The Time Window Assignment Vehicle Routing Problem

In many distribution networks, it is vital that time windows in which deliveries are made are assigned to customers for the long term. However, at the moment of assigning time windows demand is not known. In this paper we introduce the time window assignment vehicle routing problem, the TWAVRP. In this problem time windows have to be assigned before demand is known. Next the realization of demand is revealed and an optimal vehicle routing schedule has to be made that satisfies the time window constraints. We assume that different scenarios of demand realizations are known, as well as their probability distribution. The TWAVRP is the problem of assigning time windows such that the expected traveling costs are minimized. We propose a formulation of the TWAVRP and develop two variants of a column generation algorithm to solve the LP relaxation of this formulation. Numerical experiments show that these algorithms provide us with very tight LP-bounds to instances of moderate size in reasonable computation time. We incorporate the column generation algorithm in a branch and price algorithm and find optimal integer solutions to small instances of the TWAVRP. In our numerical experiments, the branch and price algorithm typically finds the optimal solution very early in the branching procedure and spends most time on proving optimality

Solving school bus routing and student assignment problems with heuristic and column generation approach.

In this dissertation, we solve a school bus routing problem of transporting students including special education (handicapped) students and assigning them in Oldham county education district. The main contribution of this research is that we consider special education students (Type-2) along with other students (Type-1) and design a comprehensive school bus schedule to transport both kinds of students at the same time. Also, a student assignment mathematical model is presented to optimize the number of bus stops in use as well as one important measure of service quality, the total student walking distance. Comparing to the classic clustering methods, heuristic methods, or other methods from previous literatures, a mathematical optimization model is developed to solve a student assignment problem and to obtain the global optimal solution. The modeling constraints include budget limit, travel time limit, equity, school time window, and etc. Especially, the main difference between our model and other models is that it takes Type-2 students into consideration along with critical constraints accordingly, and solves the resulting more complex problem. Moreover, the school bus routing model in this work is one of the most general optimization models representing the school bus routing problem. On the other hand, similar to all existing models, the developed model considers the total system cost as the objective function value to minimize, different bus capacities, and common vehicle routing constraints such as flow conservation on routes and subtour elimination. Furthermore, another main difference is that the bus scheduling and school time window is also considered and solved in the model. With two different types of students, both Type-1 and Type-2, the time restrictions are varying, resulting in more complexity and additional constraints. The results in this work present the difficulties of meeting the requirement of Type-2 student riding time limit and school time window simultaneously. Also, the constraints regarding service equity and quality are provided and they can be used by decision makers if necessary. Either densely populated urban areas or sparsely populated rural areas, the school bus routing problem is difficult to solve due to a large number of students or long travel distance. The school bus routing problem falls under vehicle routing problem (VRP) with additional requirements because each student represents one unit of capacity. In this dissertation, we present a modeling framework that solves a student assignment problem with bus stop selection, and subsequently a school bus routing problem with school time window constraints. We demonstrate the efficacy of heuristic methods as well as a column generation technique implemented to solve the problems using real data

A branch-and-cut algorithm for the Time Window Assignment Vehicle Routing Problem

This paper presents a branch-and-cut algorithm for the Time Window Assignment Vehicle Routing Problem (TWAVRP), the problem of assigning time windows for delivery before demand volume becomes known. A novel set of valid inequalities, the precedence inequalities, is introduced and multiple separation heuristics are presented. In our numerical experiments the branch-and-cut algorithm is 3.8 times faster when separating precedence inequalities. Furthermore, in our experiments, the branch-and-cut algorithm is 193.9 times faster than the best known algorithm in the literature. Finally, using our algorithm, instances of the TWAVRP are solved which are larger than the small scale instances previously presented in the literature

A Hybrid Multi-objective Genetic Algorithm for Bi-objective Time Window Assignment Vehicle Routing Problem

Providing a satisfying delivery service is an important way to maintain the customers’ loyalty and further expand profits for manufacturers and logistics providers. Considering customers’ preferences for time windows, a bi-objective time window assignment vehicle routing problem has been introduced to maximize the total customers’ satisfaction level for assigned time windows and minimize the expected delivery cost. The paper designs a hybrid multi-objective genetic algorithm for the problem that incorporates modified stochastic nearest neighbour and insertion-based local search. Computational results show the positive effect of the hybridization and satisfactory performance of the metaheuristics. Moreover, the impacts of three characteristics are analysed including customer distribution, the number of preferred time windows per customer and customers’ preference type for time windows. Finally, one of its extended problems, the bi-objective time window assignment vehicle routing problem with time-dependent travel times has been primarily studied.</p

Algoritma Ant Colony System Untuk Menyelesaikan Multi Depot Vehicle Routing Problem Dengan Variabel Travel Time

Seiring dengan berkembangnya dunia industri yang menjadikan masalah distribusi produk bertambah kompleks, perusahaan dituntut untuk dapat melakukan distribusi secara efisien. Penelitian ini membahas tentang optimasi pada distribusi hasil produksi yang mencakup sistem perancangan rute dan penentuan urutan pelayanan konsumen. Permasalahan tersebut dimodelkan sebagai Vehicle Routing Problem (VRP) dengan time window. Seiring dengan meningkatnya permintaan konsumen, suatu perusahaan dapat memiliki lebih dari satu depo untuk memenuhi permintaan. Kasus seperti ini selanjutnya dimodelkan sebagai Multi Depot Vehicle Routing Problem (MDVRP). Terdapat dua tahapan untuk menyelesaikan MDVRP yaitu clustering dan assignment. Dalam clustering digunakan metode Simplified Parallel Assignment, sedangkan untuk assignment digunakan metode Ant Colony System. Pada akhir penelitian, metode Ant Colony System dibandingkan dengan metode Simulated Annealing dan Particle Swarm Optimization. Dari hasil simulasi metode Particle Swarm Optimization mampu menghasilkan travel time minimum. Sedangkan hasil algoritma ant colony system terbukti tidak mengalami perubahan yang signifikan saat mengalami perubahan parameter, termasuk perubahan permintaan konsumen dan persediaan depo. ======================================================================================================== With the growing business and hence increase in the complexity of products distribution, minimizing the cost of logistics becomes a significant factor in reducing the overall cost. This research discuss about optimization of products distribution including route planning-system and assignment of the daily products delivery. This problem can be modelled as Vehicle Routing Problem (VRP) with time window. As the increasing of consumer’s demands, the company may have more than one storehouse / depot in a city. Thus, it can be modelled as Multi Depot Vehicle Routing Problem (MDVRP). There are two step to solve MDVRP, those are clustering and assignment. In the clustering problem, Simplified Parallel Assignment was used while to solve the assignment problem, Ant Colony System was used in this research. At the end of this research, two others method were used for comparison, those are are Simulated Annealing and Particle Swarm Optimization. As the result of simulation, Particle Swarm Optimization methods has proven give the best result with minimum travel time, while the excellence of ACS itself is not showing a major change of travel time in the change of parameter including consumer demand and depot capacity

Abnormality Management in Spatial Crowdsourcing for Multi-skilled Workers Assignment

Crowdsourcing is dependent on a number of skilled workers who are needed to accomplish spatial tasks. This has been an active area of research and is gaining wide popularity now. Most of these tasks can be completed online due to convenience, but this method fails when there is a need of completing a task at actual physical locations. This has led to a new area called Spatial crowd sourcing that consists of location-specific tasks that require people who can accomplish them to physically arrive at specific locations. The tasks which require specific skillsets, completion times or other constraints are matched with workers who can meet these constraints and complete them. In this report we consider a situation where the jobs are at different locations with sequential sub-tasks, each with time and skill constraints, and are to be completed within the given interval by workers who have those required skills and are dispersed. The aim is to finish a majority of tasks in the environment before a final cap time given the constraints of this environment. First workers are assigned to tasks appropriately so that each worker has the skill needed to complete each of the tasks allocated. After the assignment is complete, a variant of the vehicle routing problem called vehicle routing problem with time windows (VRPTW) is used to assign these workers the paths and visiting times that they need to follow to reach specific task locations and finish them within the required time intervals. The vehicle routing problem with time windows (VRPTW) is a generalization of the vehicle routing problem where the service of a customer can only begin at time within the time window defined by the earliest and the latest times. We also consider the case when a worker cannot reach a particular task location in an abnormal situation and perform a re-assignment that does not need to re-assign tasks to all workers and is faster. By following these approaches, we aim to create a technique that can be applied to many real-world problems in the spatial crowd-sourcing environment with such practical events

Exact Two-Step Benders Decomposition for Two-Stage Stochastic Mixed-Integer Programs

Many real-life optimization problems belong to the class of two-stage stochastic mixed-integer programming problems with continuous recourse. This paper introduces Two-Step Benders Decomposition with Scenario Clustering (TBDS) as a general exact solution methodology for solving such stochastic programs to optimality. The method combines and generalizes Benders dual decomposition, partial Benders decomposition, and Scenario Clustering techniques and does so within a novel two-step decomposition along the binary and continuous first-stage decisions. We use TBDS to provide the first exact solutions for the so-called Time Window Assignment Traveling Salesperson problem. This is a canonical optimization problem for service-oriented vehicle routing; it considers jointly assigning time windows to customers and routing a vehicle among them while travel times are stochastic. Extensive experiments show that TBDS is superior to state-of-the-art approaches in the literature. It solves instances with up to 25 customers to optimality. It provides better lower and upper bounds that lead to faster convergence than related methods. For example, Benders dual decomposition cannot solve instances of 10 customers to optimality. We use TBDS to analyze the structure of the optimal solutions. By increasing routing costs only slightly, customer service can be improved tremendously, driven by smartly alternating between high- and low-variance travel arcs to reduce the impact of delay propagation throughout the executed vehicle route

A satellite navigation system to improve the management of intermodal drayage

The intermodal transport chain can become more efficient by means of a good organization of the drayage movements. Drayage in intermodal container terminals involves the pick up or delivery of containers at customer locations, and the main objective is normally the assignment of transportation tasks to the different vehicles, often with the presence of time windows. The literature shows some works on centralised drayage management, but most of them consider the problem only from a static and deterministic perspective, whereas the work we present here incorporates the knowledge of the real-time position of the vehicles, which permanently enables the planner to reassign tasks in case the problem conditions change. This exact knowledge of position of the vehicles is possible thanks to a geographic positioning system by satellite (GPS, Galileo, Glonass), and the results show that this additional data can be used to dynamically improve the solution