A Heuristic Program for Locating Warehouses

Kuehn, Alfred A.; Hamburger, Michael

doi:10.1287/mnsc.9.4.643

Cited by 596 publications

(98 citation statements)

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“…Relatively few instances of approximation guarantees via local search are known. Korupolu, Plaxton, and Rajaraman [23] gave the first approximation guarantees of this type for the facility location and k-median problems based on a simple local search heuristic proposed by Kuehn and Hamburger [25]. For the k-median problem, however, they violate the constraint on the number of open facilities by a factor 1 + .…”

Section: Local Search Based Approachesmentioning

confidence: 99%

Local Search Algorithms for the Red-Blue Median Problem

2011

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In this paper, we consider the following red-blue median problem which is a generalization of the well-studied k-median problem. The input consists of a set of red facilities, a set of blue facilities, and a set of clients in a metric space and two integers k r , k b ≥ 0. The problem is to open at most k r red facilities and at most k b blue facilities and minimize the sum of distances of clients to their respective closest open facilities.We show, somewhat surprisingly, that the following simple local search algorithm yields a constant factor approximation for this problem. Start by opening any k r red and k b blue facilities. While possible, decrease the cost of the solution by closing a pair of red and blue facilities and opening a pair of red and blue facilities.We also improve the approximation factor for the prize-collecting k-median problem from 4 (Charikar et al. in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pp. 642-641, 2001) to 3 + , which matches the current best approximation factor for the k-median problem.

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Section: Local Search Based Approachesmentioning

confidence: 99%

Local Search Algorithms for the Red-Blue Median Problem

2011

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“…In order to avoid the computational problems typically posed by capacity constraints associated with facilities (see, e.g., Kuehn and Hamburger 1963), we will assume that the firm's branches have sufficient capacities to supply any reasonable number of units of the good demanded by the customers.…”

Section: The Modelmentioning

confidence: 99%

Optimizing subsidies for the location of distribution centers

Bhadury

Eiselt

2010

Ann Reg Sci

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The paper introduces a three-level model of location. On the lowest level, customers purchase the good from a firm. On the next higher level, the firm will decide how many distribution centers it will establish and where these centers are to be located. In addition to its location costs, the firm's location decision will also be guided in part by the subsidy offered by a regional planner. Finally on the highest level, the regional planner will use its own revenue that it derives from the firm's economic activities to offer a subsidy to the firm. This subsidy is assumed to be based purely on economic, rather than political considerations. In other words, the regional planner's objective is to maximize its revenue. The paper then formally constructs models for the firm and the regional planner and examines their relations. It turns out that the models can be combined and greatly simplified. Computational tests on a set of published data confirm the solvability of the model. They also reveal the strong decrease of the proportion of unmet demand as economic multipliers and/or prices increase. This also implies an increase in the subsidy that must be paid to the firm, as the regional planner wants to convince it to locate the number of centers it prefers at the sites it wants them to be. Additional tests investigate the effects that result from price and related demand changes in case of elastic demand. JEL Classification H25 · H71 · C44 · C72

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“…To avoid having to use a general integer programming code to solve this problem, a heuristic algorithm was developed based upon earlier work by Kuehn and Hamburger (1963), Feldman and others (1966), Sfi (1969), Shannon and Ignizio (1970), and Khumawala (1971). The algorithm has been summarized in Dykstra and Riggs (1977) and is described fully in Dykstra (1976).…”

Section: The Optimization Modelmentioning

confidence: 99%

Timber harvest planning—A combined optimization/simulation model

Arthur

Dykstra

1980

Environmental Management

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A special cascading fixed charge structure can be used to characterize a |orest management ptanning problem in which the objectives are to identify the optimal shape of forest harvest cutting units and simultaneously to assign facilities for logging those units. We describe a four-part methodology that has been developed to assist forest managers in analyzing areas proposed for harvesting. This methodology performs an analysis of harvesting feasibility, computes the optimal solution to the cascading fixed charge problem, undertakes a GASP IV simulation to provide additional information about the proposed harvesting operation, and permits the forest manager to perform a time-cost analysis that may lead to a more realistic, and thus improved, solution.Designing optimal forest harvest cutting areas, or units, and assigning logging equipment to them are two of the more difficult problems faced by those involved in commercial forest management. During the 1930s, forest managers became interested in the problem of defining the optimal shape of forest harvest cutting units. Matthews (1942) intuitively derived the optimal cutting unit shapes for two forest management situations. The first was an isolated cutting unit, that is, a unit without boundary interaction with adjacent units. For this case, Matthews argued that the optimal shape was circular, assuming that the timber on the area was uniformly distributed and that logging costs were composed of a fixed component plus a variable component that was linearly related to the distance from the tree to the central landing (where the logs are assembled to be loaded onto trucks). The second situation involved the same assumptions as the first, but allowed for interaction with adjacent units. For this case, Matthews thought that the optimal shape was a rectangle.Analytical work by Lussier (1961) and Peters (1978) has shown that, for the assumptions listed above, Matthews' conclusions are essentially correct. However, Peters has been able to prove that under certain conditions the boundaries between adjacent interacting units are slightly curved rather than strictly linear.Matthews' procedures for determining optimal cutting unit size and shape have been widely used in the forest industry for 35 years. For regions where his assumptions are applicable (much of the southeastern and mid-KEY WORDS: Fores1 management, Timber harvesting, Cascading fixed charge structure, Mathematical programming, Computer simulation. Environmental Management, Vol. 4, No. 6, pp. 491~.98western US, and eastern Canada), there is little motivation to revise them. In many forested areas, however, these assumptions simply do not apply. One such area is the Douglas fir region of the Pacific Northwest. This region is characterized by rugged, non-uniform terrain and by timber that is distributed in type islands, or patches, rather than uniformly over the ground. As a result, logging costs are functionally related not only to the distance from the stump to the landing but also to the terrain and the distribu...

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A Heuristic Program for Locating Warehouses

Cited by 596 publications

References 0 publications

Local Search Algorithms for the Red-Blue Median Problem

Local Search Algorithms for the Red-Blue Median Problem

Optimizing subsidies for the location of distribution centers

Timber harvest planning—A combined optimization/simulation model

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