Multi-trip Vehicle Routing Problem Research Articles

An exact algorithm for the multi-trip vehicle routing problem with time windows and multi-skilled manpower

Motivated by the challenges of non-emergency patient transportation services in the healthcare industry, this study investigated a multi-trip vehicle routing problem incorporating multi-skilled manpower with downgrading. We aimed to find an optimal plan for vehicle routing and multi-skilled manpower scheduling in tandem with the objective of minimizing the total cost, including travel and staff costs, without violating time windows and lunch break constraints. To address this, two mathematical models were formulated: an arc-flow model and a trip-based set-covering model. In addition, a branch-and-price-and-cut algorithm, based on the set-covering model, was proposed to solve practical-scale instances. To determine the feasibility of the integer solutions, we introduce a feasibility check model. To address the multi-trip characteristics of the proposed problem, a novel two-phase column generation algorithm was introduced to solve the subproblem. This approach differs from traditional one-phase labeling algorithms and involves a tailored labeling algorithm for obtaining non-dominated labels in the first phase and a strategy to identify the trip with the minimum reduced cost for each label in the second phase. Furthermore, novel and efficient staff-based inequalities were developed by improving the k-path inequalities. Extensive numerical experiments were conducted to demonstrate the solution performance of the proposed algorithm and reveal managerial insights for non-emergency ambulance operations. The results demonstrate that our algorithm can successfully solve instances with up to 50 patients to optimality within two hours. Moreover, we demonstrated the value of jointly optimizing vehicle routing and staff planning, which can result in significant cost savings of up to 19.4%.

An Iterated Local Search Heuristic for the Multi-Trip Vehicle Routing Problem with Multiple Time Windows

This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success.

An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station

This paper introduces a vehicle routing problem that simultaneously considers multiple trips, time windows, and a capacitated unloading station. This problem is a generalization of the multi-trip vehicle routing problem with time windows, which determines a set of least-cost vehicle routes to fulfill all customer demands while respecting the constraints of vehicle capacity and time windows. Due to restricted resources (e.g., equipment and labor force) at the depot, vehicles may need to wait in a queue for being unloaded when they arrive. This unloading capacity constraint significantly complicates the problem, as it causes a trip to involve three stages—traveling, waiting, and unloading. We formulate this problem as an arc flow model and a trip-based set partitioning model, where the latter is solved by a branch-price-and-cut (BPC) algorithm. To improve the computational aspect of the BPC framework, a two-phase column generation (CG) algorithm is designed. First, a bidirectional labeling algorithm is tailored to solve the pricing problem, where two accelerating strategies are employed to speed up the resolution process. Meanwhile, k-path inequalities and limited-memory subset row inequalities are utilized to tighten the linear relaxation of the master problem. Computational results based on the instances adapted from the well-known Solomon’s benchmark show that the developed BPC algorithm can solve most instances within 50 customers to optimality in a short time frame and some instances of 100 customers to optimality within a 3-hour time limit. Moreover, our BPC algorithm performs better than exact algorithms in the literature for similar problem variants in both solution quality and computing time.

GIS-Based Optimization for Gas Distribution Route Design: A Case Study of PT Gagas Energi Indonesia

PT Gagas Energi Indonesia is a company engaged in the trading and natural gas business, one of which is Gaslink C-Cyl. Route determination for Gaslink C-Cyl distribution is carried out subjectively based on the proximity of locations between customers, thus creating inefficient routes, affecting the number of vehicles needed, and causing high transportation costs. Based on this problem, this study aims to minimize transportation costs by determining the optimal route and number of vehicles needed using the Multi-Trip Vehicle Routing Problem Time Windows Simultaneous Pickup and Delivery (MTVRPTW-SPD). This problem is solved using Geographic Information System (GIS) based optimization. To evaluate GIS-based optimization performance, comparison between existing condition and optimization are done for 50 demand points. Then, two scenario was developed, 100 and 200 demand points to explain the decision implication related to demand uncertainty. Based on the optimization process for 50 demand points gives better solution than existing condition in term of number of fleets needed, total distance travelled, and total transportation cost which result 3 units, 46,5%, and 43,5% respectively.

Management of a post-disaster emergency scenario through unmanned aerial vehicles: Multi-Depot Multi-Trip Vehicle Routing with Total Completion Time Minimization

One of the most valuable and promising applications for Unmanned aerial vehicles (UAVs) is in natural disaster management, where these aircraft can operate autonomously without any need for human intervention during their flights.In this paper, we foster the interface of Operational Research with computer science in general and sensor networking in particular by focusing on managing a post-disaster emergency scenario where the use of a fleet of UAVs helps rescue teams identify people needing help inside an affected area. We model this situation as an original graph theoretical problem called Multi-Depot Multi-Trip Vehicle Routing Problem with Total Completion Time minimization (MDMT-VRP-TCT). The main novelty of the MDMT-VRP-TCT is the combination of the following three features: multi-depot, multi-trip, and completion time minimization.We propose a mixed-integer linear programming (MILP) formulation, develop a matheuristic framework to address large instances, and present an extended set of experiments to test the performance of the proposed matheuristic: first, we compare the matheuristic with the MILP formulation on a set of small instances (up to 30 nodes); then, we compare our matheuristic with two heuristics from networking literature, showing that it outperforms the existing algorithms.

Iterated variable neighborhood search for integrated scheduling of additive manufacturing and multi-trip vehicle routing problem

This study addresses a novel problem structure for integrated scheduling of additive manufacturing and delivery processes. In the manufacturing process, we consider batch production of parts, simulating Selective Laser Melting technology in parallel additive manufacturing machines with heterogeneous specifications. A batch production, referred to as a build, must consist of parts with homogenous material. During the production run, sequence-dependent material setup times occur in between builds. In the delivery process, parts are delivered in batches using a limited number of homogenous capacitated vehicles. Each vehicle might perform multi-trips. Thus, the route for each trip and departure schedule among trips must be decided. In this regard, batch delivery is independent to batch production. The problem objective function is to minimize the total completion time of all parts. For optimally solving the problem, a mixed-integer linear programming model is devised. To solve larger problems sizes under a lower computation time, an iterated variable neighborhood search algorithm with embedded rule-based heuristics is proposed. The computational experiment denotes that the proposed algorithm with route minimization rule effectively solves small-scale problems, while capacity usage maximization rule performs the best in large-scale problems and outperforms other existing metaheuristics. Further result analysis is also performed to provide managerial insights.

A hybrid genetic search and dynamic programming-based split algorithm for the multi-trip time-dependent vehicle routing problem

We design a hybrid algorithm for the multi-trip time-dependent vehicle routing problem (MT-TD-VRP). One of its components is the Time-Dependent SPlit Algorithm (TD-SPA), which is a dynamic programming-based algorithm specifically designed to handle both the multi-trip per vehicle and the time-dependent aspects of the problem. The hybrid algorithm combines the proposed TD-SPA, designed to efficiently split a giant tour into complete vehicle routes, with a genetic algorithm for generating these tours. We introduce a monotone queue optimization (MQO) technique to accelerate the TD-SPA. The effectiveness of MQO is evaluated by comparing computation times between the original split algorithm for the capacitated vehicle routing problem (CVRP) and its MQO-enhanced counterpart. Extensive numerical experiments with a real-world dataset from a Singapore food and beverage company are conducted to assess our algorithm’s performance on various MT-TD-VRP instances. The results indicate that our algorithm surpasses the performance of the commercial solver Gurobi, with an average improvement of 25.13% on the best solutions found within a prescribed duration. Our numerical simulations further reveal the algorithm’s ability to efficiently solve both the capacitated vehicle routing problem (CVRP) and the multi-trip vehicle routing problem (MTVRP), consistently producing competitive solutions. Moreover, to highlight the importance of incorporating the time-dependent (TD) factor into our model and algorithm, we demonstrate a notable enhancement in performance–averaging at 7.47% for the best solutions under TD conditions for an MTVRP dataset.

An Optimization-Based Decision Support System for Multi-trip Vehicle Routing Problems

An Optimization-Based Decision Support System for Multi-trip Vehicle Routing Problems

A three-stage matheuristic for home blood donation appointment reservation and collection routing

AbstractIn Western countries, the so-called Blood Donation Supply Chain (BDSC) provides blood units to several health services. Its first echelon is the collection of unit from donors, which requires a careful management because an unbalanced supply of units to the rest of the chain could trigger alternating periods of blood shortage and wastage. However, the management of blood collection is only marginally studied in the literature, in comparison to other BDSC echelons. In this work, we propose a new organizational model for blood collection, in which blood is collected at donor’s homes, and provide a decision support tool for its management. This new model provides a novel contribution to the understudied blood collection echelon and, at the same time, it responds to the emerging need of delocalization of health services. The proposed decision support tool consists of an interconnected matheuristic framework with three decision stages: (i) a planning model to create the donation slots that will be assigned to donors, (ii) an online allocation of these slots using a flexible set of criteria, and (iii) a Multi-Trip Vehicle Routing Problem with Time Windows (MTVRP-TW) to route the bloodmobiles that collect blood at donors’ homes. The main goals are to balance the production of blood units between days and to minimize the distance travelled by the bloodmobile fleet, while respecting time windows negotiated with donors. This framework also has the feature of immediately providing a list of slots to choose from when a donor makes a booking request. The decision support tool has been tested on data from a real Italian provider. Results confirm its effectiveness, and the capability of providing good quality and economically sustainable solutions in reasonable timeframes.

Hybridizing a matheuristic with ALNS for the optimal collection and delivery of medical specimens

AbstractThe past few years of the COVID‐19 pandemic outbreak have shown that optimal management of medical specimens is a key aspect of healthcare logistics, both for addressing the delivery of perishable items such as vaccines, and for ensuring the timely analysis of swabs and samples. Accordingly, recent optimization literature described the problem of optimal collection and delivery of medical specimens, modeled as a multitrip vehicle routing problem with time windows and a completion time objective function. Aiming to achieve good‐quality solutions in short computational times, this work describes a hybrid approach, combining a matheuristic construction phase with an adaptive large neighborhood search (ALNS). Our matheuristic relies on a clustering algorithm to yield subsets of the medical specimens that are optimally served by single vehicles of the fleet. The solutions of the matheuristic phase serve as starting points for the ALNS intensification phase. Extensive experimentation on both new and established benchmark problem instances shows that our hybrid method is able to match the optimality of the state of the art on small instances and outperforms the existing exact method by one order of magnitude on larger problems.

Multi-Trip Vehicle Routing Problem with Time Windows and Resource Synchronization on Heterogeneous Facilities

Inspired by long-distance road transport in industrial logistics in China, this paper studies a simultaneous loading scheduling and vehicle routing problem over a multi-workday planning horizon. Industrial cargo often requires specialized facilities, and these facilities vary in performance and quantity and are subject to available time constraints. Consequently, achieving coordinated optimization of vehicle routing and loading scheduling becomes a significant challenge in practice. We describe the studied problem as a multi-trip vehicle routing problem with time windows and resource synchronization on heterogeneous facilities. First, we develop a mixed integer programming model in a multi-workday setting to minimize the total travel distance and the number of vehicles. Moreover, a three-phase heuristic approach is developed. An initial solution is constructed using a sequential strategy in the first phase, and then an adaptive large neighbourhood search and a post-optimization procedure based on ejection chains are, respectively, designed to optimize the two hierarchical objective functions. Finally, extensive computational experiments are conducted to demonstrate the effectiveness of the proposed method. Specifically, the research results indicate that in long-distance road transport in industrial scenarios, expanding the planning horizon from a single workday to a multi-workday period could significantly reduce logistics operational costs and improve service quality.

Split-demand multi-trip vehicle routing problem with simultaneous pickup and delivery in airport baggage transit

In this study, we focus on the routing and scheduling of multi-carriage transit trains for airport baggage transit. It is modeled as a vehicle routing problem with cross-route dependencies caused by side constraints, including split demand, multiple trips per vehicle, and simultaneous pickup and delivery. Besides, some other practical constraints such as time windows, baggage release time, baggage waiting time, and priority of unloading are taken into account in the implementation. The joint consideration of these characteristics brings a unique challenge to determine the start time of each service for aircraft due to the interdependencies across vehicle routes. Thus, we adopt topological sort to construct the directed acyclic graph and then derive the flight service time. Based on that, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm. Moreover, in order to examine the moves quickly, a two-stage solution evaluation method is proposed, where the single tour is checked based on the segment-based evaluation method in the first stage, and the complete solution is checked using the topological sort in the second stage. The results demonstrate the superiority of our algorithm in computational time and solution quality. In addition, some insightful conclusions are drawn through detailed analyses.

A multi-trip vehicle routing problem considering time windows and limited duration under a heterogeneous fleet and parking constraints in cold supply chain logistics

ABSTRACT Cold supply chain distribution systems ensure the freshness of temperature-sensitive products during transportation. In this study, we investigated a fresh food company’s cold supply chain distribution. Making fresh food available and achieving quality and safety, requires proper planning of vehicle routing, we addressed a routing problem that simultaneously considers time windows, multiple trips per vehicle, a heterogeneous fleet, parking constraints, unloading time at customer position, and limited duration, minimizing related operational costs. We formulate this problem as a mixed-integer programming model. Since this problem is NP-hard, we also propose a genetic algorithm with two adaptive-parameter mechanisms to solve it within a reasonable computational time. Extensive experiments were conducted to assess the performance of different approaches in a real-world application. The results demonstrate that the algorithms are robust and efficient. The proposed algorithms can reduce operational costs by more than 20% compared to the current practical planning approach.

Multitrip vehicle routing with delivery options: a data-driven application to the parcel industry

To make the last mile of parcel delivery more efficient, service providers offer an increasing number of modes of delivery as alternatives to the traditional and often cost-intensive home delivery service. Parcel lockers and pickup stations can be utilized to reduce the number of stops and avoid costly detours. To design smart delivery networks, service providers must evaluate different business models. In this context, a multitrip vehicle routing problem with delivery options and location-dependent costs arises. We present a data-driven framework to evaluate alternative delivery strategies, formulate a corresponding model and solve the problem heuristically using adaptive large neighborhood search. By examining large, real-life instances from a major European parcel service, we determine the potential and benefits of different delivery options. Specifically, we show that delivery costs can be mitigated by consolidating orders in pickup stations and illustrate how pricing can be applied to steer customer demand toward profitable, eco-friendly products.

Metaheuristics with variable diversity control and neighborhood search for the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem

The planning of vehicle routes is a major issue involved in supply chains. In real environment, we can find situations involving a very large number of clients or constraints which indicate that exact methods should be avoided. In this context, this paper presents two metaheuristcs which are used to solve a complex problem named the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem (HSDMDMTPVRP). The HSDMDMTPVRP is a real problem found in the automotive industry and considers several well-known Vehicle Routing Problems (VRP). The first metaheuristic is an adaptation of the Unified Hybrid Genetic Search (UHGS) which considers an advanced diversity control, feasibility control and a restart mechanism. The second one is a new metaheuristic named Adaptive Variable Neighborhood Race (AVNR) which combines variable neighborhood search and adaptive mechanisms integrated with a shrinking population managed with a diversity mechanism. Both approaches are also used for solving some variants of the VRP: Heterogeneous VRP, Site dependent VRP, Periodic VRP and Multi-trip VRP. Our computational experiments used 398 available instances in the literature with generic code path and also present 20 new instances for the HSDMDMTPVRP. The metaheuristics solved all instances with only one set of parameters and the results outperform or present the same solutions found by several state-of-the-art algorithms, showing the good performance of the approaches. Out of the 398 previously tested literature instances, the proposed metaheuristics found 140 new best-known solutions and 209 of the best-known ones. For the remaining instances, both approaches found results very close to best ones known.

An Exact Price-Cut-and-Enumerate Method for the Capacitated Multitrip Vehicle Routing Problem with Time Windows

We consider the capacitated multitrip vehicle routing problem with time windows (CMTVRPTW), where vehicles are allowed to make multiple trips. The ability to perform multiple trips is necessary for some real-world applications where the vehicle capacity, the trip duration, or the number of drivers or vehicles is limited. However, it substantially increases the solution difficulty in view of the additional trip scheduling aspect. We propose an exact price-cut-and-enumerate method (EPCEM) that solves a novel superstructure-based formulation inspired by Paradiso et al. (2020) . The EPCEM obtains a tight lower bound by an alternating column and row generation method and computes a valid upper bound in the early stage of the algorithm. It obtains an optimal solution and further proves its optimality by a new multiphase sift-and-cut method. Computationally, the EPCEM significantly outperforms the state-of-the-art exact method that only proves optimality for 9 of the 27 test instances with 50 customers. In particular, the EPCEM solves all test instances with up to 70 customers to optimality for the first time and obtains near-optimal solutions with an average optimality gap of no more than 0.3% for instances with 80 to 100 customers. From a practical point of view, solving the CMTVRPTW by the EPCEM yields a solution that, on average, uses at least 45% fewer vehicles and increases the travel cost by no more than 7% compared with the solution to the standard CVRPTW. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.1161 .

An Improved Intelligent Auction Mechanism for Emergency Material Delivery

Emergency material delivery is vital to disaster emergency rescue. Herein, the framework of the emergency material delivery system (EMDS) with the unmanned aerial vehicle (UAV) as the vehicle is proposed, and the problem is modeled into a multi-trip time-dependent dynamic vehicle routing problem with split-delivery (MTTDDVRP-SD) in combination with the rescue reality, which provides decision support for planning disaster relief material. Due to the universality of dynamic interference in the process of material delivery, an optimization algorithm based on the traditional intelligent auction mechanism is proposed to avoid system performance degradation or even collapse. The algorithm adds pre-authorization and sequential auction mechanisms to the traditional auction mechanism, where the pre-authorization mechanism improves the capability performance of the system when there is no interference during the rescue process and the sequential auction mechanism improves the resilience performance of the system when it faces interferences. Finally, considering three types of interference comprehensively, which includes new task generations, task unexpected changes and UAV’s number decreases, the proposed algorithm is compared with DTAP (DTA based on sequential single item auctions) and CBBA-PR (consensus-based bundle algorithms-partial replanning) algorithms under different dynamic interference intensity scenarios for simulation experimental from two perspectives of the capability performance and resilience performance. The results of Friedman’s test with 99% confidence interval indicate that the proposed algorithm can effectively improve the capability performance and resilience performance of EMDS.

The multi-trip vehicle routing problem with increasing profits for the blood transportation: An iterated local search metaheuristic

This paper studies a multi-trip routing problem of a shuttle fleet to transport blood units from collection sites to a blood center. In this problem, the blood units intended to produce platelets and cryoprecipitate must be processed within eight hours from their donation and arrive at the blood center at a time less than its closing time to guarantee enough processing time. Since it is assumed that blood units are donated at a collection site following a constant ratio over its operating hours, this problem is modeled as a multi-trip vehicle routing problem with increasing profits for which a mixed-integer linear programming formulation is proposed. A hybrid iterated local search metaheuristic and an extended version are developed as solution methods. The extended version includes a mixed-integer linear programming component into the local search of the hybrid metaheuristic to optimize the decision on the departure times of the trips. The solution methods are tested on a new set of instances based on the blood collection system of Bogota, Colombia.

A branch-and-price algorithm for a routing problem with inbound and outbound requests

In this paper we present a new problem arising in the context of non-emergency transportation of patients. We consider a hospital (the depot) and a set of patients with a medical appointment. Patients require either to go from home to hospital (inbound request) or from hospital to home (outbound request). The problem can be addressed as a Pickup and Delivery Problem, but the fact that all transportation requests are connected to the depot also allows tackling it as a special Multi-Trip Vehicle Routing Problem. We adopt the second standpoint and call it the Multi-Trip Vehicle Routing Problem with Mixed Pickup and Delivery, and Release and Due dates. We propose a specialized branch-and-price algorithm and demonstrate computationally that our approach outperforms a classical branch-and-price algorithm based on the Pickup and Delivery Problem modeling. We also show how our algorithm can be adapted to the solution of the Vehicle Routing Problem with Simultaneous Pickup and Delivery and Time Windows, and obtain new optimal solutions on benchmark instances.

A Branch and Price Algorithm for the Heterogeneous Fleet Multi-Depot Multi-Trip Vehicle Routing Problem with Time Windows

The multi-trip vehicle routing problem (MTVRP) extends the well-known VRP by allowing vehicles to perform several trips in a workday. The motivation arises from the new challenges in city logistics that push companies to use smaller and cleaner vehicles such as cargo bikes. With the integration of small vehicles into the fleet, many companies start to operate with a heterogeneous fleet and use multiple depots located in the city centers to reload the small vehicles. Inspired by these new challenges the companies face, we study the heterogeneous fleet multi-depot MTVRP with time windows under shared depot resources where small and large vehicles have different travel times in certain areas. We formulate this problem using workday variables and propose a branch and price algorithm that exhibits an enhanced performance by a new heuristic algorithm based on the reduction in the graph size. The proposed algorithm introduces a new way to compute the completion bounds using the iterative structure of the state-space augmenting algorithm and eliminates the need for solving a separate relaxation. We conduct experiments on modified small- and medium-size instances from Solomon’s benchmark set. The results of our computational experiments show that the proposed algorithm is very effective and can solve instances with up to 40 customers, three depots, and two types of vehicles.