Split Pickup Research Articles

Nested column generation for split pickup vehicle routing problem with time windows and time-dependent demand

This study attempts to solve a split pickup vehicle routing problem with time windows and time-dependent demand. This is a vehicle routing problem in which demand is generated at different constant rates for different customers, and vehicles are allowed to pick up demand during the demand generation process. In this problem, the pickup time determines the quantity of demand that can be picked up, and a partial pickup is permitted during a single visit. The problem is formulated into a mixed-integer nonlinear programming model, and a sequence-extended network is designed to represent the relationship between multiple pickups. Because of the interdependences of time, load, and cost in the pricing subproblem, the classic labelling algorithm with weak dominance rules is ineffective, therefore, a nested column generation-based branch-and-price-and-cut algorithm is proposed to tackle the problem. The nested structure allows these trade-offs to be resolved in a lower-level column generation, and it can be applied to other interdependent routing problems. The computational results show that the proposed algorithm is effective in obtaining optimal solutions for small- and medium-scale instances within a reasonable time limit.

Industry 4.0 in waste management: An integrated IoT-based approach for facility location and green vehicle routing

The increasing production of solid waste rate in urban areas plays a critical role in sustainable development. To mitigate the adverse effects of waste and enhance waste management efficiency, this paper introduces a holistic approach that notably reduces the overall cost while mitigating social and environmental impacts. Central to the system's efficacy is the critical process of waste sorting, which enhances the output value of the waste management system. While previous studies have not extensively addressed simultaneous waste collection and sorting, this paper provides an innovative integrated framework. This approach Integrates waste collection with various bins, followed by their transfer to separation centers. At these centers, waste is categorized into organic and non-organic varieties, which are then dispatched to a recovery center at the second level. In the context of optimizing the routes at both levels, this paper presents a green, multi-objective location-allocation model. This model is designed to optimize the number and location of separation center facilities. Since the routing problem is influenced by the facility location model, it is addressed as a multi-depot green vehicle routing problem, integrating real-time information from IoT-equipped bins. This paper also proposes the vehicle routing problem with a split pickup, aiming to minimize cost, CO2 emissions, and visual pollution. The developed mathematical models formulate the proposed problem and it is solved by the GAMS optimization software, to apply an exact method, while Social Engineering Optimization and Keshtel algorithms are deployed to solve the routing problem for larger sizes. The proposed approach offers a comprehensive and sustainable solution to waste management, filling crucial gaps in current research and practice.

MULTI-COMPARTMENT VEHICLES FOR SPLIT PICK-UP AND SPLIT DELIVERY PROBLEM WITH TIME WINDOW

In this article, we'll look at multi-compartment vehicles, which collect goods from suppliers and deliver them to different customers who place large orders. Because some products are incompatible with each other, these goods cannot be transported by single-compartment vehicles. In addition, because customers can place large orders, some suppliers and/or customers may be visited several times by different vehicles. In this work, the aim is to satisfy a group of customers while respecting the constraints linked to the capacity of each compartment and each type of product, and to ensure that each supplier is visited before the customer. Our first step is to model our problem mathematically and then solve it using an approximate method. Given its complexity, we use the genetic algorithm to solve the problem of split pick-up and delivery with time windows by multi-compartment vehicles. Our model allows us to determine a minimum distance and a minimum cost using a reasonable number of vehicles.

A multi-depot vehicle routing problem with time windows, split pickup and split delivery for surplus food recovery and redistribution

The problem faced by the food banks operating on the front-end model is the collection of surplus food from donation points and re-distribution of it to the demand points using a fleet of vehicles available at different volunteer locations/depots within specified time windows. Further, due to the limited vehicle capacity, demand splitting is allowed at the pickup as well and delivery points. Therefore, this problem can be seen as a rich variant of the vehicle routing problem (VRP) and named as a multi-depot VRP with time windows, split pickup and split delivery (MDVRP-TW-SP-SD). The problem is to determine the optimal number of vehicles from each depot to be hired and their optimal routes (sequence for visiting pickup and demand nodes) such that the total cost of hiring the vehicles, routing cost and penalty for unmet demand are minimized and it is formulated as a mixed-integer programming problem. To the best of our knowledge, this is the first attempt to formulate the MDVRP-TW-SP-SD. To efficiently and effectively solve the problem, an elitist GA and a GA hybridized with the local search are proposed. The performance of the proposed algorithms is tested through extensive computational experiments carried out on 180 modified benchmark problem instances from the literature. The results of computational experiments show the superiority of the GA hybridized with 3-opt local search. A case of the Robin Hood Army operating in the Lucknow city of India is also presented to demonstrate the applicability of the proposed model to practice.

Intelligent pickup and delivery collocation for logistics models

In the context of sharing economy, logistics companies have begun to adopt a new collection and distribution model based on external vehicles, and external vehicles are used to provide customers with collection/distribution services. A kind of Multi-Vehicle Split Pickup and Delivery Problem with Time Windows (MVSPDPTW) is studied in the paper. The minimum total length of the vehicle’s travel path is the objective function, and a mixed-integer linear programming model is established. A high-efficiency Tabu Simulated Annealing (TSA) algorithm is proposed. Two new neighborhood search operators are designed in the algorithm, they are used to repair the violation of capacity constraints and the operation of car replacement. In the method, the neighborhood search range is expanded and the algorithm is avoided from falling into a local optimum. In addition, a taboo mechanism and a penalty mechanism for violation of constraints are added to the algorithm, the effective tailoring of the search space is realized and the algorithm’s global optimization ability is improved. Finally, a large number of simulation experiments were performed on the algorithm based on the Solomon data set and the constructed simulation data set, and the effectiveness of the algorithm is verified in the experiments.

Improved ant colony optimization for the vehicle routing problem with split pickup and split delivery

Improved ant colony optimization for the vehicle routing problem with split pickup and split delivery

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 .

The two-flight low risk helicopter transportation problem under the split pickup scenario

The paper considers a special class of routing problems with the objective of minimizing the passengers risk. A major area of application of the low risk models is helicopter transportation widely used in the petroleum industry. In general, the total risk is considered to be proportional to the number of passengers exposed to landings and takeoffs during several multi-leg flights. We give a review of most of the studied models and demonstrate their links with the known problems of combinatorial optimization, such as the minimum latency problem, the multiple deliverymen problem, single machine and parallel machine scheduling, etc. In this paper, we focus on the problem of minimizing total risk, provided that the pickup from a number of locations is performed by two flights, and it is allowed that a location is visited by both flights, splitting the pickup demand. We show that the problem in NP-hard and admits a pseudopolynomial-time dynamic programming algorithm. We also develop a fully polynomial-time approximation scheme and a fast 5/4-approximation algorithm. The results of computational experiments with our algorithms are reported.

Utilizing the Internet of Things (IoT) to address uncertain home health care supply chain network

Generally, Home Health Care (HHC) consists of a medical team that serves patients in their own homes and carries out various medical services, such as taking biological samples and administering medicine. Aging trends in developing countries, and the growing tendency of the elderly to receive healthcare services in their own homes, leads to increasing demand for such services that outgrow those available in hospitals, healthcare personnel, and other resources. Therefore, HHC services and their associate demand rates are increasing dramatically. A major opportunity normally ignored in this regard is the applicability of the Internet of Things (IoT) systems to facilitate this practice. In this work, a two-phased approach is proposed to 1) identify the potential patients and 2) collect their biological samples and send them to be analyzed. Green Split Pick-up Vehicle Routing Problem (GSPVRP) and IoT concept are employed to address the patients in both sub-models. The proposed model is investigated by data from a real-world case study in Montreal, Canada, and solved using four multi-objective metaheuristic algorithms. An extensive analysis of the results revealed that utilizing the IoT system contributes to maximizing the overall occupancy rate of the vehicles and can effectively optimize the number of trips, hence minimizing total costs and greenhouse gas emissions.

Multi-Parking Lot and Shelter Heterogeneous Vehicle Routing Problem With Split Pickup Under Emergencies

The vehicle rescue process for individuals in residential areas in disaster scenarios is a typical vehicle routing problem (VRP). However, most studies do not consider the factor of individual mobility. In residential areas, there are two types of individuals: individuals with high mobility and individuals with low mobility, such as the elderly. To improve the evacuation efficiency, besides ordinary vehicles, special vehicles equipped with wheelchairs and volunteers are also in great need. Thus, evacuation vehicles should consist of a heterogeneous fleet. Vehicles depart from parking lots, arrive at residential areas to pick up individuals, and then transport them to shelters. In other words, the origin and destination are different, but they are viewed as the same in classical VRP. Each residential area can be served directly by vehicles departing from parking lots or by vehicles that have already served others, which means demands can be split. All these make the VRP in emergency rescue more complicated than classical VRP. Therefore, we propose an integer liner program model – multi-parking lot and shelter heterogeneous vehicle routing problem with split pickup (MPSHVRPSP) model, which includes matching constraints of individuals and vehicles to satisfy the demands of different types of individuals, and considers the selectivity of parking lots and shelters too. We provide a Tabu Search (TS) algorithm with diversification strategy to solve the model and ensure the high quality of solution. A lot of experiments are carried out on various instances. Our results show that MPSHVRPSP can be applied to efficient evacuation of complicated scenarios that satisfies the demands of all individuals in residential areas. Besides, it is more reasonable compared with classical VRP, and TS can also obtain a satisfactory solution in less time. Furthermore, sensitivity analysis is conducted on factors that may affect the result of objective function.

Green Inventory Routing Problem using Hybrid Genetic Algorithm

Carbon dioxide (CO2) is known as one of the largest sources of global warming. One of the ways to curb CO2 emissions is by considering the environmental aspect in the supply chain management. This paper analyses the influence of carbon emissions on the Inventory Routing Problem (IRP). The IRP network consists of a depot, an assembly plant and multiple suppliers. The deterministic demands vary and are determined by the assembly plant. Fixed transportation cost, fuel consumption cost and inventory holding cost are used to evaluate the system’s total cost in which fuel consumption cost is determined by fuel consumption rate, distance, and fuel price. Backordering and split pick-up are not allowed. The main purpose of this study is to analyze the distribution network especially the overall costs of the supply chain by considering the CO2 emissions as well. The problem is known as Green Inventory Routing Problem (GIRP). The mixed-integer linear programming of this problem is adopted from Cheng et al. wherein this study a different Hybrid Genetic Algorithm is proposed at mutation operator. As predicted, GIRP has a higher total cost as it considered fuel consumption cost together with the transportation and inventory costs. The results showed the algorithm led to different sequences of routings considering the carbon dioxide emission in the objective function.

A routing and scheduling problem for cross-docking networks with perishable products, heterogeneous vehicles and split delivery

Cross-docking is an effective logistics strategy that has long been employed in supply chains with perishable products, where short processing time of goods is required. In this paper, a new multi-objective mixed-integer programming (MIP) model is proposed for scheduling and routing of heterogeneous vehicles carrying perishable goods across multiple cross-docking systems. Inspired by the actual business operations of a large supermarket chain, multiple cross-docks with simultaneous split pick-up and delivery tasks are considered, each of which processing either general or perishable products. In addition, all pick-up/delivery (P/D) requests for perishable products have a deadline that must be met. The main objectives of the developed model are to reduce distribution costs, accelerate distribution processing time, and maximize the cross-docking network’s capacity utilization rate. To overcome the complexity of the formulated problem, a novel hybrid solution method, namely AUGMECON2-VIKOR is developed and used in the case-study. The results reveal that AUGMECON2-VIKOR outperforms AUGMECON2, particularly when a larger number of grid points are considered in the proposed solution algorithm.

Sustainable maritime crude oil transportation: a split pickup and split delivery problem with time windows

This paper studies a novel sustainable vessel routing problem modeling considering the multi-compartment, split pickup and split delivery, and time windows concepts. In the presented problem, oil tankers transport crude oil from supply ports to demand ports around the globe. The objective is to find ship routes, as well as port arrival and departure times, in a way that minimizes transportation costs. As a second objective, we considered the sustainability aspect by minimizing the vessel energy efficiency operational indicator. Multiple products are transported by a heterogeneous fleet of tankers. Small realistic test instances are solved with the exact method.

A route decomposition approach for the single commodity Split Pickup and Split Delivery Vehicle Routing Problem

We address a single commodity Pickup and Delivery Vehicle Routing Problem from the literature. A network of customer nodes is given with both travel times and costs. A fleet of vehicles of limited capacity is exploited to satisfy node demands, and a set of routes must be found such that the vehicle capacities are never exceeded, each route does not exceed time resource, and cost is minimized. The demands of both pickup and delivery nodes can be split, and each node can be visited more than once. We provide new theoretical insights. We propose a new formulation where routes are decomposed into sequences of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We introduce valid inequalities, and design a branch-and-price algorithm, exploiting ad hoc pricing routines and branching strategies, and embedding a rounding heuristic to speed up pruning. An extensive experimental analysis shows our method to offer simultaneously more modelling flexibility and more computational effectiveness than previous attempts from the literature. Our investigation opens also interesting insights into the use of route decomposition strategies.

A branch and price approach for the Split Pickup and Split Delivery VRP

In this paper we address a Pickup and Delivery Vehicle Routing Problem where the demands of both pickup and delivery nodes can be split between several vehicles. We investigate a new formulation where the route of each vehicle is decomposed into a sequence of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We implement a branch-and-price algorithm exploiting column generation procedures that dynamically generates clusters to obtain improved dual bounds, and ad hoc branching strategies to achieve integrality.

Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study

<div data-canvas-width="542.172"><p>The well-known Vehicle Routing Problem (VRP) is to find proper sequence of routes in order to minimize transportation costs. In this paper, a mixed-integer programming model is presented for a food distributer company and the model outputs are to determine the optimal routes and amount of pickup and delivery. In the objective function, the costs of transportation, holding, tardiness and earliness are considered simultaneously. The proposed model with respect to real conditions is multi-period and has two different time periods: one for dispatching vehicles to customers and suppliers and the other for receiving customers’ orders. Time window and split pickup and delivery are considered for perishable products. The proposed model is nonlinear and will be linearized using exact techniques. At the end, model is solved using GAMS and the sensitivity analysis is performed. The results indicate that the trend of changes in holding and transportation costs in compared to tardiness and earliness costs are closed together and are not so sensitive to demand changes.</p></div>

Alternative approaches to the crude oil tanker routing and scheduling problem with split pickup and split delivery

• We solve two routing and scheduling problems with split pickup and split delivery. • Goal is to identify the most promising formulation for a column generation approach. • The discrete split model provides quicker results but less solution quality. • The arbitrary split model provides better results but cannot solve large instances. • A simplified combined version serves best for a column generation approach. The crude oil tanker routing and scheduling problem with split pickup and split delivery is a maritime transportation task where an industrial operator needs to ship different types of crude oil from production sites to oil refineries. The different crude oils are supplied and demanded in many ports in certain time windows. Pickup and delivery quantities are known in advance but no pairing of pickup and delivery needs to be predefined and can be decided together with shipment quantities during optimization. Pickup and delivery quantities may be split arbitrarily among the ships in the fleet. We compare two alternative path flow model approaches to investigate their degree of applicability in a column generation setup. For this purpose we apply route pregeneration prior to optimization. The first approach uses continuous decision variables for pickup and delivery to decide on shipment quantities. In the considerably shorter second formulation cargo quantities are discretized and included into the paths. The second approach is capable to solve larger instances and is more efficient in terms of computational performance, however solution quality may decrease due to the discretization.

Column generation heuristics for ship routing and scheduling problems in crude oil transportation with split deliveries

We propose a column generation based heuristic algorithm to solve a ship routing and scheduling problem for crude oil transportation with split deliveries. The problem is to find an optimal assignment and sequence and loading volume of demand simultaneously in order to minimize the total distance satisfying the capacity of tankers. The problem can be considered as a multi-product heterogeneous fleet split pickup ship routing problem with finite capacity and loading constraints. An efficient heuristic algorithm based on the column generation method is developed to generate a feasible solution taking into account of practical constraints. The performance of the proposed method is compared with the branch and bound algorithm and that of human operators. Computational results demonstrate the effectiveness of the proposed algorithm for a real case.

Nested column generation applied to the crude oil tanker routing and scheduling problem with split pickup and split delivery

AbstractThe split pickup split delivery crude oil tanker routing and scheduling problem is a difficult combinatorial optimization problem, both theoretically and practically. However, because of the large expenses in crude oil shipping it is attractive to make use of optimization that exploits as many degrees of freedom as possible to save transportation cost. We propose a nested column generation algorithm for this particular split pickup split delivery problem which bears several complexities such as a heterogeneous fleet, multiple commodities, many‐to‐many relations for pickup and delivery of each commodity, sequence dependent vehicle capacities, and cargo quantity dependent pickup and delivery times. Our approach builds on a branch‐and‐price algorithm in which the column generation subproblems are solved by branch‐and‐price themselves. We describe our implementation in the branch‐cut‐and‐price framework SCIP and give computational results for realistic test instances. The high quality schedules we obtain for these instances improve on those in previous studies. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Maritime crude oil transportation – A split pickup and split delivery problem

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pre-generation for this model. The results indicate possible simplifications and stimulate further research.