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Showing papers on "Assignment problem published in 1971"


Journal ArticleDOI
TL;DR: In this article, it was shown that the optimal assignment game is a dual problem of a linear programming problem dual to optimal assignment, and that these outcomes correspond exactly to the price lists that competitively balance supply and demand.
Abstract: The assignment game is a model for a two-sided market in which a product that comes in large, indivisible units (e.g., houses, cars, etc.) is exchanged for money, and in which each participant either supplies or demands exactly one unit. The units need not be alike, and the same unit may have different values to different participants. It is shown here that the outcomes in thecore of such a game — i.e., those that cannot be improved upon by any subset of players — are the solutions of a certain linear programming problem dual to the optimal assignment problem, and that these outcomes correspond exactly to the price-lists that competitively balance supply and demand. The geometric structure of the core is then described and interpreted in economic terms, with explicit attention given to the special case (familiar in the classic literature) in which there is no product differentiation — i.e., in which the units are interchangeable. Finally, a critique of the core solution reveals an insensitivity to some of the bargaining possibilities inherent in the situation, and indicates that further analysis would be desirable using other game-theoretic solution concepts.

1,751 citations


Journal ArticleDOI
TL;DR: The assignment problem, together with Munkres proposed algorithm for its solution in square matrices, is presented and an extension of this algorithm which permits a solution for rectangular matrices is developed.
Abstract: The assignment problem, together with Munkres proposed algorithm for its solution in square matrices, is presented first. Then the authors develop an extension of this algorithm which permits a solution for rectangular matrices.Timing results obtained by using an adapted version of Silver's Algol procedure are discussed, and a relation between solution time and problem size is given.

530 citations


Journal ArticleDOI
N. Tomizawa1
01 Jan 1971-Networks
TL;DR: An efficient algorithm for solving transportation problems that requires at most n3 additions and comparisons when applied to an n-by-n assignment problem, as compared with the theoretical upper bound proportional to n4 for the number of such operations required by currently available methods.
Abstract: This paper presents an efficient algorithm for solving transportation problems. The improvement over the existing algorithms of the “primal-dual” type [3], [5] consists in modifying the “potential-raising” stages of the solution process in such a way that negative-cost arcs are removed so that the Dijkstra's algorithm may be applied. Especially, the algorithm requires at most n3 additions and comparisons when applied to an n-by-n assignment problem, as compared with the theoretical upper bound proportional to n4 for the number of such operations required by currently available methods. Furthermore, auxiliary techniques of simplifying the original network by means of “reduction” and “induction” are also introduced as useful tools to treat large-scale problems and specially-structured problems with.

235 citations


Journal ArticleDOI
TL;DR: A test of an algorithm proposed for the bottleneck assignment problem against a “threshold” algorithm, and it is found that the latter is superior computationally.
Abstract: Gross has proposed an algorithm for the bottleneck assignment problem. This note reports a test of it against a “threshold” algorithm, and finds that the latter is superior computationally.

116 citations


Journal ArticleDOI
TL;DR: A systematic way of synthesizing an optimal heat exchange system is proposed by formulating the problem as an optimal assignment problem in linear programming and carrying out the optimal design of the synthesized system by the Complex method.

28 citations


Journal ArticleDOI
F. Bourgeois1, J. C. Lassalle1
TL;DR: This algorithm is a companion to [3] where the theoretical background is described and the algorithm itself is described.
Abstract: This algorithm is a companion to [3] where the theoretical background is described.

18 citations


Journal ArticleDOI
01 Jan 1971

16 citations


01 Aug 1971
TL;DR: A number of new problems such as constrained bematrix game, multi-stage Markovian assignment problem, complementary (orthogonal) planning problem, the problem of reducing a sparse matrix into an almost-triangular matrix by row and column permutations, a location problem on a rectangular network, etc., are defined and formulated as the bilinear programming problem (BLP).
Abstract: : In the paper a number of new problems such as constrained bematrix game, multi-stage Markovian assignment problem, complementary (orthogonal) planning problem, the problem of reducing a sparse matrix into an almost-triangular matrix by row and column permutations, a location problem on a rectangular network, etc., are defined and formulated as the bilinear programming problem (BLP): maximize C(supt) x + d(supt) y + x(supt) Cy subject to x belongs to X, y belongs to Y. where X and Y are m and n-dimensional polyhedral convex set, respectively. Further, it is shown that several important classical problems such as 0 - 1 integer programs, maximization problem of a convex quadratic function subject to linear constrints, two-move game, etc. are reducible to equivalent BLP's. (Author)

15 citations


Journal ArticleDOI
01 Dec 1971
TL;DR: This paper deals with the problem of finding the maximum matching of a weighted graph, having the minimum cost, via a branch and bound algorithm, derived directly from Land andDoig's technique.
Abstract: This paper deals with the problem of finding the maximum matching of a weighted graph, having the minimum cost. This problem is solved via a branch and bound algorithm, derived directly fromLand andDoig's technique. The linear programming problem associated with each step of the procedure is solved through a primal-dual algorithm.

3 citations


01 Nov 1971
TL;DR: In this article, a special quadratic assignment problem is shown to be equivalent to a linear programming problem with n cubed constraints and n squared variables where n is the number of elements to be assigned.
Abstract: : A special quadratic assignment problem is shown to be equivalent to a linear programming problem with n cubed constraints and n squared variables where n is the number of elements to be assigned. A labeling algorithm similar to that for the linear transportation problem is presented for solving the problem. An example is presented that deals with ' triangularizing' input-output matrices.

3 citations


Journal ArticleDOI
01 Dec 1971
TL;DR: It will be shown that (1) the matching problem is closely related to the linear assignment problem and (2) this property can be taken advantage of for solving the matching problems.
Abstract: In addition to the preceding paper, it will be shown that (1) the matching problem is closely related to the linear assignment problem and how (2) this property can be taken advantage of for solving the matching problem.

Journal ArticleDOI
01 Dec 1971
TL;DR: The classic plant location problem is a particular case of the problem discussed in this paper, and two algorithms are presented, which can be called a plant-storehouse location problem, which makes use of a branch and bound technique and a decomposition technique.
Abstract: This paper considers the following assignment problem. There are some groups of plants, each group producing a different commodity. There are some consumption areas, each containing a number of storehouses and wanting a certain amount of all the commodities. The problem consists of finding the assignment of storehouses to plants which minimizes the overall cost, consisting of fixed charges associated to all storehouses and plants, and of transportation costs. For the solution of this problem, which can be called a plant-storehouse location problem, two algorithms are presented. The first algorithm makes use of a branch and bound technique; the second is based on a decomposition technique, which follows directly from the Dynamic Programming.