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Generalized assignment problem

About: Generalized assignment problem is a research topic. Over the lifetime, 3728 publications have been published within this topic receiving 112930 citations.


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Journal ArticleDOI
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.

11,096 citations

Book
01 Nov 1990
TL;DR: This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.
Abstract: Introduction knapsack problem bounded knapsack problem subset-sum problem change-making problem multiple knapsack problem generalized assignment problem bin packing problem. Appendix: computer codes.

3,694 citations

Journal ArticleDOI
01 Jun 1981-Networks
TL;DR: This paper presents a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost and shows that it has outperformed the best existing heuristics on a sample of standard test problems.
Abstract: : We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.

1,050 citations

Journal ArticleDOI
TL;DR: In this article, the equivalence of the Koopmans-beckmann problem to a linear assignment problem with certain additional constraints is demonstrated, and a method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions.
Abstract: This paper presents a formulation of the quadratic assignment problem, of which the Koopmans-Beckmann formulation is a special case. Various applications for the formulation are discussed. The equivalence of the problem to a linear assignment problem with certain additional constraints is demonstrated. A method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions. Further generalizations to cubic, quartic, N-adic problems are considered.

867 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202229
202119
202019
201931
201830