Showing papers on "Assignment problem published in 1968"
TL;DR: A survey and synthesis of research on the traveling salesman problem is given and a general classification of the solution techniques and a detailed description of some of the proven methods are given.
Abstract: A survey and synthesis of research on the traveling salesman problem is given. The problem is defined and several theorems are presented. This is followed by a general classification of the solution techniques and a description of some of the proven methods. A summary of computational results is given.
513 citations
TL;DR: An algorithm is proposed for the solution of the multi-index assignment problem, based on a tree search technique of the branch-and-bound variety that uses dual subproblems to provide easily computed bounds for the primal assignment problem.
Abstract: The multidimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be thought of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch-and-bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem.
180 citations
TL;DR: In this article, the authors consider an n-job stochastic bottleneck assignment problem in which the production rates are independent random variables rather than constants and show that in either case, the assignment that maximizes the expected rate of the entire line is found by solving the deterministic assignment problem with cost matrix [λij].
Abstract: Consider an n-job stochastic bottleneck assignment problem in which the production rates are independent random variables rather than constants. Assume that the production rate, Rij, (Rij ≧ 0; i, j = 1, 2, …, n) of man i when assigned to job j is: (1) exponentially distributed with mean 1/λij or (2) Weibull distributed with scale parameter λij and shape parameter β. It is shown that in either case, the assignment that maximizes the expected rate of the entire line is found by solving the deterministic assignment problem with “cost” matrix [λij].
9 citations
TL;DR: A model of autonomous logic nets composed of n threshold elements is presented and several properties of a single threshold element are generalized to this model and it is pointed out that only periodic sequences of length 2 can be learned automatically.
Abstract: —A model of autonomous logic nets composed of n threshold elements is presented and several properties of a single threshold element are generalized to this model. The number of these nets is shown to be 2kn³(½≤k≤l) for completely specified machines. The capacity of the net is defined and conjectured to be 2, similar to the case of a single threshold element. P and NPN classifications of the machines are proposed and applied to the enumeration of all periodic sequences of length 2n(n≤4) realizable by this net. The state assignment problem of the net is also treated. The existence of transition diagrams which cannot be realized by this model for any state assignment, or of those that can be realized for any state assignment, is shown, and it turns out that almost all completely specified machines belong to the former class when n is sufficiently large. Considering the synthesis of a net, an application of learning procedure is also discussed and it is pointed out that only periodic sequences of length 2" can be learned automatically.
8 citations