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A location based heuristic for general routing problems
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Abstracts in Location Analysis
A location based heuristic for general routing problems Julien Bramel and David Simchi-Levi Operations Research Vol. 43, No. 4, 1995, p. 649 ff. We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems. Locating discretionary service Facilities, II: Maximizing market size, minimizing inconvenience Oded Berman, Dimitris Bertsimas and Richard C. Larson Operations Research Vol. 43, No. 4, 1995, p. 623 ff. Discretionary service facilities are providers of products and/or services that are purchased by customers who are traveling on otherwise preplanned trips such as the daily commute. Optimum location of such facilities requires them to be at or near points in the transportation network having sizable flows of different potential customers. N. Fouska (1988) and 0. Berman, R. Larson and N. Fouska (BLF 1992) formulate a first version of this problem, assuming that customers would make no deviations, no matter how small, from the preplanned route to visit a discretionary service facility. Here the model is generalized in a number of directions, all sharing the property that the customer may deviate from the preplanned route to visit a discretionary service facility. Three different generalizations are offered, two of which can be solved approximately by greedy heuristics and the third by any approximate or exact method used to solve the p-median problem. We show for those formulations yielding to a greedy heuristic approximate solution, including the formulation in BLF, that the problems are examples of optimizing submodular functions for which the G. Nemhauser, L. Wolsey and M. Fisher (1978) bound on the performance of a greedy algorithm holds. In particular, the greedy solution is always within 37% of optimal, and for one of the formulations we prove that the bound is tight. Lower bounds for the hub location problem Morton Kelly, Darko Skorin-Kapov and Jadranka Management Science Vol. 41, No. 4, 1995, p. 713 ff.
Skorin-Kapov
We present a new lower bound for the hub location problem (HLP) where distances satisfy the triangle inequality. Our lower bound is based on a linearization of the problem and its modification obtained by incorporating the knowledge of a known heuristic solution. A lower bound was computed for some standard data sets from the literature ranging between 10 and 2.5 nodes, with 2, 3, and 4 hubs, and for different values for the parameter CX,representing the discount for the flow between hubs. The novel approach of using a known heuristic solution to derive a lower bound in all cases reduced the difference between the upper and lower bound. This difference measures the quality of the best known heuristic solution in percentages above the best lower bound. As a result of this research, for smaller problems (all instances with 10 and 15 nodes) the average difference is reduced to 3.3%. For larger sets (20 and 25 nodes) the average difference is reduced to 5.9%. Polynomial algorithms for center location on spheres Mordechai Jaeger and Jeff Goldberg Naval Research Logistics Vol. 44, 1997, pp. 341-352 When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the one- and two-center problems on a
Abstracts in Location Analysis
A location based heuristic for general routing problems Julien Bramel and David Simchi-Levi Operations Research Vol. 43, No. 4, 1995, p. 649 ff. We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems. Locating discretionary service Facilities, II: Maximizing market size, minimizing inconvenience Oded Berman, Dimitris Bertsimas and Richard C. Larson Operations Research Vol. 43, No. 4, 1995, p. 623 ff. Discretionary service facilities are providers of products and/or services that are purchased by customers who are traveling on otherwise preplanned trips such as the daily commute. Optimum location of such facilities requires them to be at or near points in the transportation network having sizable flows of different potential customers. N. Fouska (1988) and 0. Berman, R. Larson and N. Fouska (BLF 1992) formulate a first version of this problem, assuming that customers would make no deviations, no matter how small, from the preplanned route to visit a discretionary service facility. Here the model is generalized in a number of directions, all sharing the property that the customer may deviate from the preplanned route to visit a discretionary service facility. Three different generalizations are offered, two of which can be solved approximately by greedy heuristics and the third by any approximate or exact method used to solve the p-median problem. We show for those formulations yielding to a greedy heuristic approximate solution, including the formulation in BLF, that the problems are examples of optimizing submodular functions for which the G. Nemhauser, L. Wolsey and M. Fisher (1978) bound on the performance of a greedy algorithm holds. In particular, the greedy solution is always within 37% of optimal, and for one of the formulations we prove that the bound is tight. Lower bounds for the hub location problem Morton Kelly, Darko Skorin-Kapov and Jadranka Management Science Vol. 41, No. 4, 1995, p. 713 ff.
Skorin-Kapov
We present a new lower bound for the hub location problem (HLP) where distances satisfy the triangle inequality. Our lower bound is based on a linearization of the problem and its modification obtained by incorporating the knowledge of a known heuristic solution. A lower bound was computed for some standard data sets from the literature ranging between 10 and 2.5 nodes, with 2, 3, and 4 hubs, and for different values for the parameter CX,representing the discount for the flow between hubs. The novel approach of using a known heuristic solution to derive a lower bound in all cases reduced the difference between the upper and lower bound. This difference measures the quality of the best known heuristic solution in percentages above the best lower bound. As a result of this research, for smaller problems (all instances with 10 and 15 nodes) the average difference is reduced to 3.3%. For larger sets (20 and 25 nodes) the average difference is reduced to 5.9%. Polynomial algorithms for center location on spheres Mordechai Jaeger and Jeff Goldberg Naval Research Logistics Vol. 44, 1997, pp. 341-352 When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the one- and two-center problems on a