Showing papers on "Assignment problem published in 1983"
TL;DR: This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem.
Abstract: This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem. Several heuristics are described in detail and results are given for worst-case ratio bounds, absolute bounds, and expected bounds. Applications to practical problems and some mathematical complements are also included.
206 citations
TL;DR: The relationship between Gilmore–Lawler lower bounds with decomposition for the quadratic assignment problem and a lagrangean relaxation of a particular integer programming formulation is discussed.
145 citations
TL;DR: In this paper, it was shown that the 3-dimensional assignment problem is NP-complete, and that the problem of finding perfect matchings of two bipartite graphs G 1, G 2 with the same sets of vertices is also NP-hard.
115 citations
TL;DR: In this paper, the authors considered the assignment problem when there are junction interactions and gave an objective function which measures the extent to which a traffic distribution departs from equilibrium, and an algorithm which (under certain conditions) calculates equilibria by steadily reducing the objective function to zero.
Abstract: The paper considers the assignment problem when there are junction interactions. We give an objective function which measures the extent to which a traffic distribution departs from equilibrium, and an algorithm which (under certain conditions) calculates equilibria by steadily reducing the objective function to zero. It is shown that the algorithm certainly works if the network cost-flow function is monotone and continuously differentiable, and a boundary condition is satisfied.
111 citations
01 Mar 1983
TL;DR: The state of the art in enumerative solution methods for the traveling salesman problem (TSP) is reviewed, including the results and statistical analysis of some computational experiments designed for the purposes of this review.
Abstract: : This paper reviews the state of the art in enumerative solution methods for the traveling salesman problem (TSP). The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of methods based on three different relaxations of the TSP: the assignment problem with the TSP cost function, the 1-tree problem with a Lagrangian objective function, and the assignment problem with a Lagrangean objective function. Section 5 briefly reviews some other relaxations of the TSP, while Section 6 discusses the performance of some state of the art computer codes. Besides material from the literature, the paper also includes the results and statistical analysis of some computational experiments designed for the purposes of this review.
73 citations
TL;DR: A detailed development for a computationally efficient primal-dual algorithm and extensive computational comparisons to primal simplex algorithms are presented.
Abstract: State-of-the-art computational results have shown that primal simplex algorithms are more efficient than primal-dual algorithms for general minimum cost network flow problems. There is, however, some controversy concerning their relative merits for solving assignment problems. This paper presents a detailed development for a computationally efficient primal-dual algorithm and extensive computational comparisons to primal simplex algorithms.
50 citations
TL;DR: A generalized goal programming model is used to resolve a real-world human resource allocation problem involving allocating teachers to 22 private schools in St. Louis, Missouri and provides a solution that balances cost minimization with preference goals of the teachers, administrators, and schools.
Abstract: A generalized goal programming model is used to resolve a real-world human resource allocation problem involving allocating teachers to 22 private schools in St. Louis, Missouri. The model provides a solution that balances cost minimization with preference goals of the teachers, administrators, and schools.
49 citations
TL;DR: The paper gives two user objective functions for the asymmetric assignment problem, and an algorithm of descent type which produces a sequence of flows which converges to the set of equilibria if the cost-flow function is continuous.
Abstract: The paper gives two user objective functions for the asymmetric assignment problem, and an algorithm of descent type. The algorithm produces a sequence of flows which converges to the set of equilibria if the cost-flow function is continuous.
47 citations
TL;DR: In this paper, a sufficient condition for good behavior in any network is discussed, and a related but weaker condition is shown to be necessary to guarantee good behavior, where the cost of using a link depends mainly on the flow on that link.
Abstract: Until recently, analyses of the assignment problem have considered only restricted forms of the functions which relate the costs of travel to volumes of traffic. These analyses are not applicable to networks which include detailed models of either uncontrolled junctions or signal-control policies which react to changes in traffic volumes. Recent assignment procedures are capable of modeling both these kinds of junction interaction, and it is therefore of interest to determine under what conditions the behavior of such procedures is assured. In doing so, use is made of a recently established sufficient condition for good behavior in any network. In broad terms, this condition is that the cost of using a link depends mainly on the flow on that link. The condition is discussed, and a related but weaker condition is shown to be necessary to guarantee good behavior. Analysis of detailed models of priority junctions and roundabouts shows that they give rise to cost functions which just satisfy the necessary con...
47 citations
TL;DR: This work addresses the Satellite-Switched/Time Division Multiple Access system as a 3-index bottleneck-sum assignment problem, and solves it by a heuristic that obtains consistently better results than earlier methods based on different formulations.
41 citations
TL;DR: In this paper, the authors studied the time slot assignment problem for a satellite-switched time division multiple access system where only a restricted set of all possible switching modes is to be used.
Abstract: The time-slot assignment problem for a satellite-switched time-division multiple access system where only a restricted set of all possible switching modes is to be used is studied. An efficient algorithm for finding an optimal assignment is proposed. Also, methods for selecting restricted sets of switching modes are presented.
01 Dec 1983
TL;DR: The relative difference between worst and optimal solution value tends to zero with probability tending to one as the size of the problem goes to infinity, suggesting that for high dimensional quadratic assignment problems even very simple approximation algorithms can in practice yield good suboptimal solutions.
Abstract: In this paper a surprising probabilistic behaviour of quadratic sum assignment problems is shown. The relative difference between worst and optimal solution value tends to zero with probability tending to one as the size of the problem goes to infinity. This result suggests that for high dimensional quadratic assignment problems even very simple approximation algorithms can in practice yield good suboptimal solutions.
TL;DR: The necessary and sufficient condition for finite spectrum assignability is clarified and a systematic design procedure which can straightforwardly yield a control law is presented.
Abstract: This paper is concerned with the finite spectrum assignment problem for systems with multiple commensurate delays in state variables. The necessary and sufficient condition for finite spectrum assignability is clarified. A systematic design procedure which can straightforwardly yield a control law is presented.
TL;DR: In this article, a systematic procedure for constructing the feedback law is presented on the basis of advanced elementary row operations on matrices with two variables s and z = e^{-sh}.
Abstract: This correspondence is concerned with the finite spectrum assignment problem for linear systems with delay in state variables. A systematic procedure for constructing the feedback law is presented on the basis of advanced elementary row operations on matrices with two variables s and z = e^{-sh} .
TL;DR: In this article, a polynomial primal simplex algorithm for n × n assignment with integer cost coefficients is presented, where the algorithm generates at most n 3 ln ▵ bases prior to reach the optimal basis, where ▵ is the difference between an initial extreme point and the optimal extreme point.
Abstract: We present a polynomial primal simplex algorithm for the assignment problem. For n × n assignment problem with integer cost coefficients, the algorithm generates at most n3 ln ▵ bases prior to reach the optimal basis, where ▵ is the difference in objective value between an initial extreme point and the optimal extreme point.
TL;DR: The subrout ine given here is in tended for the m a n y appl icat ions in which the Q A P s are large, but a good subopt imal solution is acceptable.
Abstract: This quant i ty m a y be viewed as the total cost of assigning n facilities to n locations, where Ci, t(i) is the fixed cost of assigning facility i to locat ion l ( i) , F o is the flow f rom facility i to facility j , and Dp, q is the cost per un i t flow ( , d ~ t a n c e ' ) f rom location p to location q. T h e formulat ion of Koopmaws and B e c k m a n n [9] omi t ted the t e r m Ci, l¢i). Exact solution [1, 6] of the QAP is a t p r e sen t impractical!: for n >:15. T h e subrout ine given here is in tended for the m a n y appl icat ions in which the Q A P s are large, but a good subopt imal solution is acceptable.
TL;DR: The SCAT and SPAT approaches can be generalized to a wide variety of personnel assignment problems in university, industry, government, and military settings.
Abstract: The personnel assignment problem involves the assignment of people to tasks, projects, etc., in a manner that maximizes a measure of aggregate utility for the assignees subject to several assignment constraints. In addition to computationally efficient solution algorithms, the effective implementation of mathematical models to solve the personnel assignment problem must include data processing systems with comprehensive error checking/resolution procedures, end user reports, documentation, and training. This paper summarizes two successful computer-based systems for solving large-scale personnel assignment problems that frequently occur in university settings. SCAT, the Student-Company Assignment Technique, assigns students to job interview slots. SPAT, the Student-Project Assignment Technique, assigns students to project teams in an MBA field project course. The SCAT and SPAT approaches can be generalized to a wide variety of personnel assignment problems in university, industry, government, and military settings.
TL;DR: In this article, sufficient conditions for existence of a solution to the pole assignment problem in a class of 2D linear systems using state feedback are given, and an algorithm for finding the feedback gain matrix is presented and illustrated by simple numerical example.
Abstract: Sufficient conditions for existence of a solution to the pole assignment problem in a class of 2-D linear systems using state feedback are given. An algorithm for finding the feedback gain matrix for a class of 2-D linear systems is presented and illustrated by simple numerical example.
09 Mar 1983
TL;DR: The paper surveys the techniques used for designing the most efficient algorithms for finding a maximal (cardinality or weighted) matching in graphs and lists some open problems concerning possible improvements and the existence of fast parallel algorithms for these problems.
Abstract: The paper surveys the techniques used for designing the most efficient algorithms for finding a maximal (cardinality or weighted) matching in (general or bipartite) graphs It also lists some open problems concerning possible improvements and the existence of fast parallel algorithms for these problems
TL;DR: The FORTRAN implementation of an efficient algorithm which solves the Assignment Problem for sparse matrices is given and results are presented, showing the proposed method to be generally superior to the best known algorithms.
Abstract: The FORTRAN implementation of an efficient algorithm which solves the Assignment Problem for sparse matrices is given. Computional results are presented, showing the proposed method to be generally superior to the best known algorithms.
TL;DR: In this article, the problem of optimization of a quality inspection process structure is identified with designing an optimal arrangement of inspection operations in a production process, and three mathematical models for the cases of specialized and versatile inspection stations are formulated.
Abstract: The paper deals with the problem of optimization of a quality inspection process structure. The problem is identified with designing an optimal arrangement of inspection operations in a production process (linkages of the quality inspection process with manufacturing and accessory processes). Three mathematical models for the cases of specialized and versatile inspection stations are formulated. It is shown that the problem can be treated as a particular case of a standard assignment problem. An optimization procedure, grounded on Balas' algorithm, is proposed. A numerical example, based on real data, is given.
TL;DR: In this article, a preprocessing technique requiring sorting of ( 2 m n -arrays once is outlined, which is capable of reducing the dimension and eliminating several arcs for such a problem.
01 Jan 1983
TL;DR: New techniques for logic and topological design of PLA-based systems are introduced and the optimal state assignment problem is studied in connection with logic minimization of the combinational component of the FSM.
Abstract: VLSI (Very Large Scale Integration) circuit design requires the use of computer aids in conjunction with a structured and hierarchical methodology to be economically feasible.
Programmable Logic Arrays (PLAs) are regular structures widely used in the design of complex digital circuits, such as microprocessors. PLA-based systems can implement combinational and sequential functions and are amenable to automated synthesis.
Optimal automated design of PLA-based systems is addressed here. Design of PLAs involves four basic steps: functional, logic, topological and physical design. In particular, new techniques for logic and topological design of PLA-based systems are introduced.
Folding and partitioning are two topological design techniques that involve the reorganization of the array to reduce the silicon area occupied and improve the switching-time performance.
Folding allows to implement a PLA in a smaller area, by rearranging the positions of the active devices and interconnections. Optimal PLA compaction is studied in connection with the problem of interconnecting the array to other circuit building-blocks. A new technique, multiple constrained folding, allows to achieve a minimal PLA area implementation with constrained positions of electrical inputs and outputs. Several new folding algorithms are described. Experimental results, obtained by computer program PLEASURE, are reported.
Partitioning exploits the use of redundant columns and/or rows to transform a PLA into an array having the same functionality and a conveniently partitionable structure. Partitioned PLAs are implemented as block-folded arrays or as the parallel connection of PLA sub-units. An algorithm based on a graph representation of the PLA partitioning problem is presented. Experimental results, obtained by computer program SMILE, are reported.
Logic design of PLA-based implementations of sequential functions, represented by Finite State Machines (FSMs), is then addressed. In particular, the optimal state assignment problem is studied in connection with logic minimization of the combinational component of the FSM. A binary encoding of the states (assignment) is optimal when the unfolded/unpartitioned PLA area is minimal. Due to the computational complexity of the problem, a heuristic technique for state assignment is presented. First the class of present-state assignments that minimize the PLA rows is determined. Then a minimal-length assignment (leading to a minimal-column PLA) is selected. Experimental results, obtained by computer program KISS, are reported.
01 Jan 1983
TL;DR: The state feedback pole assignment problem in control system design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. as discussed by the authors ), and a number of formally constructive methods for eigen value assignment by feedback are described in the literature, but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem.
Abstract: The state feedback pole assignment problem in control system design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf Fletcher, in these proceedings) A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature [13] [11], [1], but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references [2], [5], [6]), but these procedures are designed to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory
01 Jan 1983
TL;DR: In this paper, a stochastic version of the knapsack problem is considered, where a certain component is essential for its operation and must be replaced with a new component when it fails.
Abstract: Publisher Summary
This chapter deals with the problems of scheduling, assigning, and ordering. The chapter presents a model for maximizing the expected reward earned in a fixed time. It also considers the problems consisting of two processors and n jobs needing to be processed. The time until all jobs have been processed is called the makespan, and the objective is to determine the schedule that minimizes the expected makespan. Therefore, in both the models, the purpose is to minimize the expected time until all work is completed. Minimizing the expected difference of the times at which the processors become idle leads to minimizing the expected makespan. The chapter discusses stochastic versions of two deterministic optimization problems: (1) the knapsack problem and (2) the assignment problem. A stochastic knapsack model states that a system must operate for t units of time. A certain component is essential for its operation and must be replaced with a new component, when it fails.
01 Dec 1983
01 Jan 1983
TL;DR: An algorithm for the solution of the continuous assignment problem is described, which is a continuous analogue of the usual transportation algorithm.
Abstract: In this paper continuous forms of the transportation problem and the assignment problem are formulated and discussed. An algorithm for the solution of the continuous assignment problem is described. This algorithm is a continuous analogue of the usual transportation algorithm.
TL;DR: A new interpretation of the stable marriage problem posed by Gale and Shapley is presented, which enables one to solve efficiently this version of the assignment problem when it is known that the preference information is inaccurate or when there is a need to reduce the computational requirements of the problem.
Abstract: A new interpretation of the stable marriage problem posed by Gale and Shapley is presented. This approach enables one to solve efficiently this version of the assignment problem when it is known that the preference information is inaccurate or when there is a need to reduce the computational requirements of the problem. Savings on the order of 30% for CPU time have been demonstrated in test cases.
01 Jan 1983
TL;DR: In this article, the authors describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria, which guarantee that the assi~ned eigenvalues are as insensitive to perturbations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system.
Abstract: design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. Fletcher, in these proceedings). A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature ,13J OlJ, 11 J, but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system. Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references '2], '5J, [6J), but these procedures are desi~ned to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory. The basic difficulty in develoning an algorithm for the inverse eigenvalue problem is that the solution is not uniquely determined. In the special case of a single-input control system, only one solution to the eigenvalue assignment problem may exist, and a numeri cally stable technique for computing the feedback is available [9l. For the nUlti-input problem additional criteria must be imposed to restrict the degrees of freedom in the problem. In this paper we describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria. These criteria guarantee that the assi~ned eigenvalues are as insensitive to pertur bations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system. In the next section the pole assignment problem is defined in detail, and theoretical considerations are discussed. In Section 3 we describe the numerical al~orithm.
TL;DR: It is shown that a reduction to an upper block Hessenberg form enables the multi-input pole assignment problem to be replaced by a number of lower order single- input pole assignment problems.