A VNS-based Heuristic for Solving the Vehicle Routing Problem with Time Windows and Vehicle Preventive Maintenance Constraints

AbstractWe address a vehicle routing problem with time windows (VRPTW) that also contains vehicle with preventive maintenance constraints (VRPTW-PM) and propose a MIP mathematical formulation as well as a general variable neighborhood search metaheuristic (VNS) to solve with large instance the problematic situation. First we create a initial solution using Solomon heuristic then we minimize the number of used routes, and then the total travelled distance by all vehicles is minimized. Computational results show the efficiency of the proposed approach

Simulation-based optimisation for stochastic maintenance routing in an offshore wind farm

Scheduling maintenance routing for an offshore wind farm is a challenging and complex task. The problem is to find the best routes for the Crew Transfer Vessels to maintain the turbines in order to minimise the total cost. This paper primarily proposes an efficient solution method to solve the deterministic maintenance routing problem in an offshore wind farm. The proposed solution method is based on the Large Neighbourhood Search metaheuristic. The efficiency of the proposed metaheuristic is validated against state of the art algorithms. The results obtained from the computational experiments validate the effectiveness of the proposed method. In addition, as the maintenance activities are affected by uncertain conditions, a simulation-based optimisation algorithm is developed to tackle these uncertainties. This algorithm benefits from the fast computational time and solution quality of the proposed metaheuristic, combined with Monte Carlo simulation. The uncertain factors considered include the travel time for a vessel to visit turbines, the required time to maintain a turbine, and the transfer time for technicians and equipment to a turbine. Moreover, the proposed simulation-based optimisation algorithm is devised to tackle unpredictable broken-down turbines. The performance of this algorithm is evaluated using a case study based on a reference wind farm scenario developed in the EU FP7 LEANWIND project

Waste Collection Vehicle Routing Problem Model with Multiple Trips, Time Windows, Split Delivery, Heterogeneous Fleet and Intermediate Facility

Waste Collection Vehicle Routing Problem (WCVRP) is one of the developments of a Vehicle Routing Problem, which can solve the route determination of transporting waste. This study aims to develop a model from WCVRP by adding characteristics such as split delivery, multiple trips, time windows, heterogeneous fleet, and intermediate facilities alongside an objective function to minimize costs and travel distance. Our model determines the route for transporting waste especially in Cakung District, East Jakarta. The additional characteristics are obtained by analyzing the characteristics of waste transportation in the area. The models are tested using dummy data to analyze the required computational time and route suitability. The models contribute to determining the route of transporting waste afterward. The WCVRP model has been successfully developed, conducted the numerical testing, and implemented with the actual characteristics such as split delivery, multiple trips, time windows, heterogeneous fleets, and intermediate facilities. The output has reached the global optimal for both dummy and real data

Optimisation of scheduling and routing for offshore wind farm maintenance

The growing increase in the size and scope of offshore wind farms motivates the need for industry to have access to mathematical tools that reduce costs by efficiently performing daily operations and maintenance activities. Key offshore activities require the transportation of technicians to and within offshore wind farms to complete corrective and preventive maintenance tasks to keep turbines operating efficiently. We provide a new deterministic mixed integer linear programming formulation for deciding the optimal vessel routes for transporting technicians around a wind farm and the scheduling of crew transfers, by minimising downtime, travel and technician costs. The model contains sufficient flexibility to account for multiple vessels, shifts and task profiles, whilst being able to prioritise and omit tasks in environments containing limited resources. Computational experiments are performed which quantify and confirm the impact of key instance characteristics such as technician availability, task profiles and weather conditions. We implement and evaluate the impact of a novel industry safety constraint. The complexity of larger instances motivates a second continuous time formulation, in which preventive maintenance again requires no minimum duration of work before it can provide benefit. We employ a specific decomposition structure to take advantage of variable preventive maintenance and utilise an adaptive large neighbourhood search procedure to solve instances. We evaluate several distinct acceptance criteria in conjunction with random and adaptive operator selection to determine the best option for our model. We produce a statistical model of offshore weather conditions to help quantify the likelihood of limited vessel accessibility to offshore wind farms. We model the joint distribution of key meteorological and oceanographic variables over time whilst accounting for seasonal trends using multivariate kernel density estimation. Our method generates alternative metocean realisations from historical data and reproduces the important long term persistence statistics of good and adverse offshore conditions

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects

On a Vehicle Routing Problem with Customer Costs and Multi Depots

The Vehicle Routing Problem with Customer Costs (short VRPCC) was developed for railway maintenance scheduling. In detail, corrective maintenance jobs for unexpected occurring failures are planned to a short time horizon. These jobs are geographically distributed in the railway net. Furthermore, dependent on the severity of the failure, it can be necessary to reduce the top speed on the track section in order to avoid safety risks or a too fast deterioration. For fatal failures, it can even be necessary to close the track section. The resulting limitations on railway service lead to penalty costs for the maintenance operator. These must be paid until the track is repaired and the restrictions are removed. By scheduling the maintenance tasks, these penalty costs can be reduced by proceeding corresponding maintenance tasks earlier. However, this may in return lead to increased costs for moving the maintenance machines and crews. For this scheduling problem, the VRPCC was developed. With it, for each maintenance vehicle and crew, a route is defined that describes the order to proceed maintenance tasks. Two kinds of costs are considered: Firstly, travel costs for machinery and crew; and secondly, penalty costs for an unsafe track condition that have to be paid for each day from failure detection to maintenance completion. To model the penalties, the novel customer costs are defined. In detail, for each maintenance activity a customer cost coefficient is given which incur for each day between failure detection and failure repair. The objective function of this problem is defined by the sum of travel costs and time-dependent customer costs. With it, the priority of customers can be taken into account without losing the sight on travel costs. This new vehicle routing problem was introduced in this thesis by a non-linear partition and permutation model. In this model, a feasible solution is defined by a partition of the job set into subsets that represent the allocation of jobs to vehicles and a permutation for each subset that represent the order of processing the jobs. Then, the start times of the jobs were calculated based on the order given by the permutations. It was taken into account that work can only be done in eight hour shifts during the night. Based on the start times, the customer cost value of each job is computed which equals to the paid penalty costs. Then, the costs of a schedule are calculated via the sum of travel costs and customer costs. To solve the VRPCC by a commercial linear programming solver, different formulations of the VRPCC as mixed-integer linear program were developed. In doing so, the start times became decision variables. It turned out that including customer costs led to problems harder to solve than vehicle routing problems where only travel costs are minimized. Further, in the thesis several construction heuristics for the VRPCC were designed and investigated. Also two local search algorithms, first and best improvement, were applied. The computational experiments showed that the solutions generated by the local search algorithm were much better than the solutions of the construction heuristics. The main part of this thesis was to design a Branch-and-Bound algorithm for the VRPCC. For this purpose, new lower bounds for the customer cost part of the objective function were formulated. The computational experiments showed that a lower bound computed from the LP relaxation of a specific bin packing problem had the best trade-off between computational effort and bound quality. For the travel cost part of the objective function, several known lower bounds from the TSP were compared. To design a Branch-and-Bound algorithm, beside efficient lower bound, also suitable branching strategies are necessary to split the problem space into smaller subspaces. In this thesis two branching strategies were developed which are based on the non-linear partition and permutation model to take advantage from the problem structure. To be more precise, new branches are generated by appending or including a job to an uncompleted schedule. Consequently, the start times can be computed directly from the so far planned jobs and more tight lower bounds can be computed for the so far unplanned jobs. By means of computational experiments, the developed Branch-and-Bound algorithms were compared with the classical approach, which means solving a mixed-integer linear program of the VRPCC by a commercial solver. The results showed that both Branch-and-Bound algorithms solved the small instances faster than the classical approach

Distributed Services with Foreseen and Unforeseen Tasks: The Mobile Re-allocation Problem

In this paper we deal with a common problem found in the operations of security and preventive/corrective maintenance services: that of routing a number of mobile resources to serve foreseen and unforeseen tasks during a shift. We define the (Mobile Re-Allocation Problem) MRAP as the problem of devising a routing strategy to maximize the expected weighted number of tasks served on time. For obtaining a solution to the MRAP, we propose to solve successively a multi-objective optimization problem called the stochastic Team Orienteering Problem with Multiple Time Windows (s-TOP-MTW) so as to consider information about known tasks and the arrival process of new unforeseen tasks. Solving successively the s-TOP-MTW we find that considering information about the arrival process of new unforeseen tasks may aid in maximizing the expected proportion of tasks accomplished on time.location;reliability;routing;distributed services