Periodic Vehicle Routing Problem Research Articles

A comparative study of alternative formulations for the periodic vehicle routing problem

This study investigates the periodic vehicle routing problem (PVRP) and its variant with time windows with a particular focus on alternative formulation approaches that can be solved by a state-of-the-art commercial solver. We propose a new vehicle flow formulation for the PVRP and strengthen it with valid inequalities. We also investigate two prominent formulations for the PVRP available in the literature: a commodity flow formulation, referred to as the load-based formulation, and a cut-based formulation which is adapted from a formulation originally developed for a variant of the PVRP. We also extend these formulations to model the PVRP with time windows (PVRPTW) and employ valid inequalities to tighten the resulting formulations. A comprehensive computational study is then carried out to compare the performances of alternative PVRP and PVRPTW formulations on various sets of benchmark instances with different characteristics. The results attest to the robustness and the consistency of the proposed formulation and its strengthened versions in producing good quality solutions, especially for large instances although the load-based formulations tend to perform well in small instances.

Effect of formulations over a Periodic Capacitated Vehicle Routing Problem with multiple depots, heterogeneous fleet, and hard time-windows.

This article presents a novel contribution to the Periodic Vehicle Routing Problem (PVRP) by introducing two new problem formulations which differ in the usage of the crucial flow variable. The formulations are tailored to meet the specific demands of the vending machine industry in Medellín, Colombia, and require considering a PVRP with time windows, a heterogeneous fleet, and multiple depots. This scenario, tailored to address real-world complexity and computational challenges, brings to light an exponential surge in integer variables as customer numbers increase. The research presents an analysis of PVRPs that include the four mentioned attributes, compares their similarities, and delves into their nuances. From the analysis it is derived that the variant of the PVRP presented has not been considered previously, taking into account not only these attributes, but also the restrictions involved. Empirical experiments are conducted to examine the intricate interplay between the two proposed formulations, highlighting their impact on the performance of the GUROBI solver. The study provides valuable insights into problem-specific adaptations and algorithmic approaches, emphasizing the significance of the proposed formulations in addressing multifaceted PVRPs. In essence, this research positions the introduction of these two formulations as a pioneering step, offering a new paradigm for approaching the PVRP.

Model for route planning of freight buses

This paper introduces freight buses as a novel solution for city logistics, aiming to replace other freighters currently operated by various private logistics firms within city centers. The focus lies on investigating the route planning challenge associated with integrating freight buses into an city distribution framework. Each freight bus follows a predefined route, repeatedly traversing from a distribution center to multiple depots before returning to the distribution center. All depots are serviced by multiple freight buses on a consistent basis. This route planning problem presents a fresh iteration of the periodic vehicle routing problem. To tackle this challenge, the paper proposes a Mixed-Integer Linear Programming model, serving as a fundamental framework for future research endeavors concerning freight buses.

On the multi-period combined maintenance and routing optimisation problem

This paper focuses on the combined maintenance and routing optimisation problem in a multi-period environment that consists of scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and corrective operations. This study uses a two-step approach based on column generation. The first step consists of a maintenance model that determines the optimal time until the next preventive maintenance operation, and each machine’s maintenance frequency while minimising the total expected maintenance costs. The second step involves a routing model that assigns and schedules maintenance operations for each technician over the planning horizon while minimising the routing and maintenance costs. We formulate the second step problem as a periodic vehicle routing problem and to solve it, we propose a column generation approach. The master problem is a set partitioning formulation that indicates which machines must be visited in the planning horizon. This decomposition has two auxiliary problems: the first one is an elementary shortest-path problem to find a feasible path for each period and the second one finds a set of visiting periods for each machine. Our approach balances the maintenance cost, routing cost, and failure probabilities.

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.

A Comparative Study of Alternative Formulations for the Periodic Vehicle Routing Problem

A Comparative Study of Alternative Formulations for the Periodic Vehicle Routing Problem

Periodic Vehicle Routing Problem with Driver Consistency and service time optimization

The Periodic Vehicle Routing Problem with Driver Consistency is an extension of the classic Vehicle Routing Problem in which routes for several vehicles have to be determined over a time horizon of several days. Each customer has an associated set of possible visit schedules and must be visited always by the same vehicle. In this paper, we study a variant of the PVRP-DC in which, in addition to routes and visit schedules, service times of customers have to be determined in order to maximize the utility of the service to the company. We call this problem the Periodic Vehicle Routing Problem with Driver Consistency and Service Time Optimization. We present a mixed-integer linear programming formulation for the problem, propose three branch-and-cut methods to solve it, two of which are based on Benders reformulations, and report computational results on benchmark instances with different features.

A hub-location periodic vehicle routing problem in offshore oil and gas logistics

A hub-location periodic vehicle routing problem in offshore oil and gas logistics

A stochastic optimization approach for the supply vessel planning problem under uncertain demand

This paper presents a two-stage stochastic programming with recourse methodology to solve the Supply Vessel Planning Problem with Stochastic Demands (SVPPSD), a problem arising in offshore logistics and which generalizes the Periodic Vehicle Routing Problem with Stochastic Demands and Time Windows. In the SVPPSD, a fleet of vessels is used to deliver a regular supply of commodities to a set of offshore installations to ensure continuous production, with each installation requiring one or more visits per week and having stochastic demands. Both the onshore depot where the product to be distributed is kept and the offshore installations have time windows, and voyages are allowed to span more than one day. A solution to the SVPPSD consists in the identification of an optimal fleet of vessels and the corresponding weekly schedule. As a solution methodology, we embed a discrete-event simulation engine within a genetic search procedure to approximate the cost of recourse and arrive at the minimized expected cost solution. We make comparisons with two alternative approaches: an expected value problem with upscaled demand, and a chance-constrained algorithm. While alternative methodologies yield robust schedules, robustness is achieved mainly through an increase in fleet size. In contrast, a two-stage stochastic programming with recourse algorithm, by accounting for the cost of recourse in the search phase, and exploring a wider solution space, allows arriving at robust schedules with a smaller fleet size, thereby yielding significant cost savings. For the tested problem instances, the proposed algorithm leads to savings of approximately 10 to 15 million USD per year.

Periodic distributed delivery routes planning subject to operation uncertainty of vehicles travelling in a convoy

ABSTRACT This paper considers a Problem of Periodic Routing of Vehicles Platoons (PRVPP), which is a novel extension of the Periodic Vehicle Routing Problem (PVRP). The PRVPP boils down to scheduling of the fleet of vehicles travelling in a convoy while constituting the timetable for the passage of individual vehicles along the planned routes. The imprecise nature of transport/service operation times means there is a need to take into account the fact that the accumulating uncertainty of previously performed operations results in increased uncertainty of timely execution of subsequent operations. This raises the question as to the method required to avoid additional uncertainty introduced during aggregating uncertain operation execution deadlines. Due to the above fact, an algebraic model for calculating fuzzy schedules for individual vehicles, and for planning time buffers enabling the adjustment of the currently calculated fuzzy schedules, is developed. The model uses Ordered Fuzzy Numbers (OFNs) to reflect the uncertainty of times. The conducted research demonstrated that the proposed model allows us to develop conditions following the calculability of arithmetic operations of OFNs and guarantee the interpretability of the results obtained.

Branch-and-price for a combined order selection and distribution problem in online community group-buying of perishable products

As a new social e-commerce model, online community group-buying of perishable products has been under examined. This paper addresses a real-world delivery problem faced in common by an online community group-buying operators, in which operators may suffer revenue loss from product deterioration during delivery. Since delivery quantities of candidate orders may be beyond capacity resources, this paper investigates a new combined order selection and periodic vehicle routing problem with time windows for perishable products. An online community group-buying operator can design daily online community group-buying delivery plan by deciding to serve which customers, to deliver which products and delivery quantities to be transported. To solve this problem, we propose a branch-and-price algorithm that strongly relies on a new label setting algorithm with partial label dominance and a strong bounding strategy based on the definition of Pareto-optimal delivery patterns. Since en-route delivery quantities depend on the interval between two consecutive services, our label setting algorithm is also applicable to the pricing subproblem for the discrete split delivery vehicle routing problem. We conduct a case study on a real-world instance and propose management insights into the structure of delivery plan facing inadequate capacity resources. Numerical experiments on 64 randomly generated instances demonstrate the effectiveness of the proposed branch-and-price algorithm.

The Heterogeneous Flexible Periodic Vehicle Routing Problem: Mathematical formulations and solution algorithms

The aim of this paper is to introduce the Flexible Periodic Vehicle Routing Problem with Heterogeneous Fleet, a variant of the Periodic Vehicle Routing Problem. Flexibility is introduced in service schedules and delivered quantities, heterogeneity comes from different vehicles capacities and speeds. Three Mixed-Integer Linear Programming formulations and a matheuristic, based on Kernel Search, are proposed. Computational tests are made to evaluate the performance of the three formulations and to assess the quality of the solutions provided by the matheuristic.

Hybrid algorithm for the solution of the periodic vehicle routing problem with variable service frequency

This document addresses the problem of scheduling and routing a specific number of vehicles to visit a set of customers in specific time windows during a planning horizon. The vehicles have a homogeneous limited capacity and have their starting point and return in a warehouse or initial node, in addition, multiple variants of the classic VRP vehicle routing problem are considered, where computational complexity increases with the increase in the number of customers to visit, as a characteris-tic of an NP-hard problem. The solution method used consists of two connected phases, the first phase makes the allocation through a mixed-integer linear programming model, from which the visit program and its frequency in a determined plan-ning horizon are obtained. In the second phase, the customers are grouped through an unsupervised learning algorithm, the routing is carried out through an Ant Colony Optimization metaheuristic that includes local heu-ristics to make sure com-pliance with the restrictive factors. Finally, we test our algorithm by performance measures using instances of the literature and a comparative model, and we prove the effectiveness of the proposed algorithm.

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.

Exact and heuristic algorithms for the fleet composition and periodic routing problem of offshore supply vessels with berth allocation decisions

This paper presents a branch-and-cut algorithm and an adaptive large neighborhood search (ALNS) heuristic for the periodic supply vessel planning problem (PSVPP) arising in the upstream offshore petroleum logistics chain. Platform supply vessels support the offshore oil and gas exploration and production activities by transporting all the necessary material and equipment back and forth between offshore units and an onshore supply base according to a delivery schedule. The PSVPP consists of solving a periodic vehicle routing problem and simultaneously determining an optimal fleet size and mix of heterogeneous offshore supply vessels, their weekly routes and schedules for servicing the offshore oil and gas installations, and the berth allocations at the supply base. The branch-and-cut algorithm considers a reduced formulation for the problem which performs much better than the complete one, and easily finds optimal solutions for the smaller and most of the clustered instances. The ALNS heuristic contains new features which include multiple starts and spaced local searches. These algorithms were tested on instances with up to 79 offshore units, providing better results than the best available.

Period sewage recycling vehicle routing problem based on real-time data

Abstract The period vehicle routing problem (PVRP) is an important extension of the vehicle routing problem, in which customers have a certain frequency of service. This paper studies a real-time period vehicle routing system: Daniudi gas field sewage recycling, which differs from the classic PVRP because the frequency of customer service is uncertain. A “prediction + two-stage” strategy is proposed to solve the problem. First, the integrated model predicts customers’ sewage data generated that day to calculate the warning line so that customers who reach the warning line can be served on that day. Then, because the customer’s sewage production changes in real time, a two-stage “pre-optimization + real-time optimization” model is proposed for each day in the period. The two-stage “pre-optimization + real-time optimization” model uses differential evolution (DE) algorithm based on niche clearing to plan the sewage recycling route. The computational results indicate that the proposed technique can reduce actual sewage recycling costs by 17.3%. By performing comparison experiments, we find that the five algorithms examined (i.e., jDE-niche, jDE, DE, GA, and ACO) reduce costs by 17.3%, 12.00%, 10.70%, 9.02% and 8.18%, respectively. Furthermore, the fifteen combined prediction models confirm the validity and effectiveness of our proposed “prediction+two-stage” strategy and jDE-niche algorithm.

A Hybrid Multiobjective Memetic Algorithm for Multiobjective Periodic Vehicle Routing Problem With Time Windows

Periodic vehicle routing problem with time windows (PVRPTWs) is an important combinatorial optimization problem that can be applied in different fields. It is essentially a multiobjective optimization problem due to the problem nature. In this paper, a typical multiobjective PVRPTW with five objectives is first defined and new nonsymmetric real-world multiobjective PVRPTW instances are generated. Then, a hybrid multiobjective memetic algorithm is proposed for solving multiobjective PVRPTW. In the proposed algorithm, a two-phase strategy is devised to improve the comprehensive performance in terms of the convergence and diversity. In this strategy, several extreme solutions near an approximate Pareto front (PF) are identified at Phase I, and then the approximate PF is extended at Phase II. The proposed algorithm is extensively tested on both real-world instances and traditional instances. Experiment results show that the proposed algorithm outperforms two representative competitor algorithms on most of the instances. The effectiveness of the two-phase strategy is also confirmed.

Mathematical models for the periodic vehicle routing problem with time windows and time spread constraints

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

A unified model framework for the multi-attribute consistent periodic vehicle routing problem.

Modeling real-life transportation problems usually require the simultaneous incorporation of different variants of the classical vehicle routing problem (VRP). The periodic VRP (PVRP) is a classical extension in which routes are determined for a planning period of several days and each customer has an associated set of allowable visit schedules. This work proposes a unified model framework for PVRP that consists of multiple attributes or variants not previously addressed simultaneously, such as time-windows, time-dependence, and consistency -which guarantees the visits to customer by the same vehicle-, together with three objective functions that respond to the needs of practical problems. The numerical experimentation is focused on the effects of three factors: frequency, depot centrality, and the objective function on the performance of a general-purpose MILP solver, through the analysis of the achieved relative gaps. Results show higher sensitivity to the objective functions and to the problem sizes.

A variable neighborhood search algorithm with reinforcement learning for a real-life periodic vehicle routing problem with time windows and open routes

This paper studies a real-life container transportation problem with a wide planning horizon divided into multiple shifts. The trucks in this problem do not return to depot after every single shift but at the end of every two shifts. The mathematical model of the problem is first established, but it is unrealistic to solve this large scale problem with exact search methods. Thus, a Variable Neighbourhood Search algorithm with Reinforcement Learning (VNS-RLS) is thus developed. An urgency level-based insertion heuristic is proposed to construct the initial solution. Reinforcement learning is then used to guide the search in the local search improvement phase. Our study shows that the Sampling scheme in single solution-based algorithms does not significantly improve the solution quality but can greatly reduce the rate of infeasible solutions explored during the search. Compared to the exact search and the state-of-the-art algorithms, the proposed VNS-RLS produces promising results.