Variant Of Vehicle Routing Problem Research Articles

A Multi‐Trip Vehicle Routing Problem With Release Dates and Interrelated Periods

ABSTRACTThis article proposes a new multi‐trip vehicle routing problem variant, originally motivated by a practical application, namely a car components distribution to repair centers (warehouses). The problem is named the multi‐trip vehicle routing with release dates and interrelated periods (MTVRP‐RDIP). The routes may start at different pre‐defined periods, called departure periods, and may have different durations. Thus, two routes that start at different periods may be active at the same period, leading to the so‐called interrelated periods. Moreover, a route may only start at a period if a vehicle is available, and the availability of the vehicle depends not only on the existing vehicles but also on the active routes at that time period. The clients are classified according to their importance and represent warehouses that require car components that are made available throughout the time horizon, thus leading to the consideration of release dates. Delays in satisfying client orders and not serving orders in the time horizon result in penalty costs that must be minimized. The objective to minimize also includes routing costs and vehicle utilization costs. Two metrics are defined to compute an order's delay, each leading to a different mixed integer linear model. Computational results showed that one model clearly outperforms the other and even this one is only suited to address the smallest instances. A matheuristic based on a rolling‐horizon process that iteratively solves the better‐performing model with fewer periods was designed to tackle the largest instances. The matheuristic can provide feasible solutions for all test instances in an efficient manner that are, on average, better than the ones provided by the model in most of the compared key performance indicators.

Collaborative vehicle routing for equitable and effective food allocation in nonprofit settings

Purpose Inspired by a food bank distribution operation, this paper aims to study synchronized vehicle routing for equitable and effective food allocation. The primary goal is to improve operational efficiency while ensuring equitable and effective food distribution among the partner agencies. Design/methodology/approach This study introduces a multiobjective Mixed Integer Programming (MIP) model aimed at addressing the complex challenge of effectively distributing food, particularly for food banks serving vulnerable populations in low-income urban and rural areas. The optimization approach described in this paper places a significant emphasis on social and economic considerations by fairly allocating food to food bank partner agencies while minimizing routing distance and waste. To assess the performance of the approach, this paper evaluates three distinct models, focusing on key performance measures such as effectiveness, equity and efficiency. The paper conducts a comprehensive numerical analysis using randomly generated data to gain insights into the trade-offs that arise and provide valuable managerial insights for food bank managers. Findings The results of the analysis highlight the models that perform better in terms of equity and effectiveness. Additionally, the results show that restocking the vehicles through the concept of synchronization improves the overall quantity of food allocation to partner agencies, thereby increasing accessibility. Research limitations/implications This paper contributes significantly to the literature on optimization approaches in the field of humanitarian logistics. Practical implications This study provides food bank managers with three different models, each with a multifaceted nature of trade-offs, to better address the complex challenges of food insecurity. Social implications This paper contributes significantly to social responsibility by enhancing the operational efficiency of food banks, ultimately improving their ability to serve communities in need. Originality/value To the best of the authors’ knowledge, this paper is the first to propose and analyze this new variant of vehicle routing problems in nonprofit settings.

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.

Two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization

The multi-echelon distribution strategy has been widely applied in city logistics systems. This study develops a mixed-integer linear programming model for a new variant of vehicle routing problem, namely, a two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization, in which customers are divided into multiple customer regions according to different geographical characteristics. The pickup and delivery activities with hard time windows are performed simultaneously by the same vehicles from depots to satellites in the first echelon and from satellites to customers in different customer regions in the second echelon. A vehicle speed function is developed for each echelon based on traffic conditions. The function depends on commuter traffic and urbanization level. Satellites with storage buffer capacities for split and consolidation are allowed. Thus, demand unloading, storage, and reloading are synchronized. Costs of transportation, loading/unloading, inventory, and environment during one complete distribution process are considered. A memetic algorithm (MA) is proposed including a split algorithm for chromosome decoding and a three-phase construction heuristic for initial population generation. Self-adaptive operators of crossover, mutation, and local search are designed, and a neighborhood route improvement strategy is devised that includes distance-related destroy, route-based destroy, distance-based greedy repair, and time-distance cluster repair operators. Results of different scales of numerical experiments and sensitivity analysis show the effectiveness of the model and MA by comparing it with an exact algorithm, CPLEX, and adaptive large neighborhood search.

Code and Data Repository for VRPSolverEasy: A Python Library for the Exact Solution of a Rich Vehicle Routing Problem

VRPSolverEasy is a Python package which provides a simple interface for VRPSolver, a state-of-the-art Branch-Cut-and-Price exact solver for vehicle routing problems (VRPs). The simplified interface is accessible for users without operations research background, meaning you do not need to know how to model your problem as an Integer Programming problem. As a price to pay for the simplicity, this interface is restricted to some standard VRP variants, which involve the following features and their combinations: capacitated vehicles customer time windows heterogeneous fleet multiple depots open routes optional customers with penalties parallel links to model transition time/cost trade-off incompatibilities between vehicles and customers customers with alternative locations and/or time windows To our knowledge, VRPSolver is the most efficient exact solver available for VRPs. Its particularity is to focus on finding and improving a lower bound on the optimal solution value of your instance. It is less efficient in finding feasible solutions but still can be better than available heuristic solvers for non-classic VRP variants.

VRPSolverEasy: A Python Library for the Exact Solution of a Rich Vehicle Routing Problem

The optimization community has made significant progress in solving vehicle routing problems (VRPs) to optimality using sophisticated branch-cut-and-price (BCP) algorithms. VRPSolver is a BCP algorithm with excellent performance in many VRP variants. However, its complex underlying mathematical model makes it hardly accessible to routing practitioners. To address this, VRPSolverEasy provides a Python interface to VRPSolver that does not require any knowledge of mixed integer programming modeling. Instead, routing problems are defined in terms of familiar elements, such as depots, customers, links, and vehicle types. VRPSolverEasy can handle several popular VRP variants and arbitrary combinations of them. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by Faperj [Grant E-26/202.887/2017] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 305684/2022-1]. 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.2023.0103 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0103 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

An adaptive large neighborhood search for the robust rig routing

In the oil and gas industry, there is a need for constructing auxiliary maintenance and storage buildings nearby exploration sites. As the initial stage for such constructing purposes, it is required to drill wells for construction piles. To this end, there is a fleet of mobile drilling rigs traveling from one exploration site to another, performing the work on drilling wells. For each site, we have a time window for completing all the work on drilling. To complete all the work among all the exploration sites in time, it may be necessary to allow several drilling rigs to perform work at the same site. Yet, in the real world, unforeseen circumstances can affect drilling time, and that, if disregarded, can lead to a disruption of the work plan. Thus, in this problem, we maximize possible deviations of drilling times from expected values when there is still a feasible solution to perform all well-drilling requests in time. At the same time, total traveling costs must be no more than a given threshold. It is a so-called threshold robustness approach. The described Drilling Rig Routing Problem (DRRP) differs from other well-studied variants of Vehicle Routing Problem (VRP) in that the work splitting affects the service time. There is a limited number of papers dealing with such problems and no papers about the robust formulation for them. This research proposes a mathematical model for the novel formulation of the DRRP with uncertainties and an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it. The destruction operators work either at the route, customer, or visit level. The reconstruction operators take into account a possibility to change the work partition. Computational results for the algorithm and Gurobi solver show the dominance of the ALNS scheme for medium- and large-sized instances.

Vehicle routing for customized on-demand bus services

This study investigates a variant of the Vehicle Routing Problem (VRP) for customized on-demand bus service platforms. In this problem, the platform plans customized bus routes upon receiving a batch of orders released by passengers and informs the passengers of the planned pick-up and drop-off locations. The related decision process takes into account some passenger-side time window-related requirements, walking limits, the availability and capacities of various types of buses. A mixed-integer linear programming model of this new VRP variant with floating targets (passengers) is formulated. To solve the model efficiently, a solution method is developed that combines the branch-and-bound and column generation algorithms and also includes embedded acceleration techniques such as the multi-labeling algorithm. Experiments based on real data from Dalian, China are conducted to validate the effectiveness of the proposed model and efficiency of the algorithm; the small-scale experimental results demonstrate our algorithm can obtain optimal results in the majority of instances. Additionally, sensitivity analysis is conducted, and model extensions are investigated, to provide customized bus service platform operators with potentially useful managerial insights; for example, a platform need not establish as many candidate stops as possible, a wide range of walking distance may not bring early arrival at destinations for customers, more mini-buses should be deployed than large buses in our real-world case. Moreover, the rolling horizon-based context and zoning strategies are also investigated by extending our proposed methodology.

Edge-Enhanced Attentions for Drone Delivery in Presence of Winds and Recharging Stations

Existing variants of vehicle routing problems have limited capabilities in describing real-world drone delivery scenarios in terms of drone physical restrictions, mission constraints, and stochastic operating environments. To that end, this paper proposes a specific drone delivery problem with recharging (DDP-R) characterized by directional edges and stochastic edge costs subject to wind conditions. To address it, the DDP-R is cast into a Markov decision process over a graph, with the next node chosen according to a stochastic policy based on the evolving observation. An edge-enhanced attention model (AM-E) is then suggested to map the optimal policy via the deep reinforcement learning (DRL) approach. The AM-E comprises a succession of edge-enhanced dot-product attention layers and is designed with the aim of capturing the heterogeneous node relationship for DDP-Rs by incorporating adjacent edge information. Simulations show that edge enhancement facilitates the training process, achieving superior performance with less trainable parameters and simpler architecture in comparison with other deep learning models. Furthermore, a stochastic drone energy cost model in consideration of winds is incorporated into validation simulations, which provides a practical insight into drone delivery problems. In terms of both nonwind and windy cases, extensive simulations demonstrate that the proposed DRL method outperforms state-of-the-art heuristics for solving DDP-Rs, especially at large sizes.

A systematic literature review of the vehicle routing problem in reverse logistics operations

The increasing rate at which goods ranging from food products to electronic products are consumed has led to rapidly increasing waste worldwide. This huge amount of waste poses an environmental threat but can have economic value. Thus, governments argue that this waste should be collected and included in recycling processes. However, collecting these wastes can pose some logistical problems, such as the large amounts of carbon emissions created and the need for transportation plans to collect these costly wastes. Many researchers and industrial practitioners have developed vehicle routing systems for reverse logistics operations to address and model these logistical challenges. To date, few efforts have been made to systematically review vehicle routing models in the reverse logistics process. This paper provides a literature review of 109 published articles in international scientific journals related to the vehicle routing problem in the reverse logistics domain between 2000 and 2022. Six carefully designed questions are proposed and answered in this article regarding modelling approaches, solution techniques, vehicle routing problem variants, sustainability aspects, waste types, and future research opportunities. According to the results of the review, some important points were highlighted and discussed.

Ant Colony Optimization Ant Colony Optimization untuk menyelesaikan perutean distribusi Snack dengan Vehicle Routing Problem

One of the main challenges faced by the community in their daily activities is the problem of transportation. Transportation of goods and services is an important topic that attracts the attention of the business world today. Closely related to the transportation sector is the Vehicle Routing Problem (VRP).
 The VRP variant used in this study is the Capacitated Vehicle Routing Problem (CVRP) which uses the capacity limit of the vehicle used. CVRP is used to minimize the distribution route of goods at IKM Snack FITRIA located in Sidoarjo. The problem of distribution at IKM Snack FITRIA is how to manage the route of shipping goods from the warehouse to a number of shops/customers scattered in various places in Surabaya, Sidoarjo and Gresik efficiently. This research includes planning the route of each transport vehicle in delivering products to consumers spread over several points originating from one depot. The vehicle in one day sends goods from the warehouse to the customer with one delivery. While the algorithm used is Ant Colony Optimization (ACO). ACO is used because it is able to show the best route for the optimal solution of 98%. And get a minimum total mileage with a low level of variance.

Strategi Optimasi Jaringan Distribusi Sampah Organik di Tangerang Selatan

South Tangerang City is the youngest city that officially separated from the Tangerang Regency in 2008. Area of South Tangerang City 147,19 km2 or 1,63 percent from the area of Banten Province with the widest area of Pondok Aren subdistrict with an area of 2.988 hectares. While administratively, South Tangerang City has 7 sub-districts namely Pamulang, Setu, Ciputat, East Ciputat, Serpong, North Serpong and Pondok Aren, and has 54 villages. Optimizing the distribution network of organic waste supply chain can be formulated in Vehicle Routing Problem (VRP) model. Variants of VRP include Capacitated Vehicle Routing Problem (CVRP) can be used as a model in optimizing the waste transport route and the determination of the fastest route for the transport process of organic waste in all intermediate transfer points spread in South Tangerang city. The results of this research formulate some models of optimization organic waste transport routes in each sub-district in South Tangerang city. As in Setu district there is one optimum route, Serpong district there are 7 optimum route, Pamulang district have 6 optimum route, Ciputat district have 3 optimum route, East Ciputat District have 1 optimum route, Pondok Aren district have 4 optimum route, North Serpong there are 2 optimum routes.

Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems

Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem’s constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.

A genetic algorithm model for optimizing vehicle routing problems with perishable products under time-window and quality requirements

The Vehicle Routing Problem (VRP) has recently piqued the interest of researchers seeking to improve the efficiency and efficacy of the transportation system in distributing commodities. Many scholars have proposed using a heterogeneous fleet in vehicle routing to minimize distribution costs further. When perishable items need to be distributed at numerous demand points during specific time intervals, the situation becomes more difficult. This paper discusses this variant of VRP and the restriction on accepting products with a minimum stated quality level. This research aims to create and optimize a mathematical model that incorporates the quality issue of a perishable commodity into the distribution process. The given product’s worth is decreasing as its quality deteriorates. This problem is mathematically represented as a Mixed Integer Non-Linear Programming Problem (MINLP). A Genetic Algorithm-based heuristic is also recommended due to the computational complexity required in applying the model to solve real-world situations. The proposed approach is used to solve numerical cases and perform sensitivity analysis.

Time window optimization for attended home service delivery under multiple sources of uncertainties

We consider a vehicle routing problem variant to optimize time window assignments together with vehicle routing and scheduling decisions, under the uncertainties of trip time, service time and possible customers’ cancellations. We minimize the expected cost of vehicles’ overtime, idleness, and customer waiting, when also allowing to add new customers to existing schedules. We formulate a two-stage stochastic mixed-integer programming model using finite samples of the uncertain parameters, where in the first stage, we optimize vehicle routes and assign service time windows to customers, and in the second stage, we construct a linear program to compute the resultant undesirable cost given routes and time windows. We also propose a re-optimization method and an insertion-based linear program for accommodating real-time requests in a rolling horizon way for dynamic operations. To speed up computation, we further decompose the problem into three phases and propose Assignment–Routing–Scheduling heuristics. We first design three clustering algorithms based on spatial similarities to assign customers to vehicles, and then combine the nearest-neighbor and smallest-variance rules to decide the route for each vehicle. Finally, we cast the scheduling part as a Newsvendor problem variant and apply inventory approximations to derive closed-form solutions for determining time windows. We conduct numerical studies on diverse instances generated using both well-established benchmark data sets and Ford’s mobile service data, to compare different approaches and demonstrate the benefits of allowing flexible time-window assignments.

Hybrid Genetic Algorithms for the Asymmetric Distance-Constrained Vehicle Routing Problem

We aim to suggest a simple genetic algorithm (GA) and other four hybrid GAs (HGAs) for solving the asymmetric distance-constrained vehicle routing problem (ADVRP), a variant of vehicle routing problem (VRP). The VRP is a difficult NP-hard optimization problem that has numerous real-life applications. The VRP aims to find an optimal tour that has least total distance (or cost) to provide service to n customers (or nodes or cities) utilizing m vehicles so that every vehicle starts journey from and ends journey at a depot (headquarters) and visits every customer only once. The problem has many variations, and we consider the ADVRP for this study, where distance traveled by every vehicle must not exceed a predefined maximum distance. The proposed GA uses random initial population followed by sequential constructive crossover and swap mutation. The HGAs enhance the initial solution using 2-opt search method and incorporate a local search technique along with an immigration procedure to obtain effective solution to the ADVRP. Experiments have been conducted among the suggested GAs by solving several restricted and unrestricted ADVRP instances on asymmetric TSPLIB utilizing several vehicles. Our experiments claim that the suggested HGAs using local search methods are very effective. Finally, we reported a comparative study between our best HGA and a state-of-the-art algorithm on asymmetric capacitated VRP and found that our algorithm is better than the state-of-the-art algorithm for the instances.

Metaheuristic, models and software for the heterogeneous fleet pickup and delivery problem with split loads

This paper addresses a rich variant of the vehicle routing problem (VRP) that involves pickup and delivery activities, customer time windows, heterogeneous fleet, multiple products and the possibility of splitting a customer demand among several routes. This variant generalizes traditional VRP variants by incorporating features that are commonly found in practice. We present two mixed-integer programming models and propose a metaheuristic based on Adaptive Large Neighborhood Search for the addressed problem. Additionally, to facilitate the use of the proposed approaches in real-world decision-making, we develop an open-source, publicly available web interface that allows one to set and solve VRP variants with the mentioned features. Computational experiments using benchmark instances with up to 150 customers show that the approaches can be used to obtain good-quality solutions in a reasonable time frame in practice.

Implementation of the ACS-RVND algorithm on the VRP variant and its application to distribution optimization

Distribution optimization has an important role to distribute products to consumers. The selection of the right route will have an impact on the distribution process resulting in minimal costs. The application of graph theory that can be used to determine the optimum route in the distribution process is the study of the Vehicle Routing Problem (VRP) variant. The VRP variants discussed in this article are MDVRP and VRPTW. The method used to solve the VRP variant of this article is the ACS-RVND algorithm. The ACS-RVND algorithm consists of several main stages, namely the initial solution formation stage using the ACS algorithm, the solution improvement stage using the RVND procedure and the acceptance criteria stage. The data needed for the application of the ACS-RVND algorithm in solving the distribution optimization problem of MDVRP cases are the number of depots, the number of customers, the capacity of the vehicle, the number of ants, the number of iterations, the number of customer requests and the distance between customers. While in the case of VRPTW data multiple depots are replaced by time windows depot and service time. The results of solving distribution optimization problems in the form of the route, the total distance traveled and the result of the route in the graph model. The performance of the ACS RVND algorithm can be compared with the performance of the ant colony optimization (ACO) algorithm and the Hybrid Ant Coloy Optimization (HACO) algorithm. Analysis of the results using several dataset test cases showed that the ACS RVND algorithm on MDVRP obtained a better solution than the ACO algorithm and the ACS RVND algorithm on VRPTW was better than the Hybrid Ant Coloy Optimization (HACO) algorithm when viewed from the total distance distribution route.

MODEL OF VEHICLE ROUTING PROBLEM WITH SPLIT DELIVERY, MULTI TRIPS, MULTI PRODUCTS AND COMPARTMENTS FOR DETERMINING FUEL DISTRIBUTION ROUTES

The industrial development in Indonesia encourages companies to have high sensitivity in competing to meet consumer demands promptly by considering minimum distribution costs. One of the factors that can affect distribution costs is route determination. Determining the distribution route is the Vehicle Routing Problem (VRP). The purpose of VRP is to arrange the order of distribution routes to produce a minimum total distance. This study aims to determine the fuel distribution route at TBBM Rewulu in one delivery period to obtain the optimal distribution route and minimize the vehicle mileage. Delivery is carried out using three types of tanker trucks with heterogeneous capacities. This study uses a mathematical model of Mixed Integer Linear Programming (MILP) by considering split delivery, multi trips, multi-products, and compartments.The branch and bound method in the LINGO solver has been used to solve this problem. This model was tested on a simple case using data of 8 customers with different distances and demand shipped by truck. The results obtained indicate that no boundaries are violated, and all consumers are served. The mathematical model built is still general, so it can solve similar cases. A model can be developed for further research by adding VRP variants such as time windows and adding the product types to represent the entire existing system.

VRP variants applicable to collecting donations and similar problems: A taxonomic review

This paper presents a taxonomic review of Vehicle Routing Problem (VRP) with Time Windows (VRPTW), Pick-up and Delivery Problem (PDP), and Periodic Vehicle Routing Problem (PVRP). We focus on the problems of collection goods and similar. The applications of these models are typical like found in the literature; however, not applications specifically about collecting donations were found. Because of concern for the environment, social equity, and business efficiency, specific research fields related to green and reverse logistics have arisen; thus, optimization of waste (second-hand goods, food, recyclable/no recyclable waste, etc.) collection routes gain interest. In the literature reviewed, we found several VRP models of goods collection applied to picks-up of returned items, End-of-Life (EOL) products, Municipal Solid Waste collection (MSW), and Waste Collection Problem (WCP). The primary purpose of this paper is to structure the taxonomy of VRPTW, PDP and PVRP problems applicable to collecting donations according to its features, solution methods, and mathematical formulation. Likewise, provide the reader with an outline orderly and differentiated from the VRP models associated with pick up items and delivery orders (VRPPD), backhauling customers (VRPB), collection waste, and similar problems to propose our problem. For clarity, Appendix A includes the acronym used in these types of problems. This paper is part of a larger research project called “CVRPTW model applied to collecting food donations,” intending to contribute to a new perspective on the routing problems little explored.