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Valid inequalities and facets of the capacitated plant location problem
 Mathematical Programming
, 1989
"... Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitate ..."
Abstract

Cited by 9 (1 self)
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Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
An Exact Algorithm for Multi – Product Bulk Transportation Problem
"... Abstract: — The paper investigates an NPHard nature Problem, where several commodities are produced in several plant sites with capacity constraints, and distributed to several destination sites according to demands and transportation constraints. We deal with the special case where the cost of the ..."
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Abstract: — The paper investigates an NPHard nature Problem, where several commodities are produced in several plant sites with capacity constraints, and distributed to several destination sites according to demands and transportation constraints. We deal with the special case where the cost of the transportation of the goods from plants to warehouse is a bulk cost. The problem becomes MultiProduct Bulk Transportation Problem (MPBTP) where one desires to get the requirement of different products depending on the availability from any plants. The model intends to minimize the total cost of the bulk transportation for meeting the demands of all products specified over the planning horizon of various warehouses while satisfying the capacity availability of the production plants without according priorities to them at a given time/facility. The practical restriction is that the entire requirement of each warehouse is to meet from one or more plants and a plant can supply to any number of destinations subject to the capacity available of the product at it. For this problem we developed a Pattern Recognition Technique based Lexi Search Algorithm, which comes under the exact methods. The concepts and the algorithm involving in this problem are discussed with a suitable numerical example. We programmed the proposed Lexi Search algorithm using C. This algorithm takes less CPU run time and hence it suggested for solving the higher dimensional problems.