Networks and vehicle routing for municipal waste collection

Beltrami, Edward; Bodin, Lawrence

doi:10.1002/net.3230040106

Cited by 397 publications

(208 citation statements)

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“…most notahly those suggested by Beltrami and Bodin [7] and by Yellow [80]. In this paper, we emphasize data structures and list processing and discuss a new implementation of the Clarke-Wright algorithm which is motivated by (i) optimality considerations,…”

Section: Heuristic Solution Techniques For Single Depot Problemsmentioning

confidence: 96%

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Implementing vehicle routing algorithms

1977

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Heuristic programming algorithms frequently address large problems and require manipulation and operation on massive data sets. The algorithms can be improved by using efficient data structures. With this in mind, we consider heuristic algorithms for vehicle routing, comparing techniques of Clarke and Wright, Gillett and Miller, and Tyagi, and presenting modifications and extensions which permit problems involving hundreds of demand points to be solved in a matter of seconds. In addition, a multi‐depot routing algorithm is developed. The results are illustrated with a routing study for an urban newspaper with an evening circulation exceeding 100,000.

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Section: Heuristic Solution Techniques For Single Depot Problemsmentioning

confidence: 96%

“…Finally, the subtourn~. 7 breaking constraints (3.9) can be any of the equations specified previously.…”

Section: Vehicle Dispatchingmentioning

confidence: 99%

Implementing vehicle routing algorithms

1977

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“…Both constrained p-median and set-covering models have been developed to optimize the locations of these bins (Devotta et al 2008). The next task is to devise efficient routes (Beltrami and Bodin 1974). The garbage collection problem has an added complexity due to randomness in the volume of trash.…”

Section: Solid Waste Collection and Disposalmentioning

confidence: 99%

Unary NP-Complete (NP-Hard)

2013

Encyclopedia of Operations Research and Management Science

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A transportation problem in which the total amount to be shipped (supply) is not equal to the total demand. The unbalanced problem can be stated as a standard transportation problem by the addition of a fictitious destination when the supply is greater than the demand, or by adding a fictitious origin if the demand is greater than the supply. In the first case, the demand at the fictitious destination is the difference between the total supply and total demand, while in the second case, the supply at the fictitious origin is the difference between the total demand and total supply. See ▶ Transportation Problem Unbounded Optimal SolutionA solution to a constrained optimization problem in which the objective function value can be shown to increase (or decrease) without bound on the feasible region. A real-world problem whose mathematical model exhibits an unbounded optimal solution must have an incorrect formulation. Unconstrained OptimizationAriela Sofer George Mason University, Fairfax, VA, USA IntroductionUnconstrained optimization is concerned with finding the minimizing or maximizing points of a nonlinear function, where the variables are free to take on any value. Unconstrained optimization problems occur in a wide range of applications in science and engineering. A rich source of unconstrained optimization problems are data-fitting problems, in which some model function with unknown parameters is fitted to data, using some criterion of best fit. This criterion may be the minimum sum of squared errors, or the maximum of a likelihood or entropy function. Unconstrained problems also arise from constrained optimization problems, since these are often solved by solving a sequence of unconstrained problems.In mathematical terms, an unconstrained minimization problem can be written in the form minimize f ðxÞ; where x ¼ ðx 1 ; . . . ; x n Þ T is a vector of unrestricted variables in the n-dimensional space < n . Ideally, one would like to find a global minimizer of the function, i.e., a point x Ã that yields the lowest value of f. Such a solution satisfies If the inequality above holds strictly, i.e., f ðx Ã Þ < f ðxÞ for all x, then x Ã is a strict global minimizer.In many cases, finding a global minimizer is extremely difficult. For this reason, most algorithms attempt only to find a local minimizer of the function, i.e., a point x Ã that satisfies f ðx Ã Þ f ðxÞ for all x in some neighborhood of x Ã . If the objective f is a convex function (see the next section), a local minimizer will also be a global minimizer; however, for nonconvex functions this property does not generally hold.There is no inherent difference between minimization problems and maximization problems, since maximizing f can be accomplished by minimizing À f and then multiplying the optimal objective values by À 1. For this reason it is sufficient to focus only on unconstrained minimization problems. BackgroundMuch of the research in unconstrained optimization has focused on functions with continuous derivatives. Throughout this discussion it ...

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“…In industry this approach is known as common frequency routing (Chuah and Yingling 2005). The structure of the resulting problem resembles that of the periodic vehicle routing problem, PVRP (Beltrami and Bodin 1974;Russell and Igo 1979;Christofides and Beasley 1984). The MCP was interpreted as PIRP in a series of works.…”

Section: Literature Reviewmentioning

confidence: 99%