On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Routing Applications in Newspaper Delivery

-The goal of this report is to give an up-to-date account of routing applications in the newspaper business. We describe the newspaper supply chain, and focus on the “last mile” distribution that has been advocated as an application of arc routing in the literature. A literature survey is provided, followed by a discussion of the arc routing model and its adequacy to newspaper applications. A more general and normally more adequate model: The Node, Edge, and Arc Routing Problem, is discussed. Characteristics of routing problems in carrier delivery are presented, together with a case study from the development of a web-based route design and revision system. Finally, summary, conclusions, and prospects for the future are given

The stochastic vehicle routing problem : a literature review, part I : models

Building on the work of Gendreau et al. (Eur J Oper Res 88(1):3–12; 1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems. The numerous variants of the problem that have been studied in the literature are described and categorized. Keywords: vehicle routing (VRP), stochastic programming, SVRPpublishedVersio

Solving the Traveling Salesman Problem with release dates via branch and cut

In this paper we study the Traveling Salesman Problem with release dates (TSP-rd) and completion time minimization. The TSP-rd considers a single vehicle and a set of customers that must be served exactly once with goods that arrive to the depot over time, during the planning horizon. The time at which each requested good arrives is called release date and it is known in advance. The vehicle can perform multiple routes, however, it cannot depart to serve a customer before the associated release date. Thus, the release date of the customers in each route must not be greater than the starting time of the route. The objective is to determine a set of routes for the vehicle, starting and ending at the depot, where the completion time needed to serve all customers is minimized. We propose a new Integer Linear Programming model and develop a branch and cut algorithm with tailored enhancements to improve its performance. The algorithm proved to be able to significantly reduce the computation times when compared to a compact formulation tackled using a commercial mathematical programming solver, obtaining 24 new optimal solutions on benchmark instances with up to 30 customers within one hour. We further extend the benchmark to instances with up to 50 customers where the algorithm proved to be efficient. Building upon these results, the proposed model is adapted to new TSP-rd variants (Capacitated and Prize-Collecting TSP), with different objectives: completion time minimization and traveling distance minimization. To the best of our knowledge, our work is the first in-depth study to report extensive results for the TSP-rd through a branch and cut, establishing a baseline and providing insights for future approaches. Overall, the approach proved to be very effective and gives a flexible framework for several variants, opening the discussion about formulations, algorithms and new benchmark instances

REVISIÓN DE LA LITERATURA DEL PROBLEMA DE RUTEO DE VEHÍCULOS EN UN CONTEXTO DE TRANSPORTE VERDE

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master's and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green-VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed. En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable. Document type: Articl

Revisión de la literatura del problema de ruteo de vehículos en un contexto de transporte verde

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master’s and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green- VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed.En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable

Demand robust counterpart open capacitated vehicle routing problem time windows and deadline model of garbage transportation with LINGO 13.0

Demand robust counterpart-open capacitated vehicle routing problem with time windows and deadline (DRC-OCVRPtw,d) model formed and explained in this paper, is the model used to find the minimum distance and the time needed for vehicles to transport garbage in Sukarami Sub-District, Palembang that consists of the time it takes for the vehicle to pass through the route. Time needed to transport garbage to the vehicle is called time windows. Combination of the thoses times is called deadline. The farther the distance passed by vehicle and the more garbage transported, the longer the deadline is needed. This DRC-OCVRPtw,d model is completed by LINGO 13.0 to obtain the optimal route and time deadline for Sukarami Sub-District. The model shows that the improved model of open vehicle routing problem involving the robustness, time windows and deadline can achieve the optimal routes that enable driver to save operational time in picking up the garbage compared to similar problem not involving no-time windows and deadline stated in previous research

Routing Optimization Under Uncertainty

We consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized. The objective is to obtain optimal routing solutions that would, as much as possible, adhere to a set of specified requirements after the uncertainty is realized. These problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain, and sending multiple capacitated vehicles to different nodes to meet the customers’ uncertain demands. We introduce a precise mathematical framework for defining and solving such routing problems. In particular, we propose a new decision criterion, called the Requirements Violation (RV) Index, which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur. The criterion can handle instances when probability distributions are known, and ambiguity when distributions are partially characterized through descriptive statistics such as moments. We develop practically efficient algorithms involving Benders decomposition to find the exact optimal routing solution in which the RV Index criterion is minimized, and we give numerical results from several computational studies that show the attractive performance of the solutions