Vehicle Routing Problem Analysis

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2.3 VEHICLE ROUTING PROBLEM
A vehicle routing problem can be described as the problem of designing least cost routes from one depot (dumpsite) to a set of geographically scattered points (garbage collection points). The routes must be designed in such a way that each point is visited only once by exactly one vehicle, all routes start and end at the depot, and the total garbage collected at all collection points on one particular route must not exceed the capacity of the collection vehicle. The vehicle routing problem with time windows is a generalization of the standard vehicle routing problem involving the added complexity that every garbage collection point should be collected within a given time window. Genetic algorithms are best suited
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The overall objective is to serve a set of customers at minimum cost with a fleet of vehicles of finite capacity operating out at a central depot (i.e. each route starts and ends at the depot). In this application, the objective is to minimize the number of routes and for the same number of routes, to minimize the total route time. To be feasible, the routes must also satisfy three different types of constraints. First, each customer has a certain demand, like a quantity of goods to be delivered. Since the capacity of each vehicle is finite, the total quantity of goods to bedelivered on a route cannot exceed the capacity of the vehicle assigned to their route. Second, there is a time window or time internal associated with each customer. No vehicle is allowed to arrive too late at a customer locationi.e. after the end of the time window. However, a vehicle can wait if it arrives too early, finally a time window is also included at the depot or garage. Each route must start and end within its time bounds. Time window acts similarly as capacity constraint, by expanding either the vehicle capacity or the time window at the depot; through this more customers can be serviced by the same vehicle (Potvin et al 1996).

The vehicle routing problem is of two types - Single Vehicle Routing Problem (SVRP) and Multiple Vehicle Routing Problem (MVRP). A SVRP is an umbrella description of three classical problems in operations research and transportation engineering, namely (i) the traveling salesman problem (TSP) (ii) the single vehicle pick-up and delivery problems (SVPDP) and (iii) the single vehicle pick-up and delivery problem with time window (SVPDPTW). Partha Chakroborty and Arijit Mandal (2005) published an optimization algorithm for the general

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