A framework for the rechargeable energy for multi-vehicle Travelling Salesman Problem with single repository
TL;DR: Fuzzy Multi Objective Linear Programming is formulated to solve the multiple TSP with single repository with numerical computations to reduce the overall travelling expenses and travelling space by the different Electric Vehicles.
Abstract: This paper deals with the optimisation of various resources in a network under multiple objectives such as project duration and cost criteria. In this work, the Multiple electric Vehicles a...
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01 Jan 1970TL;DR: A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
Abstract: By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined.
An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples.
Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value.
The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
6,919 citations
"A framework for the rechargeable en..." refers background in this paper
...Bellman and Zadeh (1970) primarily projected the choice devising notion in Fuzzy atmosphere with numerous objectives....
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01 Jan 2001
TL;DR: In this paper, the authors present a comprehensive overview of the most important techniques proposed for the solution of hard combinatorial problems in the area of vehicle routing problems, focusing on a specific family of problems.
Abstract: 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. The book is composed of three parts containing contributions from well-known experts. The first part covers basic VRP, known more commonly as capacitated VRP. The second part covers three main variants of VRP with time windows, backhauls, and pickup and delivery. The third part covers issues arising in real-world VRP applications and includes both case studies and references to software packages. The book will be of interest to both researchers and graduate-level students in the communities of operations research and matematical sciences. It focuses on a specific family of problems while offering a complete overview of the effective use of the most important techniques proposed for the solution of hard combinatorial problems. Practitioners will find this book particularly usef
3,395 citations
TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
3,357 citations
"A framework for the rechargeable en..." refers methods in this paper
...The projection for converting multiple objective Linear Programming to a single objective Linear Programming in Fuzzy was inflict by Zimmerman (1978)....
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TL;DR: The multiple traveling salesman problem (mTSP) as discussed by the authors is a generalization of the well-known TSP, where more than one salesman is allowed to be used in the solution.
Abstract: The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Moreover, the characteristics of the mTSP seem more appropriate for real-life applications, and it is also possible to extend the problem to a wide variety of vehicle routing problems (VRPs) by incorporating some additional side constraints. Although there exists a wide body of the literature for the TSP and the VRP, the mTSP has not received the same amount of attention. The purpose of this survey is to review the problem and its practical applications, to highlight some formulations and to describe exact and heuristic solution procedures proposed for this problem.
1,019 citations
"A framework for the rechargeable en..." refers methods in this paper
...Bektas (2006) discussed the formulations and solution procedures for the multiple TSP. Ghafurian and Javadian (2011) discussed the ant colony algorithm for themultiple travelling salesmanwith fixedmultiple depot....
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TL;DR: In this article, an extension of the classical Vehicle Routing Problem (VRP) with a broader and more comprehensive objective function that accounts not just for the travel distance, but also for the amount of greenhouse emissions, fuel, travel times and their costs is presented.
Abstract: The amount of pollution emitted by a vehicle depends on its load and speed, among other factors. This paper presents the Pollution-Routing Problem (PRP), an extension of the classical Vehicle Routing Problem (VRP) with a broader and more comprehensive objective function that accounts not just for the travel distance, but also for the amount of greenhouse emissions, fuel, travel times and their costs. Mathematical models are described for the PRP with or without time windows and computational experiments are performed on realistic instances. The paper sheds light on the tradeoffs between various parameters such as vehicle load, speed and total cost, and offers insight on economies of ‘environmental-friendly’ vehicle routing. The results suggest that, contrary to the VRP, the PRP is significantly more difficult to solve to optimality but has the potential of yielding savings in total cost.
924 citations
"A framework for the rechargeable en..." refers background in this paper
...…of incorporating the electric-energy-based restrictions into routing problems (Golden, Raghavan, andWasil 2008); examples are the minimisation of emissions (Figliozzi 2010), energy consumption (Erdoğan and Miller-Hooks 2012), reverse logistics and others (Bektaş and Laporte 2011; Lin et al. 2014)....
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