Integer Linear Programming Formulation of the Generalized Vehicle Routing Problem Imdat Kara, Tolga Bektas Baskent University, Dept. of Industrial Engineering, Baglica Kampusu, Eskisehir Yolu 20. km., Ankara, Turkey Abstract The Generalized Vehicle Routing Problem (GVRP) is an extension of the Vehicle Routing Problem (VRP) deﬁned on a graph ...

1 Introduction. The Vehicle Routing Problem with Multiple Synchronization constraints (VRPMS) can be used to model many real-world applications, like home care delivery, aircraft ﬂeet assignment, vehicle routing and scheduling, and forest operations, as reported in Rousseau et al. (2013). A Mathematical model for the Flexible Periodic Vehicle Routing Problem (FPVRP) is proposed.A Load-based formulation is developed to solve the FPVRP.A set of several inequalities are proposed to reinforce the load-based FPVRP formulation.A Load-based formulation for the Periodic Vehicle Routing Problem (PVRP) and a load-based formulation for the Flexible Periodic Vehicle Routing Problem with ... VARIABLE-DEPTH ADAPTIVE LARGE NEIGHBOURHOOD SEARCH ALGORITHM FOR OPEN PERIODIC VEHICLE ROUTING PROBLEM WITH TIME WINDOWS . Binhui Chen(a) , Rong Qu(b), Hisao Ishibuchi(c) (a),(b)School of Computer Science, The University of Nottingham, United Kingdom there are a large number of problems of this type, and that they areincludedinproblems that are known as Vehicle Routing Problem (VRP). 1. Vehicle Routing Problem In general, we can say that a VRP consist of determining a set of minimum cost routes starting and ending in the depots, with a set of The Vehicle Routing Problem, which main objective is to ﬁnd the lowest-cost set of routes to deliver goods to customers, has many applications in transportation services. In the past, costs have been mainly associated to the number of routes and the travel distance, however, in real-world problems there exist additional objectives.

Keywords: Dynamic, Multi-Period, Multi-Objective, Vehicle Routing, Variable Neighborhood Search. 1 Introduction The purpose of this paper is to model and solve the Dynamic Multi-Period Vehicle Routing Problem (DMPVRP). Our study is motivated by the case of Lantmännen, a large distributor operating in cost of a vehicle is the total of the traveling time and distance, waiting time and service time taken to visit a set of customers. The periodic vehicle routing problem (PVRP) involves designing a set of routes which minimizes costs for each day of a given T-day period. Each customer has a visit frequency for the period and can have at most one ... The Vehicle Routing Problem was rst introduced by Dantzig and Ramsey [4] in what they called The Truck Dispatching Problem. It was formulated as a branch of the Traveling Salesman Problem (TSP) with multiple vehicles and routes. Subsequently, many other extensions that include time windows, di erent depots, pick-up and delivery options, heterogeneous

the problem, the solution method and the results obtained. Mendez et al. [13] solved the infectious waste collection problem as a Periodic Vehicle Routing Problem, using a hybrid technique that involves an evolutionary algorithm for optimal planning of the collection days, and a local search algorithm to

For example, a popular restaurant may need daily visits, whereas a resident may need visited once per week. This problem is referred to as a Periodic Vehicle Routing Problem (PVRP), an extension of the vehicle routing problem (VRP). In the vehicle routing problem, multiple trucks are used to visit customers no more than once. vehicle routing problem has been defined as a broad field of study (Ombuki-Berman and Hanshar, 2009), which is not limited to merely a few academic courses that apply it only for traffic management. The general VRP model includes a set of customers, so that the demand of each customer is clear Vehicle Routing Problems (1/4) . Vehicle Routing Problems are at the core of a huge number of practical applications in the area of the distribution of goods and services. Summary. This chapter presents an overview of the Period Vehicle Routing Problem, a generalization of the classic vehicle routing problem in which driver routes are constructed over a period of time. We survey the evolution of the PVRP and present a synopsis of modeling and solution methods, including classical heuristics, metaheuristics,...

Vehicle Routing for ... Routing Problems in the Literature Periodic Vehicle Routing Problem (PVRP) C2 C1 C5 C6 C8 C7 0 C3 [q2, s2, f2] C4 [q3, s3, f3] Abstract. This paper deals with a case study which is a variant of the Periodic Vehicle Routing Problem (PVRP). As in the traditional Vehicle Routing Problem (VRP), customer locations each with a certain daily demand are given, as well as a set of capacitated vehicles. considered is the special case of a single vehicle, i.e. the Periodic Traveling Salesman Problem (PTSP). It is shown that slight changes of the proposed VNS procedure is also competitive for the PTSP. Keywords: Periodic Vehicle Routing Problem, Periodic Traveling Sales-man Problem, Metaheuristics, Variable Neighborhood Search 1 Introduction

(CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP). In the CVRP one has to deliver goods to a set of customers with known demands on minimum-cost vehicle routes originating and terminating at a depot. The vehicles are assumed to The Capacitated vehicle routing problem, which is been consider in this research, is one of the variants of the vehicle routing problem. In classical VRPs, typically the planning period is a single day. In the case of the Period Vehicle Routing Problem (PVRP), the classical VRP is generalized by extending the planning period to M days. We define the problem as follows: Objective. The objective is to minimize the vehicle fleet and the sum of travel time needed to supply all customers. (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP). In the CVRP one has to deliver goods to a set of customers with known demands on minimum-cost vehicle routes originating and terminating at a depot. The vehicles are assumed to Location-routing problem. Abstract. This paper presents a new Mixed-Integer Non-Linear Programming (MINLP) model for a Supply Vessel Planning (SVP) problem. The traditional SVP, which is a maritime transportation problem, is developed into a Maritime Fleet Sizing Mix Periodic Location-Routing Problem with Time Windows (MFSMPLRPTW) by considering

Vehicle routing problems that involve the periodic collection and delivery of goods and ser-vices as mail delivery or trash collection are of great practical importance. Simple variants of these real problems can be modeled naturally with graphs. Unfortunately even simple variants of vehicle routing problems are NP-hard.

The flexible periodic vehicle routing problem: modeling alternatives and solution techniques by Diana Lucia Huerta Muñoz ADVERTIMENT La consulta d’aquesta tesi queda condicionada a l’acceptació de les següents In this paper, it is considered a HFVRPTWSD problem (Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Split Deliveries) consisting of four instances (4 days of planning) with dimension of 40 clients, each with an associated demand and a specific time window to fulfill.

and Green Vehicle Routing has emerged. Vehicle Routing Problem (VRP) has been a very active area of the literature with contributionfrommanyresearchersoverthelastthreedecades.WiththecomputationalconstraintsofsolvingVRPwhichis NP-hard,metaheuristicshavebeenappliedsuccessfullytosolveVRPsintherecentpast.Thisisathreefoldstudy.First,itcritically

and Green Vehicle Routing has emerged. Vehicle Routing Problem (VRP) has been a very active area of the literature with contributionfrommanyresearchersoverthelastthreedecades.WiththecomputationalconstraintsofsolvingVRPwhichis NP-hard,metaheuristicshavebeenappliedsuccessfullytosolveVRPsintherecentpast.Thisisathreefoldstudy.First,itcritically Heuristics for Time Slot Management: A Periodic Vehicle Routing Problem View Florent Hernandez1,2, Michel Gendreau1,2, Jean-Yves Potvin1,3,* 1 Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT) The problem is then called Periodic Heterogeneous Vehicle Routing Problem (PHVRP). The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling of fleet and driver and routing policies of the vehicles.

R. Baldacci; N. Christofides; A. Mingozzi, An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts, in: Prooceedings of the AIRO2007, XXXVIII Conferenza Annuale Associazione Italiana Ricerca Operativa, s.l, s.n, 2007, pp. 1 - 1 (atti di: AIRO2007, XXXVIII Conferenza Annuale Associazione ... The vehicle routing problem (VRP), which is an extension of the well-known traveling salesman problem (TSP) , is considered NP-hard within the research area of combinatorial optimization problems. In TSP, a list of cities and the distances between each pair of cities are used to find the path that minimizes the distance traveled.