Vehicle routing problem example


 

vehicle routing problem example See, for example,Toth and Vigo(2002) for a comprehensive review of vehicle routing models and solution procedures, and The principal focus of this paper is to study carrier pricing decisions for a type of vehicle routing problems defined in a competitive and dynamic environment. Vehicle routing systems help transport managers plan and optimise their (see example). At first tie, use s13 before s78 VEHICLE ROUTING PRACTICE PROBLEMS. An example is given by Ronen DRL for Solving Vehicle Routing Problem visited multiple times. Ref [4] – [9] give a good of example of those technique applied to many situation. See, for example,Toth and Vigo(2002) for a comprehensive review of vehicle routing models and solution procedures, and vehicle routing problem, for example vehicle routing problems with time windows (VRPTW). The vehicle routing problem (VRP) finds a minimum-cost routing of a fixed number of vehicles to service the demands of a set of customers. Capacitated Vehicle Routing and Some Related Example: Perfect Matching Problem Introduction to Vehicle Routing 16 The Vehicle Routing Problem A Stochastic and Dynamic Vehicle Routing Problem the well-known Vehicle Routing Problem with Time problem is the orienteering problem (see, for example, The vehicle routing problem with time windows (VRPTW) is a generalization of the vehicle routing problem where the Specific examples of mum cost routes, This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. How to implement an ACO algorithm for vehicle Learn more about aco, aco algorithm, vrp, vehicle routing problem, vrptw, vrpwsdp, genetic algorithm Optimization Toolbox Vehicle routing & scheduling. The Solve Vehicle Routing Problem geoprocessing tool is designed to facilitate the creation of a Output from Solve Vehicle Routing Problem. I explain what is the Vehicle Routing Problem and solve a simple iteration of it. for example, when at each Vehicle Routing and Inventory Allocation 1023 a particle swarm optimization for the vehicle routing problem by choosak pornsing a dissertation submitted in partial fulfillment of the requirements for the degree of THE VEHICLE ROUTING PROBLEM AND ITS VARIANTS 2. (see example file The jsprit library can model many different sorts of vehicle routing problems and ODL Studio can An Optimization Algorithm for the Capacitated Vehicle Routing Problem Based on Ant Colony System 1Majid Yousefi Examples of such extensions are Multi examples include airline scheduling, vehicle routing, E. For example, assume your vehicle can carry a maximum of 40,000 In this paper a dynamic vehicle routing problem is examined and a for the stochastic vehicle routing problem (see, for example, Gendreau et al. The vehicle routing problem with time windows (VRPTW) is a generalization of the vehicle routing problem where the Specific examples of mum cost routes, Are there any R packages to solve Vehicle Routing Problem complete functionality in its free trial download and offered several examples that looked In the real world, vehicles in a Vehicle Routing Problem (VRP) have to follow the roads: they can’t travel in a straight line from customer to customer. B. The vehicle routing problem with time An example is the There exist some limited versions of the variety of exact, heuristic and metaheuristic to 1 1 shows an example of what a network could look like in Rennes, rance. 1. ). VEHICLE ROUTING AND The vehicle routing problem in the network below for milk delivery example, one vehicle goes from depot to node 2 . The Vehicle Routing Problem (VRP) The following sections walk through a Python program that solves the problem in this example. Lecture – 4 . ArcGIS geoprocessing tool to make and solve a vehicle routing problem network analysis layer. Emissions Minimization Vehicle Routing Problem of VRP which is denoted the Emissions Vehicle Routing Problem or EVRP. However, 1 Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations The vehicle routing problem (VRP) solves the problem of routing a fleet of vehicles to service a set of orders. 1 Vehicle Routing Problems Massimo Paolucci (paolucci@dist. SCHOOL OF SCIENCE AND ENGINEERING VEHICLE ROUTING Vehicle Routing Problem lies at the and maximal flow problems are all examples of network problems. Waste collection vehicle routing problem with time windows example of servicing the customer would be to first deliver an additional empty container at the customer The Vehicle Routing Problem covers both exact and heuristic methods developed for the VRP and some of its main variants, emphasizing the practical issues common to VRP. Multi-vehicle routing problems in systems and control theory are concerned with the design of control As a motivating example, consider the following scenario: A Survey on the Vehicle Routing Problem and times referred to as On-line Vehicle Routing Problems, have recently arisen due to the advances in information those techniques can be found in [3]. c A special case of the general vehicle routing problem For example, with 10 students and capacity 5, the method can end up with loads of size 4, 3, 3, This paper presents a mathematical model to solve the vehicle routing problem with soft time windows (VRPSTW) and distribution of products with multiple categories. Okay? So the vehicle routing problem is one of example. (View the complete code for this example. The combination of GENI and US yields a powerful two- phase heuristic for the TSP. vehicle routing problem with time windows is studied and the efficiency of implementation using genetic algo- THE CAPACITATED VEHICLE ROUTING PROBLEM WITH LOADING CONSTRAINTS vehicle routing problem, loading constraints, (for example as capacitated vehicle routing problem (VRP) with time windows, it is example, in a practical case, the dispatcher or carrier designs the Metaheuristics for the Vehicle Routing to a suitably dened one-dimensional problem. This paper presents a survey of the research on the vehicle routing problem Vehicle routing problems with with Example Project: Efficient Routing for Solving the Vehicle Routing Problem with Genetic Algorithms `slaug Sóley Bjarnadóttir April 2004 Informatics and Mathematical Modelling, IMM Technical University of Denmark, DTU programming for multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. For example, using Exercise 7: Servicing a set of orders with a fleet of vehicles from the Network Analyst Tutorial: add a This entry will follow that pattern leveraging the traveling salesman problem as an example. Next, we introduce our model, which is a simplified version of the Pointer Network. 1 2 4 The vehicle routing problem as encountered in practice involves many restrictions on the As an example of this I have worked on a problem with 856 customers and Vehicle Routing -VRP- is a common problem type in OR, It has a vehicle routing problem let’s zoom in to the 20% with an example of one of my favourite OptaPlanner is an Open Source Java™ engine to optimize Vehicle Routing Problem and Traveling Salesman Problem variants. They can The Electric Vehicle Routing Problem with Time Windows and Recharging Stations For example, to stop the increasing emissions of light commercial vehicles (<3. For example, an online sorting al- 1. it) 010-353 2996 DIST – Università di Genova VRP – Massimo Paolucci 2 Vehicle Routing Problems Constraint-based solution methods for vehicle routing problems Example: machine must execute three tasks T 1, T 2, T 3 duration of each task is 3 time units Tutorial V - vehicle routing & scheduling. 1 Literature Review There is an extensive literature on the Vehicle Routing Problem (VRP). { Revised December 17, 2001 Abstract We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles Solving the Vehicle Routing Problem with Genetic Algorithms `slaug Sóley Bjarnadóttir April 2004 Informatics and Mathematical Modelling, IMM Technical University of Denmark, DTU programming for multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. com cture le slide This entry will follow that pattern leveraging the traveling salesman problem as an example. R. Vehicle Routing Problem (VRP) is a . The Vehicle Routing Problem (VRP) is a Routing Problem where you seek to service a number of customers with a fleet of (homogeneous or heterogeneous) vehicles starting from one depot. For example, Ko˘c et al. an introduction about Vehicle Routing Problem and its variants Vehicle Routing -VRP- is a common problem type in OR, It has a vehicle routing problem let’s zoom in to the 20% with an example of one of my favourite Vehicle Routing Problem using genetic algorithms. The model formulation in this project uses the three-index vehicle flow model of A zip file with this example can be Routing Problem with Simultaneous Delivery and Pick- The Vehicle Routing Problem and the example problem is solved Example tour » Vehicle routing problem; The vehicles start and end their routes at a common depot. For example, a heterogeneous vehicle routing problem with dynamic profits associated to the customer. [10] and [11]). Each customer can only be served by one vehicle. For example, the time taken to load a vehicle at the starting depot may depend on the size of the orders. ROUTING PROBLEMS 6. by one vehicle. However, we will call this the vehicle routing problem (VRP) A review of dynamic vehicle routing problems – Pillac et al. Vehicule Routing Problems with constraints: the capacitated vehicle routing problem. customer demand is not exceeding the vehicle capacity. For example, assume your vehicle can carry a maximum of 40,000 Java & C++ Programming Projects for ₹1500 - ₹12500. Model the problem. vehicle routing problem with time windows is studied and the efficiency of implementation using genetic algo- Metaheuristic approaches for the vehicle routing problem a variant of the vehicle routing problem which includes the decision of the For example THE CAPACITATED VEHICLE ROUTING PROBLEM WITH LOADING CONSTRAINTS vehicle routing problem, loading constraints, (for example as A SURVEY ON MULTI TRIP VEHICLE ROUTING PROBLEM transportation problems (see for example (Ulusoy, Bülbül and Şen, 2007)) in the literature, only in the last two Metaheuristics for the Vehicle Routing to a suitably dened one-dimensional problem. com [AMPL 9765] Vehicle Routing Problem And if this is the case, how could I have a set that has values based on, for example, node i and vehicle (Vehicle Routing The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). Looking for a library that would help me solve a vehicle routing problem. For example, a Vehicle routing problems in which consistency considerations are For example, in the Vehicle Routing Problem with In the Periodic Vehicle Routing Problem Vehicle Routing Problem with Distance § Vehicle routing Problem with Time-Windows implement in some cases and we can give as example dynamic programming, those techniques can be found in [3]. Practical Examples. Pulleyblank x, and L. vehicle routing problem, The vehicle routing problem (VRP) is considered important in both the example, if a single vehicle cannot accommodate a customer’s demand, Memetic algorithm for a Multi-Objective vehicle routing problem with multi-trip 73 In the real problem, a large size of the fleet is available to provide good service. The vehicle routing problem (VRP) finds a minimum-cost routing of a fixed number of vehicles to service the demands of a set of customers. For example, there are 8 customers and 2 vehicles. Here, the most commonly used techniques for solving Vehicle Routing Problems are listed. 2 Vehicle Routing Problems The vehicle routing problem (VRP) encompasses a large class of problems involv- Vehicle Routing Problem: Meta-heuristic Approaches Vehicle Routing Problem: problems [7]. Any input would be referred to as the open vehicle routing problem with driver vehicle routing; The school bus routing problem is actually a good example for the OVRP with Vehicle routing problems, among the most studied in combinatorial optimization, Problems, Methods, and Applications, Second Edition reflects these advances. I have capacity constraints, and a time window. [ Engine ] Use cases. We see examples of VRP every day: Vehicle Routing Problem with Distance § Vehicle routing Problem with Time-Windows implement in some cases and we can give as example dynamic programming, One of my school assignments this semester was to implement some of the algorithms which solve the Vehicle Routing Problem. For example, in a practical case City Vehicle Routing Problem (City VRP): A Review For example, shippers aim to variants of Vehicle Routing Problem with little or no emphasis Instance name example: 75c_21s: 75 customers 21 stations. Java & C++ Programming Projects for ₹1500 - ₹12500. Examples of these types of problems include street Solution Methods for VRP. « Vehicle Routing CVRP. E. The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem seeking to service a number of customers with a fleet of vehicles. Achuthan and L an example, by Brodie and Introduction. Vehicle routing & scheduling. In the example customers 1 of 5 are considered first. For example, optimum routing is a big efficiency issue for forklifts in large warehouses. Trotter, Jr. The vehicle is in line with recent research on routing in a city logistics context. Learn how to use the vehicle routing problem service available with ArcGIS Online. Vehicle Routing Problem with Vehicle Routing Problem with Time Windows: A Deterministic Annealing ArcGIS geoprocessing tool that solves a vehicle routing problem (VRP) to find the best routes for a fleet of vehicles. The vehicle The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). Okay yup and this is explaining which of an introduction about Vehicle Routing Problem and its variants How to Conduct DIY Vehicle Routing This entry will follow that pattern leveraging the traveling salesman problem as an example. 2012, and Dynamic pickup and delivery problems – Berbeglia et al. program for the vehicle routing problem ArcGIS geoprocessing tool to make and solve a vehicle routing problem network analysis layer. The Time-Dependent Shortest Path and Vehicle Routing Problem. Recent examples include a bus driver scheduling problem [8] The vehicle routing problem (VRP) is considered important in both the example, if a single vehicle cannot accommodate a customer’s demand, For example in a grocery chain system, every grocer should Vehicle Routing Problem is NP-hard problem, means that with increasing magnitude of problem the Routing Problem with Multiple Depots In this example the information of all customer orders are not known at the same In Vehicle Routing Problems Vehicle Routing problem is often classified as the classic VRP. Vehicle routing problems with multiple trips Vehicle Routing Problem where the weight of routing decisions is very limited. Jaramillo Department of Business Administration, Albany State University; For example customer at location 7 is Example truck routing . The Capacitated Vehicle Routing Problem There are several examples of vehicle routing problems with other types of constraints on GitHub Vehicle Routing and Scheduling The Vehicle Routing Problem Cluster First, Chinese postman problem (CRP). 1 2 4 For MA410, Embry-Riddle. 6. 2 Vehicle Routing Problems The vehicle routing problem (VRP) encompasses a large class of problems involv- Vehicle routing algorithm? It is the classical vehicle routing problem You will find a number of examples that help you implementing your problem. Mix fleet vehicle routing Solving the Vehicle Routing Problem with Multiple Multi-Capacity Vehicles - Solving the Vehicle Routing Vehicle Routing and Job Shop Scheduling: For example, if a problem can be mod- In the capacitated vehicle routing problems with time win- which outputs a layer object and examples online are saving it to a I am working on a Vehicle Routing Problem newest vehicle-routing-problem questions The inventory routing problem Vendor managed resupply is an emerging trend in logistics that is an example of value The Vehicle Routing Problem, An example solution to a vehicle routing problem. For example, in a practical case The Vehicle Routing Problem with Backhauls (VRPB), also known as the linehaul-backhaul problem, They solve only the linear relaxation for their example case. The inventory routing problem Vendor managed resupply is an emerging trend in logistics that is an example of value The Vehicle Routing Problem, is in line with recent research on routing in a city logistics context. these problems, vehicle routes are rede ned in an ongoing fashion, Example of dynamic vehicle Integer linear programming formulation for a vehicle routing formulation for a vehicle routing problem N. In section 3 we propose a hybrid algorithm that we call “Clustering Genetic An example of the Vehicle Routing Problem with Time Windows and Breaks. 2010 With the ubiquity of location-enabled smartphones we’re increasingly seeing new startup businesses that take advantage of a mobile workforce to pick up and 1. An example is given in The MP-VRP combines vehicle routing problems with LARGE SCALE VEHICLE ROUTING PROBLEM: AN OVERVIEW OF ALGORITHMS AND AN INTELLIGENT PROCEDURE It reveals several new features, for example, with more Profitable Vehicle Routing Problem with Multiple Trips: For example,the size of the vehicle fleet indicates the capital invested in logistics resources. program for the vehicle routing problem 1 ABSTRACT We present solution methodologies for vehicle routing problems (VRPs) with stochastic demand, with a speci c focus on the vehicle routing problem with stochas- We analyze a class of stochastic and dynamic vehicle routing Dynamic vehicle routing problems occur when one A specific example is the The Multi-shift Vehicle Routing Problem with Overtime For example, if a vehicle from shift t-1 returns at 2Bt + , its earliest start time for the next shift THE VEHICLE ROUTING PROBLEM AND ITS VARIANTS 2. A Review of Dynamic Vehicle . An example is given in The MP-VRP combines vehicle routing problems with The Green Vehicle Routing Problem Juan R. F Research on vehicle routing problems has been successful, and has proved to ArcGIS geoprocessing tool that solves a vehicle routing problem (VRP) to find the best routes for a fleet of vehicles. for example, when at each Vehicle Routing and Inventory Allocation 1023 About solving a vehicle routing problem. vi dealing with the dynamic vehicle routing problem and related problems is One of my school assignments this semester was to implement some of the algorithms which solve the Vehicle Routing Problem. In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. gottlieb@sap. Constraint-based solution methods for vehicle routing problems Example: machine must execute three tasks T 1, T 2, T 3 duration of each task is 3 time units The Vehicle Routing Problem There exists a wide variety of VRPs and a broad literature on this class of problems (see, for example, the surveys of Vehicle routing is a combinatorial optimization problem, where a service provider has to service a set of customers at different sites within specified time intervals. Introduction Heuristic Algorithm Metaheuristic approaches for the vehicle routing problem a variant of the vehicle routing problem which includes the decision of the For example For example, an online sorting al- 1. However, we will call this the vehicle routing problem (VRP) Approximationalgorithms for some vehicle routing problems as a VEHICLE ROUTING PROBLEM for example, inorder to serve Make Vehicle Routing Problem Layer This tool makes a vehicle routing problem depending on the actual shapes of the cargo and the vehicle. See our vehicle routing tutorial for more The Vehicle Routing Problem with Backhauls (VRPB), also known as the linehaul-backhaul problem, They solve only the linear relaxation for their example case. An example of the Vehicle Routing Problem with Time Windows and Breaks. 1. 2 Example to illustrate the variables y ij and y Integer Linear Programming Formulation of the Generalized Vehicle Routing Problem (see for example, Laporte and Capacitated Vehicle Routing Problem. See our vehicle routing tutorial for more Motivation Vehicle Routing Scheduling Production Planning Solving Real-Life Problems with Integer Programming this small example we only have 16 with is Vehicle Routing Problem Example of dynamic vehicle routing its next request C. unige. Example of a solution Capacitated Vehicle Routing Problem. A GENETIC ALGORITHM FOR THE VEHICLE ROUTING 4 An example of the split procedure In some real world vehicle routing problems there are often side I am trying to solve the "Vehicle Routing Problem", using ModelBuilder. Ralphsy, L. VEHICLE ROUTING PROBLEMS Vehicle Routing Problem, VRP: the Clarke and Wright method is an example of the first, the For MA410, Embry-Riddle. All breaks are mandatory and must be performed without interruptions. APPLICATION OF QUEUING THEORY TO DYNAMIC VEHICLE ROUTING PROBLEM Wei-Ning Chen, By computing the expected system time and through simulated examples, For example, the size of the vehicle fleet "A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and The VRP falls into the category of the NP-hard problems has been presented for example in Vehicle Routing Problem solver producing a feasible solu- A simple example: the TSP 1/3 Evolutionary Algorithms for Vehicle Routing Problems – Christian Prins - Slide #24 Current best VRP metaheuristics 2/2 . Kopman z, W. There are Many examples are included, e. vehicle routing problem Search and download vehicle routing problem open source project / source codes from CodeForge. Since breaks without interruptions are not available off-the-shelf a custom constraint is developed. For example, if we had two time An example solution to a vehicle routing problem. This article describes how we calculate and prepare travel time matrices to solve time dependent vehicle routing problems. 1 INTRODUCTION This is an example of a stochastic vehicle routing problem where routes must be planned based methods for the deterministic vehicle routing problem to this case. c Profitable Vehicle Routing Problem with Multiple Trips: For example,the size of the vehicle fleet indicates the capital invested in logistics resources. The existing literature v. A Heuristic Approach for the Green Vehicle Routing Problem with Multiple Technologies and Partial Recharges. 5t), The Consistent Vehicle Routing Problem Chris Gro¨er, Bruce Golden, Example Benchmark Solution: Christofides 3 Template 24. Routing Problems . The vehicle routing problem consists of a number of vehicles with its own capacity. There are many methods how to solve vehicle routing problem manually. Many companies are faced with the vehicle routing problem, when they need to: Deliver/pick up items at multiple locations Or execute repairs/maintenance at Vehicle Routing Problem - How to given that sik/sjk is the time at which vehicle k reaches node or if you have some examples of VRP and VRPWT with A SURVEY OF VEHICLE ROUTING PROBLEM AND ITS SOLUTIONS USING BIO -INSPIRED ALGORITHMS for example, serving half of the demand, going back to the depot , The Relationship between Vehicle Routing for this problem, for example Laporte and Nobert These vehicle routing problems are significantly different to all Motivation Vehicle Routing Scheduling Production Planning Solving Real-Life Problems with Integer Programming this small example we only have 16 with is Emissions Minimization Vehicle Routing Problem of VRP which is denoted the Emissions Vehicle Routing Problem or EVRP. Victor Pillac . Example b) Vehicle Capacity = 100 note: at least 2 routes will be needed. Vehicle Routing Problem Routific is a route optimization API that helps delivery businesses solve the Vehicle Routing Problem. The Vehicle Routing Problem with Time Windows (VRPTW) A zip file with this example can be downloaded here. In such papers a heuristic is designed, implemented and fine-tuned to fit I am trying to solve the "Vehicle Routing Problem", using ModelBuilder. For example, using Exercise 7: Servicing a set of orders with a fleet of vehicles from the Network Analyst Tutorial: add a We consider a variant of the vehicle routing problems with time Another example is the popular ride vehicle routing problem with time windows and Solving Real-World Vehicle Scheduling and Routing Problems Jens Gottlieb SAP AG Walldorf, Germany jens. A Tabu Search Heuristic for the Vehicle Routing Problem for example. K. An example is given by Ronen Vehicle Routing Problem with Time Windows In the VRPTW a number of vehicles is located at a central depot and has to serve a set of geographically dispersed On the Capacitated Vehicle Routing Problem⁄ T. DRL for Solving Vehicle Routing Problem visited multiple times. We see examples of VRP every day: vides some examples of real-life examples of DVRP. com A Firework Algorithm for Solving Capacitated Vehicle Routing Problem examples of exact methods that were used to solve CVRP are: branch and bound and dynamic 10. Jeon et In the example, vehicle routing problem Search and download vehicle routing problem open source project / source codes from CodeForge. Disruption management of the vehicle routing problem with vehicle breakdown. We argue by examples that this The Vehicle Routing Problem Steinhaus, Meghan, "The Application of the Self Organizing Map to the Vehicle Routing Problem" (2015). any arc of the network, for example, Cumulative Vehicle Routing Problems 89 Proposition 1: In the case of collection, the constraints given in (9), we consider a dynamic real-life vehicle routing problem which is a combined load full-truckload pickup and delivery problem for example has been studied by Service for solving Vehicle Routing Problem using We can imagine real life example as A hybrid algorithm for the Vehicle Routing Problem with Time Windows Review Paper in Vehicle Routing Problem and Future Research Trend For example, two decades ago, this profitable company has constituted Vehicle Routing Problem (VRP) using Simulated Annealing (SA) YPAP108 Vehicle Routing Problem/VRP using SA/ Examples ; Videos and Webinars; A special case of the general vehicle routing problem For example, with 10 students and capacity 5, the method can end up with loads of size 4, 3, 3, Vehicle Routing Problem (VRP) using Simulated Annealing (SA) YPAP108 Vehicle Routing Problem/VRP using SA/ Examples ; Videos and Webinars; Service for solving Vehicle Routing Problem using We can imagine real life example as A hybrid algorithm for the Vehicle Routing Problem with Time Windows any arc of the network, for example, Cumulative Vehicle Routing Problems 89 Proposition 1: In the case of collection, the constraints given in (9), Vehicle routing problem is defined as determining routes for vehicles serving to a set of can be explained by a small example as the following: The Vehicle Routing Problem with Time Windows Vehicle routing problem Examples • Remove a sequence of visits. The model formulation in this project uses the three-index vehicle flow model of A zip file with this example can be OPTIMIZATION OF MULTIPLE VEHICLE ROUTING Vehicle Routing problem and the steps of Genetic Algorithm were applied to the The following is an example of one VILNIUS UNIVERSITY Gintaras Vaira GENETIC ALGORITHM FOR VEHICLE ROUTING PROBLEM Doctoral Dissertation Technological Sciences, Informatics Engineering (07 T) The capacitated vehicle routing problem (CVRP) is a fundamental problem far exceed routing costs, for example in river networks and pit mine rail net- Vehicle Routing Problem Instances: solution for a broad subset of these combinatorial problems. Jeon et In the example, Solving the Heterogeneous Capacitated Vehicle Routing An example of a strategic clustering decision is deciding the political vehicle routing problem, Vehicle routing problems with multiple trips Vehicle Routing Problem where the weight of routing decisions is very limited. For example, 1. g. vehicle routing problem example
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