (Studi Kasus: Pengiriman Produk di PT Sinarmas Distribusi Nusantara)

PT Sinarmar Distribusi distributes its products to all Distribution Center (DC) every day. Currently PT Sinarmas Distribution Nusantara uses a predetermined route every day using Colt Diesel Double vehicles with maximum transport capacity of 500 cartons. Currently the number of products carried by each vehicle never reaches its maximum carrying capacity. PT Sinarmas Distribusi Nusantara wants vehicle transport capacity to be used optimally. This route problem at PT Sinarmas Distribusi Nusantara can be defined as Split Delivery Vehicle Routing Problem (SDVRP). Ant Colony Optimization (ACO) is a metaheuristic that can be used to solve SDVRP. By using ACO the resulting route is always shorter than the current route and the number of vehicles used is smaller.

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

Cloud‐fog assisted human tracing and disaster evacuation framework

AbstractMany kinds of natural hazards and man‐made calamities have occurred in recent years, each of which has left a huge number of victims and has been challenging to deal with. The solution is an effective evacuation planning system, which is gaining the interest of governments, academic institutions, and industries all across the world. This study focuses on quick and organized evacuation from densely populated areas during disasters to decrease damage successfully. This research proposes a fog‐cloud‐assisted effective disaster evacuation framework. The data accumulation layer uses IoT, mobile networks, and GPS technologies to collect environmental and location‐based data to track the inhabitants. The fog layer is utilized for (i) disaster event detection and (ii) human tracing and crowd density analysis. A cloud layer makes it easier for an evacuation algorithm to produce an evacuation map that will point evacuees to the exit while computing a quick and safe path utilizing environmental and inhabitant information gathered from the fog. The findings reveal that the performance of Model A surpasses the split delivery vehicle routing problem model with the minimum demand of vehicles and with improvement of 38.1% average. Also, A* takes less time (18.3 s) than other state‐of‐the‐art techniques to find the best optimal route for evacuation. Implementation and performance analysis demonstrate the efficiency and effectiveness of the proposed framework.

Reinforcement learning for humanitarian relief distribution with trucks and UAVs under travel time uncertainty

Effective humanitarian relief operations are challenging in the aftermath of disasters, as trucks are often faced with considerable travel time uncertainties due to damaged transportation networks. Efficient deployment of Unmanned Aerial Vehicles (UAVs) potentially mitigates this problem, supplementing truck fleets in an impactful manner. To plan last-mile relief distribution in this setting, we introduce a multi-trip, split-delivery vehicle routing problem with trucks and UAVs, soft time windows, and stochastic travel times for last-mile relief distribution, formulated as a stochastic dynamic program. Within a finite time horizon, we aim to maximize a weighted objective function comprising the number of goods delivered, the number of different locations visited, and late arrival penalties. Our study offers insights into dealing with travel time uncertainty in humanitarian logistics by (i) deploying Unmanned Aerial Vehicles (UAVs) as partial substitutes for trucks, (ii) evaluating dynamic solutions generated by two deep reinforcement learning (RL) approaches – specifically value function approximation (VFA) and policy function approximation (PFA) – and (iii) comparing the RL solutions with solutions stemming from mathematical programming and dynamic heuristics. Experiments are performed on both Solomon-based instances and two real-world cases. The real-world cases – the 2015 Nepal earthquake and the 2018 Indonesia tsunami – are based on locally collected field data and real-world UAV specifications, and aim to provide practical insights. The experimental results show that dynamic decision-making improves both performance and robustness of humanitarian operations, achieving reductions in lateness penalties of around 85% compared to static solutions based on expected travel times. Furthermore, the results show that replacing half of the trucks with UAVs improves the weighted objective value by 11% to 56%, benefitting both reliability and location coverage. The results indicate that both the deployment of UAVs and the use of dynamic methods successfully mitigate travel time uncertainties in humanitarian operations.

A New Family of Route Formulations for Split Delivery Vehicle Routing Problems

We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the literature, the exact delivery quantities are not always explicitly known in this new family. The validity of these formulations is ensured by an exponential set of nonrobust constraints. Additionally, we explore a property of optimal solutions that enables us to determine a minimum delivery quantity based on customer demand and vehicle capacity, and this number is often greater than one. We use this property to reduce the number of possible delivery quantities in our formulations, improving the solution times of the computationally strongest formulation in the family. Furthermore, we propose new variants of nonrobust cutting planes that strengthen the formulations, namely limited-memory subset-row covering inequalities and limited-memory strong k-path inequalities. Finally, we develop a branch-cut-and-price (BCP) algorithm to solve our formulations enriched with the proposed valid inequalities, which resorts to state-of-the-art algorithmic enhancements. We show how to effectively manage the nonrobust cuts when solving the pricing problem that dynamically generates route variables. Numerical results indicate that our formulations and BCP algorithm establish new state-of-the-art results for the variant with time windows, as many benchmark instances with 50 and 100 customers are solved to optimality for the first time. Several instances of the variant without time windows are solved to proven optimality for the first time. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 306033/2019-4, 313220/2020-4, and 314088/2021-0], the Région Nouvelle Aquitaine, France [Grant AAPR2020A-2020-8601810], the Agence Nationale de la Recherche [Grant ANR-20-CE40-0021-01], the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 13/07375-0, 16/01860-1, and 19/23596-2], and the Paraíba State Research Foundation [Grants 261/2020 and 041/2023]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0085 .

Split Delivery Vehicle Routing Problem for Transportation - A Case Study

Split Delivery Vehicle Routing Problem for Transportation - A Case Study

An Improved Genetic Algorithm for the Granularity-Based Split Vehicle Routing Problem with Simultaneous Delivery and Pickup

The Split Vehicle Routing Problem with Simultaneous Delivery and Pickup (SVRPSDP) consists of two subproblems, i.e., the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP) and the Split Delivery Vehicle Routing Problem (SDVRP). Compared to the subproblems, SVRPSDP is much closer to reality. However, some realistic factors are still ignored in SVRPSDP. For example, the shipments are integrated and cannot be infinitely subdivided. Hence, this paper investigates the Granularity-based Split Vehicle Routing Problem with Simultaneous Delivery and Pickup (GSVRPSDP). The characteristics of GSVRPSDP are that the demands of customers are split into individual shipments and both the volume and weight of each shipment are considered. In order to solve GSVRPSDP efficiently, a Genetic-Simulated hybrid algorithm (GA-SA) is proposed, in which Simulated Annealing (SA) is inserted into the Genetic Algorithm (GA) framework to improve the global search abilities of individuals. The experimental results indicate that GA-SA can achieve lower total costs of routes compared to the traditional meta-algorithms, such as GA, SA and Particle Swarm Optimization (PSO), with a reduction of more than 10%. In the further analysis, the space utilization and capacity utilization of vehicles are calculated, which achieve 86.1% and 88.9%, respectively. These values are much higher than those achieved by GA (71.2% and 74.8%, respectively) and PSO (60.9% and 65.7%, respectively), further confirming the effectiveness of GA-SA. And the superiority of simultaneous delivery and pickup is proved by comparing with separate delivery and pickup. Specifically, the costs of separate delivery and pickup are more than 80% higher than that of simultaneous delivery and pickup.

A branch-and-cut embedded matheuristic for the inventory routing problem

This paper presents an improved version of the solution method that won the inventory routing problem track of the 12th DIMACS Implementation Challenge. The solution method is a branch-and-cut embedded matheuristic where a matheuristic is called every time a new primal solution is found in a branch-and-cut method. The matheuristic consists of a construction heuristic and an improvement heuristic. The construction heuristic uses a giant tour method and a shifting assignments method to generate a set of promising routes which, in turn, are combined into a feasible solution to the problem by solving a route-based mathematical program. The improvement heuristic then solves a series of extended route-based mathematical programs where clusters of customers may be inserted and/or removed from the routes of the initial feasible solution. We have, to the best of our knowledge, gathered all detailed results from previously published methods for the inventory routing problem and made this overview available online. Compared with these results, the proposed method found the best-known solution for 741 out of 878 multi-vehicle inventory routing instances, where 247 of them are strictly better than the previously best-known solutions. Furthermore, we prove optimality for 458 of these solutions. The proposed method is also able to find the best-known solution for 116 out of 226 benchmark instances for the split delivery vehicle routing problem, and improve three best-known solutions from the CVRPlib for the capacitated vehicle routing problem.

An Approximation Algorithm for k-Depot Split Delivery Vehicle Routing Problem

A multidepot capacitated vehicle routing problem aims to serve customers’ demands using a fleet of capacitated vehicles located in multiple depots, such that the total travel cost of the vehicles is minimized. We study a variant of this problem, the k-depot split delivery vehicle routing problem (or k-DSDVRP in short), for the situation where each customer’s demand can be served by more than one vehicle, and the total number of depots, denoted by [Formula: see text], is a fixed constant. This is a challenging problem with broad applications in the logistics industry, for which no constant ratio approximation algorithm is known. We develop a new approximation algorithm for the k-DSDVRP, ensuring an approximation ratio of [Formula: see text] and a polynomial running time for any fixed constant [Formula: see text]. To achieve this, we propose a novel solution framework based on a new relaxation of the problem, a cycle splitting procedure, and a vehicle assignment procedure. To further enhance its efficiency for practical usage, we adapt the newly developed approximation algorithm to a heuristic, which runs in polynomial time even when k is arbitrarily large. Experimental results show that this heuristic outperforms a commercial optimization solver and a standard vehicle routing heuristic. Moreover, our newly proposed solution framework can be applied to developing new constant ratio approximation algorithms for several other variants of the k-DSDVRP with [Formula: see text] being a fixed constant. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 71971177, 71725001, U1811462], Research Grants Council of Hong Kong SAR, China [Grant 15221619], and Guangdong Basic and Applied Basic Research Foundation [Grant 2023A1515030260]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2021.0193 . 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.2021.0193 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0193 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A New Exact Algorithm for Single-Commodity Vehicle Routing with Split Pickups and Deliveries

We present a new exact algorithm to solve a challenging vehicle routing problem with split pickups and deliveries, named as the single-commodity split-pickup and split-delivery vehicle routing problem (SPDVRP). In the SPDVRP, any amount of a product collected from a pickup customer can be supplied to any delivery customer, and the demand of each customer can be collected or delivered multiple times by the same or different vehicles. The vehicle fleet is homogeneous with limited capacity and maximum route duration. This problem arises regularly in inventory and routing rebalancing applications, such as in bike-sharing systems, where bikes must be rebalanced over time such that the appropriate number of bikes and open docks are available to users. The solution of the SPDVRP requires determining the number of visits to each customer, the relevant portions of the demands to be collected from or delivered to the customers, and the routing of the vehicles. These three decisions are intertwined, contributing to the hardness of the problem. Our new exact algorithm for the SPDVRP is a branch-price-and-cut algorithm based on a pattern-based mathematical formulation. The SPDVRP relies on a novel label-setting algorithm used to solve the pricing problem associated with the pattern-based formulation, where the label components embed reduced cost functions, unlike those classical components that embed delivered or collected quantities, thus significantly reducing the dimension of the corresponding state space. Extensive computational results on different classes of benchmark instances illustrate that the newly proposed exact algorithm solves several open SPDVRP instances and significantly improves the running times of state-of-the-art algorithms. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72222011, 71971090, 71821001, 72171112], by the Young Elite Scientists Sponsorship Program by CAST [Grant 2019QNRC001], and by the Research Grants Council of Hong Kong SAR, China [Grant 15221619]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.1249 .

A general variable neighbourhood search for the commodity constrained split delivery vehicle routing problem

A general variable neighbourhood search for the commodity constrained split delivery vehicle routing problem

Iterated clustering optimization of the split-delivery vehicle routing problem considering passenger walking distance

The user-oriented, demand-driven nature of customized shuttle bus (CSB) services forces operators to pay more attention to service quality. However, the bus route planning of CSB and other similar systems in established studies rarely took service quality into consideration while minimizing operating costs. This study proposed an open split-delivery weighted vehicle routing problem with iterated clustering (OSDWVRP-IC) to simultaneously optimize the route of bus and passenger walking distance. A max–min ant system (MMAS) algorithm is developed to solve the OSDWVRP-IC. The effectiveness of the proposed model is validated using a range of classical benchmark instance sets. The simulation results indicate that the algorithm proposed in this study sacrifices a very limited in-vehicle distance in exchange for a significant reduction in passenger walking distance.

A Multi Depot Multi Product Split Delivery Vehicle Routing Problem with Time Windows: A Real Cash in Transit Problem Application in Istanbul, Turkey

A Multi Depot Multi Product Split Delivery Vehicle Routing Problem with Time Windows: A Real Cash in Transit Problem Application in Istanbul, Turkey

Multi-Depot Routing with Split Deliveries: Models and a Branch-and-Cut Algorithm

We study the multi-depot split-delivery vehicle routing problem (MDSDVRP) that combines the advantages and potential cost savings of multiple depots and split deliveries and develop the first exact algorithm for this problem. We propose an integer programming formulation using a small number of decision variables and several sets of valid inequalities. These inequalities focus on ensuring the vehicles’ capacity limits and that vehicles return to their initial depot. As we show that the new constraints do not guarantee these aspects, our branch-and-cut framework also includes an efficient feasibility check for candidate solutions and explicit feasibility cuts. The algorithm that also uses a comparably simple, yet effective heuristic to compute high-quality initial solutions is tested on the MDSDVRP and two well-known special cases, the split-delivery vehicle routing problem (SDVRP) and the multi-depot traveling salesman problem (MDTSP). The results show that the new inequalities tighten the linear programming relaxation, increase the performance of the branch-and-cut algorithm, and reduce the number of required feasibility cuts. We report the first proven optimal results for the MDSDVRP and show that our algorithm significantly outperforms the state-of-the-art for the MDTSP while being competitive on the SDVRP. For the latter, 20 instances are solved for the first time, and new best primal and dual bounds are found for others. Funding: This work was supported by the Fundação para a Ciência e a Tecnologia [Project UIDB/04561/2020]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1179 .

General Edge Assembly Crossover-Driven Memetic Search for Split Delivery Vehicle Routing

The split delivery vehicle routing problem is a variant of the well-known vehicle routing problem, where each customer can be visited by several vehicles. The problem has many practical applications, but it is computationally challenging. This paper presents an effective memetic algorithm for solving the problem with a fleet of limited or unlimited vehicles. The algorithm features a general edge assembly crossover to generate promising offspring solutions from the perspective of assembling suitable edges and an effective local search to improve each offspring solution. The algorithm is further reinforced by a feasibility-restoring procedure, a diversification-oriented mutation, and a quality-and-distance pool updating technique. Extensive experiments on 324 benchmark instances indicate that our algorithm is able to update 143 best upper bounds in the literature and match the best results for 156 other instances. Additional experiments are presented to obtain insight into the roles of the key search ingredients of the algorithm. The method was ranked second in the SDVRP track at the 12th DIMACS Implementation Challenge on Vehicle Routing Problems. Funding: Support from the China Scholarship Council (CSC) [Grant 201906850087] for the first author is acknowledged.