Search results for "routing"
showing 10 items of 587 documents
Yet Another New Variant of Szász–Mirakyan Operator
2021
In this paper, we construct a new variant of the classical Szász–Mirakyan operators, Mn, which fixes the functions 1 and eax,x≥0,a∈R. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of Mn and a direct quantitative estimate are obtained. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Our results improve and extend similar ones on this topic, established in the last decade by many authors.
On the existence of the exponential solution of linear differential systems
1999
The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.
Vehicle routing with private and shared delivery locations
2021
Abstract The rapid growth of e-commerce has led to an increase of home delivery requests. Providing efficient distribution systems for services on the last mile has become a challenging issue for logistics companies, where a trade-off between the classical approaches, attended home delivery (AHD) and usage of shared delivery locations (SDLs) has been identified. AHD provides a higher quality of service but implies very high costs for the company, while usage of SDL requires customers to perform the very last mile by themselves. For companies, this bears the risk of a decrease in the perceived service quality. However, due to consolidation effects, transportation costs can be considerably mi…
The collaborative consistent vehicle routing problem with workload balance
2021
Abstract The rising competition in the logistics sector forces companies to be more economically efficient. One of the major sources of inefficiency is the incomplete usage of available resources, such as vehicles’ capacities. Mechanism that allow to better exploit such resources by enabling carrier collaborations are on the rise. Our study examines a centrally organized multi-period collaborative vehicle routing problem, where carriers can exchange customers who have to be serviced on a regular basis. Collaborations, where carriers serve frequent customers, are supposed to face the problem of (i) time consistency in terms of visiting time, and of (ii) service consistency. The latter ensure…
Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs
2019
Two critical yet frequently conflicting objectives for logistics and transportation service companies are improving customer satisfaction and reducing transportation cost. In particular, given a network of customer requests with preferred service times, it is very challenging to find vehicle routes and service schedules simultaneously that respect all operating constraints and minimize the total transportation and customers’ inconvenience costs. In this paper, we introduce the vehicle routing problem with time windows and convex node costs (VRPTW-CNC), in which we model each customer’s inconvenience cost as a convex function of the service start time at that customer. The VRPTW-CNC combine…
The min-max close-enough arc routing problem
2022
Abstract Here we introduce the Min-Max Close-Enough Arc Routing Problem, where a fleet of vehicles must serve a set of customers while trying to balance the length of the routes. The vehicles do not need to visit the customers, since they can serve them from a distance by traversing arcs that are “close enough” to the customers. We present two formulations of the problem and propose a branch-and-cut and a branch-and-price algorithm based on the respective formulations. A heuristic algorithm used to provide good upper bounds to the exact procedures is also presented. Extensive computational experiments to compare the performance of the algorithms are carried out.
Producing Routing Systems Flexibly Using a VRP Metamodel and a Software Product Line
2012
Routing problems occur in a wide variety of situations. Due to the heterogeneity of cases we do not yet know how to manage the complexity of addressing all the relevant aspects in logistic planning and solving the variety of different problem types in a cost-efficient way. In the last decade, we have witnessed an emergence of systematic approach into managing variation within a set of related software systems. This paper presents an application of these advances from software engineering into vehicle routing: we suggest the construction of a higher-level (meta-) model of routing problems and the application of a software product line approach. The proposed approach results in a flexible pro…
Automating the Parameter Selection in VRP: An Off-line Parameter Tuning Tool Comparison
2014
Vehicle route optimization is an important application of combinatorial optimization. Therefore, a variety of methods has been proposed to solve different challenging vehicle routing problems. An important step in adopting these methods to solve real-life problems is to find appropriate parameters for the routing algorithms. In this chapter, we show how this task can be automated using parameter tuning by presenting a set of comparative experiments on seven state-of-the-art tuning methods. We analyze the suitability of these methods in configuring routing algorithms, and give the first critical comparison of automated parameter tuners in vehicle routing. Our experimental results show that t…
A computational study of several heuristics for the DRPP
1995
The problem of designing a route of minimum length for a postman that starts and finishes at his office and has to deliver the mail along a set of streets in a city is known as the Rural Postman Problem. When the postman has to obey the directions of the streets, we have the directed version of this problem. Finding an exact solution, in the general case, is intractably difficult. Hence, we have implemented three heuristic algorithms for approximately solving this problem and a procedure for obtaining a lower bound to the optimal length. Also, we present numerical experimentations based on a collection of random instances with up to 30 connected components, 240 vertices and 801 arcs. A lowe…
Heuristics for the bi-objective path dissimilarity problem
2009
In this paper the path dissimilarity problem is considered. The problem has previously been studied within several contexts, the most popular of which is motivated by the need to select transportation routes for hazardous materials. The aim of this paper is to formally introduce the problem as a bi-objective optimization problem, in which a single solution consists of a set of p different paths, and two conflicting objectives arise, on one hand the average length of the paths must be kept low, and on the other hand the dissimilarity among the paths in the set should be kept high. Previous methods are reviewed and adapted to this bi-objective problem, thus we can compare the methods using th…