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Showing papers on "Assignment problem published in 1977"


Journal ArticleDOI
TL;DR: This paper shows that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov.
Abstract: In a distributed computing system a modular program must have its modules assigned among the processors so as to avoid excessive interprocessor communication while taking advantage of specific efficiencies of some processors in executing some program modules. In this paper we show that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov. A solution to the two-processor problem is given, and extensions to three and n-processors are considered with partial results given without a complete efficient solution.

740 citations


Journal ArticleDOI
TL;DR: Topological design problems for large-scale topological design systems, including the concentrator location problem, the terminal assignment problem,The terminal layout problem (the constrained minimum spanning tree problem), and the distributed network topological layout problem are discussed.
Abstract: A cost-effective structure for a large network is a multilevel hierarchy consisting of a backbone network and a family of local access networks. The backbone network is generally a distributed network, while the local access networks are typically centralized systems. In special cases, the network may consist primarily of either centralized or distributed portions. This paper discusses topological design problems for such systems, including the concentrator location problem, the terminal assignment problem, the terminal layout problem (the constrained minimum spanning tree problem), the distributed network topological layout problem, and the backbone node location problem. Recent algorithm research, including exact and heuristic problem solutions, are described and computational experience is given. Finally, open problems in large-scale topological design are reported.

295 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose simplicial approximation, which locates and approximates the boundary of the feasible region of an n-dimensional design space with a polyhedron of bounding (n − 1 )-simplices.
Abstract: The basis of a method for designing circuits in the face of parameter uncertainties is described. This method is computationally cheaper than those methods which employ Monte Carlo analysis and nonlinear programming techniques, gives more useful information, and more directly addresses the central problem of design centering. The method, called simplicial approximation, locates and approximates the boundary of the feasible region of an n -dimensional design space with a polyhedron of bounding ( n - 1 )-simplices. The design centering problem is solved by determining the location of the center of the maximal hyperellipsoid inscribed within this polyhedron. The axis lengths of this ellipsoid can be used to solve the tolerance assignment problem. In addition, this approximation can be used to estimate the yield by performing an inexpensive Monte Carlo analysis in the parameter space without any need for the usual multitude of circuit simulations.

216 citations


Journal ArticleDOI
TL;DR: This report also appears as Working Paper No. 260, Western Management Science Institute, University of California, Los Angeles, November 1976.
Abstract: A complete description is given of the design, implementation and use of a family of very fast and efficient large scale minimum cost (primal simplex) network programs. The class of capacitated transshipment problems solved is the most general of the minimum cost network flow models which include the capacitated and uncapacitated transportation problems and the classical assignment problem; these formulations are used for a large number of diverse applications to determine how (or at what rate) a good should flow through the arcs of a network to minimize total shipment costs. The presentation tailors the unified mathematical framework of linear programming to networks with special emphasis on data structures which are not only useful for basis representation, basis manipulation, and pricing mechanisms, but which also seem to be fundamental in general mathematical programming. A review of pertinent optimization literature accompanies computational testing of the most promising ideas. Tuning experiments for...

193 citations


Journal ArticleDOI
TL;DR: A new primal extreme point algorithm for solving assignment problems which both circumvents and exploits degeneracy is presented, and is substantially more efficient than previously developed primal and primal-dual extreme point methods for assignment problems.
Abstract: The purpose of this paper is to present a new primal extreme point algorithm for solving assignment problems which both circumvents and exploits degeneracy. The algorithm is based on the observation that the degeneracy difficulties of the simplex method result from the unnecessary inspection of alternative basis representations of the extreme points. This paper characterizes a subsetQ of all bases that are capable of leading to an optimal solution to the problem if one exists. Using this characterization, an extreme point algorithm is developed which considers only those bases inQ. Computational results disclose that the new algorithm is substantially more efficient than previously developed primal and primal-dual extreme point (“simplex”) methods for assignment problems.

147 citations


Journal ArticleDOI
TL;DR: An optimizing model which minimizes average generalized trip cost subject to constraints on the entropy is shown to have the gravity model with exponential separation function as its solution.

117 citations


Journal ArticleDOI
TL;DR: In this paper, the authors generalize the results obtained by Daganzo (1977) in a previous paper by showing how to incorporate link capacities into any equilibrium traffic assignment algorithm and define an equivalent uncapacitated traffic equilibrium problem (EP).

91 citations


Book ChapterDOI
TL;DR: Three implicit enumeration algorithms for solving the asymmetric traveling salesman problem with subtour elimination using the assignment problem relaxation similar to the previous approaches by Eastman, Shapiro and Bellmore and Malone are developed and computationally test.
Abstract: In this paper we develop and computationally test three implicit enumeration algorithms for solving the asymmetric traveling salesman problem. All three algorithms use the assignment problem relaxation of the traveling salesman problem with subtour elimination similar to the previous approaches by Eastman, Shapiro and Bellmore and Malone. The present algorithms, however, differ from the previous approaches in two important respects: (i) lower bounds on the objective function for the descendants of a node in the implicit enumeration tree are computed without altering the assignment solution corresponding to the parent node – this is accomplished using a result based on “cost operators”, (ii) a LIFO ( Last In , First Out) depth first branching strategy is used which considerably reduces the storage requirements for the implicit enumeration approach. The three algorithms differ from each other in the details of implementing the implicit enumeration approach and in terms of the type of constraint used for eliminating subtours. Computational experience with randomly generated test problems indicates that the present algorithms are more efficient and can solve larger problems compared to (i) previous subtour elimination algorithms and (ii) the 1-arborescence approach of Held and Karp (as implemented by T. H. C. Smith) for the asymmetric traveling salesman problem. Computational experience is reported for up to 180 node problems with costs (distances) in the interval (1,1000) and up to 200 node problems with bivalent costs.

52 citations


Journal ArticleDOI
TL;DR: A polynomial bounded algorithm for solving the generalized assignment problem of a class of objective functions that can be chosen from a totally ordered commutative semigroup which obeys a divisibility axiom.
Abstract: For assignment problems a class of objective functions is studied by algebraic methods and characterized in terms of an axiomatic system. It says essentially that the coefficients of the objective function can be chosen from a totally ordered commutative semigroup, which obeys a divisibility axiom. Special cases of the general model are the linear assignment problem, the linear bottleneck problem, lexicographic multicriteria problems,p-norm assignment problems and others. Further a polynomial bounded algorithm for solving this generalized assignment problem is stated. The algebraic approach can be extended to a broader class of combinatorial optimization problems.

46 citations


Journal ArticleDOI
TL;DR: In this paper, a new approach for solving the bottleneck assignment problem is presented, where the problem is treated as a special class of permutation problems which are called max-min permutations problems.
Abstract: In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is shown that any critical solution yields a global optimum. This theorem is then used as a basis to develop a general method to solve max-min permutation problems.

46 citations


Posted Content
TL;DR: It is shown that the network design problem with congestion reduces to an all-or nothing traffic assignment problem under some assumptions on the congestion function and the investment cost function.
Abstract: Three design problems are discussed in this article. First, it is shown that the network design problem with congestion reduces to an all-or nothing traffic assignment problem under some assumptions on the congestion function and the investment cost function. Second, the land use design problem is formulated as an extension of the Koopmans-Beckmann problem and a heuristic is proposed to solve this problem. Third, it is shown that the seemingly more complex problem of designing jointly a land-use plan and a transportation network reduces to a pure land-use design problem. All that is needed to solve the joint optimization problem is a shortest path algorithm and a heuristic to solve the land use design problem. Computational experience is reported for each algorithm.

01 Jan 1977
TL;DR: A method for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and the "optimal routing of packet switched messages" in communication networks is presented.
Abstract: A method is presented for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and as the "optimal routing of packet switched messages" in communication networks. The acceleration of the convergence of this algorithm is achieved with a nontrivial adaptation of Wolfe's suggestion of an "away" step in the linear approximation method and a variant of this adaptation based on restriction.

Proceedings ArticleDOI
01 Dec 1977
TL;DR: In this article, the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the equilibrium traffic assignment problem in transportation networks and as the optimal routing of packet switched messages in communication networks is presented.
Abstract: We present a method for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and as the "optimal routing of packet switched messages" in communication networks. The acceleration of the convergence of this algorithm is achieved with a non trivial adaptation of Wolfe's suggestion of an "away" step in the linear approximation method and a variant of this adaptation based on restriction.

Journal ArticleDOI
TL;DR: In this paper, a primal algorithm for finding an optimal independent assignment was proposed, which is of a primal type in that we start from a maximum independent matching and that we get maximum independent matchings having smaller total weights than the old ones as the computation proceeds.
Abstract: We show a theorem which characteri:2:es optimal independent assignments. Based on the theorem, we propose an algorithm for finding an optimal independent assignment, which is of a primal type in that we start from a maximum independent matching and that we get maximum independent matchings having smaller total weights than the old ones as the computation proceeds.

Journal ArticleDOI
TL;DR: Rules are introduced that pay special attention to the zero pivot phenomenon, and significantly reduce CPU time in both phase-1 (generating the initial basic feasible solution) and in phase-2 (selecting the variable leaving the base and the variable entering the base).
Abstract: Transportation and assignment models have been widely used in many applications. Their use was motivated, among other reasons, by the existence of efficient solution methods and their occurrence as sub-problems in the solution of combinatorial problems. A previous study [10] observed that, in large-scale Transportation and Assignment Problems, 95 percent of the pivots were zero or degenerate pivots. This study investigates the ratio of zero pivots to the total number of pivots and verifies the above observation under conditions of small rim variability. Rules are introduced that pay special attention to the zero pivot phenomenon, and significantly reduce CPU time in both phase-1 (generating the initial basic feasible solution) and in phase-2 (selecting the variable leaving the base and the variable entering the base). When these rules were applied, they reduced the CPU time substantially: a 500×500 assignment problem was solved in 1.3 seconds.

Journal ArticleDOI
TL;DR: A heuristic algorithm of a building, or construction, nature is described which evaluates many constraints in developing efficient work force tour assignment solutions in a U.S. Postal Service Sectional Center Facility.

Journal ArticleDOI
01 Aug 1977
TL;DR: In this paper, a simple expression for the closed loop characteristic polynomial in terms of the unity-rank proportional and derivative feedback matrices is given for the problem of pole assignment in linear multivariable systems using output feedback.
Abstract: The paper studies the problem of pole assignment in linear multivariable systems using proportional-plus-derivative output feedback. A simple expression is obtained for the closed loop characteristic polynomial in terms of the unity-rank proportional and derivative feedback matrices. It is shown that when the system order does not exceed twice the number of inputs or outputs, all system poles can be assigned arbitrarily, and the required feedback matrices are obtained from linear equations. When the system order exceeds this value, the pole assignment problem becomes nonlinear and may be solved using the available numerical methods. Examples are given for illustration.

Journal ArticleDOI
TL;DR: A branch and bound algorithm for assigning men to machines in a production system when a single operator can service several semi-automatic machines simultaneously and a strict cyclic service discipline is assumed.
Abstract: This paper presents a branch and bound algorithm for assigning men to machines in a production system The labor assignment problem of concern in this paper occurs when 1) a single operator can service several semi-automatic machines simultaneously, 2) the service and machine processing times are different among the machines and are deterministic, 3) a strict cyclic service discipline is assumed, and 4) the combined costs of idle labor and machine time are to be minimized The paper includes a formal definition of the labor assignment problem, a description of the branch and bound algorithm, and a discussion of the computational experience with the algorithm

Journal ArticleDOI
TL;DR: In this paper, the authors considered the weighted in de pendent linkage problem, which is a natural extension of the independent assignment problem recently treated by M. Iri and N. Tomizawa.
Abstract: This pa per considers the weighted in de pendent linkage problem which is a natural extension of the independent assignment problem recently treated by M. Iri and N. Tomizawa. Given a directed graph with two specified vertex subsets VI and V2 on which matroidal structures are defined respectivcl y, an independent linkage is a set of pair wise-a rc-disjoint paths from VI to V 2 such that the set of the initial vertices (resp. terminal vertices) of those paths is an independent set on Vl·(resp. V2)' The problem is to find an optimal independent linkage, i.e., a maximum independent linkage having the smallest total weight among all maximum independent linkages, 'where a weight is given to each arc. Wc present an algorithm for finding an optimal independent linkage.



Book ChapterDOI
01 Jan 1977
TL;DR: In this article, a simple model of the assignment of functions among the jurisdictional levels that make up the public sector is presented, which is based on the notion that it is possible to classify the activities of individuals and governments who participate in public sector and to impute costs to these activities.
Abstract: This paper contains a simple model of the assignment of functions among the jurisdictional levels that make up the public sector. The model rests on the notion that it is possible to classify the activities of individuals and governments who participate in the public sector and to impute costs—sometimes called transaction costs—to these activities. Following a description of the nature of these activities and costs, it is argued that an equilibrium assignment table, i.e. a cross-classification of functions on jurisdictional levels, can be determined. The paper then notes how misassignment problems can be dealt with by the use of interjurisdictional grants.

01 Jan 1977
TL;DR: Results indicated that Catnap is an improvement over existing transportation network codes, particularly for solving the network design problem.
Abstract: This document describes the results of research into the application of the mathematical programming technique of decomposition to practical transportation network problems. A computer code called Catnap (for Control Analysis Transportation Network Analysis Program) has been developed in the course of this study; this code has the capability to solve the following problems: (1) The traffic assignment problem with fixed demands; (2) The transportation network design problem with or without a budget constraint; (3) The optimal staging problem for transportation network investments over a fixed time horizon. In this report the authors describe the basic structure and algorithms employed in Catnap and give actual numerical results obtained in some representative sample problems. These results indicated that Catnap is an improvement over existing transportation network codes, particularly for solving the network design problem.


01 Jun 1977
TL;DR: In this article, an entropy-maximizing formulation of the trip matrix is proposed for minimizing the average generalized trip cost subject to constraints on the entropy of a transportation system. But the authors do not consider the problem of minimizing the trip cost of a bus.
Abstract: The entropy of the trip matrix is used as a broad measure of accessibility within a transportation system. An optimizing model which minimizes average generalized trip cost subject to constraints on the entropy is shown to have the gravity model with exponential separation function as its solution. The relation to entropy-maximizing formulations is discussed. The transportation problem of linear programming and a trivial solution are obtained as limiting cases. Extensions to the combined distribution and assignment problem and a bus problem are pointed out.