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Showing papers on "Assignment problem published in 1984"


Journal ArticleDOI
Masao Fukushima1
TL;DR: It is shown that the modified algorithm can be implemented without much increase in computational effort over the original one and Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the modification.
Abstract: This paper presents a very simple modification of the Frank-Wolfe algorithm for the solution of the traffic assignment problem. It is shown that the modified algorithm can be implemented without much increase in computational effort over the original one. Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the modification.

154 citations


Journal ArticleDOI
TL;DR: A convergent simplicial decomposition algorithm for the variational inequality formulation of the asymmetric traffic assignment problem alternates between generating minimum path trees based on the cost function evaluated at the current iterate and the approximate solving of a master Variational inequality subject to simple convexity constraints.
Abstract: This paper presents a convergent simplicial decomposition algorithm for the variational inequality formulation of the asymmetric traffic assignment problem. It alternates between generating minimum path trees based on the cost function evaluated at the current iterate and the approximate solving of a master variational inequality subject to simple convexity constraints. Thus it generalizes the popular Frank-Wolfe method (where the master problem is a line search) to the asymmetric problem. Rules are given for dropping flow patterns which are not needed to express the current iterate as a convex combination of previous patterns. The results of some computational testing are reported.

125 citations


Journal ArticleDOI
TL;DR: In this paper, the Simple Assembly Plan problem (SAP) is defined and solved by separating the SAP problem into the Bin Assignment Problem (BAP) and the Pick-Insert Sequencing (PIS) problems.
Abstract: In robotic assembly stations robots pick a series of component parts from bins and then insert and assemble them. Several approaches are described and formulated for optimizing bin organization, picking, and insertion sequence and route. Solution procedures are developed for several modes of assembly tasks. The Simple Assembly Plan problem (SAP) is defined and solved. Extensions to this problem are heuristically solved by separating the SAP problem into the Bin Assignment Problem (BAP) and the Pick-Insert Sequencing (PIS) problem. We then define and formulate a new version of the assignment problem which is termed the Minimax Assignment Problem (MAP). An algorithm for the solution of this problem is developed and tested.

105 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of minimizing the differenc value between the largest and smallest value used should be as small as possible, and the authors showed that if we can efficiently answer the feasibility question then we can also solve the optimization problem.

100 citations


Journal ArticleDOI
TL;DR: It is shown that the MBA problem is NP-complete and an asymptotically optimal algorithm is presented, and some computational results are illustrated which prove the efficiency of the algorithm.

81 citations


Journal ArticleDOI
TL;DR: In this article, a necessary and sufficient condition for finite spectrum assignability of systems with multiple commensurate delays in both states and control is presented, and a systematic design procedure of the control law is presented.
Abstract: This paper presents a necessary and sufficient condition for finite spectrum assignability of systems with multiple commensurate delays in both states and control. A systematic design procedure of the control law is presented. The important point of the proposed method is that finite spectrum assignment can be accomplished without any extra integrators, in contrast to the suggestion given by Manitius and Olbrot (1979).

51 citations


Journal ArticleDOI
TL;DR: The general assignment problem is shown to be NP-complete and O ( n log n ) algorithms for two special cases of the problem are presented.

47 citations


Journal ArticleDOI
TL;DR: In this article, the duality of two formulations of the asymmetric traffic assignment problem is shown, and conditions for convexity and differentiability of the objective functions are given.
Abstract: Recently introduced optimization formulations of the asymmetric traffic assignment problem are developed. The duality of two formulations is shown, and conditions for convexity and differentiability of the objective functions are given. Convexity conditions are also given for the family of formulations recently introduced by Smith (1983). When the travel cost vector is affine and monotone, all of the formulations are shown to be convex programming problems. Algorithmic implications of the results are discussed.

43 citations


Journal ArticleDOI
Giorgio Gallo1
TL;DR: An efficient algorithm to solve the maximum cardinality matching problem in convex bipartite graphs is presented and use is made of a special data structure based on a binary heap.

26 citations


Journal ArticleDOI
TL;DR: The following assignment problem is considered and it is shown that whereas, for many integer problems, the standard scalar weighting factor approach will not produce all the efficient solutions, in this case it will.
Abstract: The following assignment problem is considered. There are n activities to be assigned to n personnel. The cost of assigning activity i to person j is cij. It is required to find all the efficient assignments, i.e. those for which there exists no other assignment which has at least as small costs for each person and strictly smaller costs for at least one person. The main results are as follows. In Theorem 1 it is shown that whereas, for many integer problems, the standard scalar weighting factor approach will not produce all the efficient solutions, in this case it will. In Theorem 2 it is shown that when each efficient vector is determined by a single assignment solution, the efficient set is identical to the set of efficient vertices of the convex hull of the assignment solution set.

21 citations


Journal ArticleDOI
Ulrich Derigs1
TL;DR: A new rather efficient labeling technique to be used in the shortest augmenting path method and a hybrid procedure combining the advantages of both concepts are developed.
Abstract: We analyse two strategies for solving the bottleneck assignment problem — the threshold method and the shortest augmenting path concept —, show their theoretical equivalence and computational behaviour. We develop a new rather efficient labeling technique to be used in the shortest augmenting path method and a hybrid procedure combining the advantages of both concepts. Extensive computational results are reported.

Journal ArticleDOI
TL;DR: In this paper, the separation assignment problem for q-dimensional systems is formulated and sufficient conditions for the existence of a solution to the problem are presented, and an algorithm for finding the feedback gain matrix is given and illustrated by an example of a 4-D system.
Abstract: Separability-assignment problem for q-dimensional system is formulated. Sufficient conditions for the existence of a solution to the problem are presented. An algorithm for finding the feedback-gain matrix is given and illustrated by an example of a 4-D system.

Book
01 Jan 1984
TL;DR: In this article, the authors consider the problem of finding the shortest simple path in a graph and propose a heuristic algorithm for solving the problem, based on the idea of the minimum sets of feedback arcs.
Abstract: 0. Introduction.- 1. Flows and tensions on networks.- 1.1. Basic concepts.- 1.2. Properties of flows and tensions.- 1.3. The maximum flow problem.- 1.3.1. Introduction.- 1.3.2. The theorem of Ford and Fulkerson.- 1.3.3. Generalized theorem of Ford and Fulkerson.- 1.3.4. The multi-terminal problem.- 1.4. The maximum tension problem.- 1.4.1. The existence theorem for a tension.- 1.4.2. The problems of the shortest and the longest paths as potential problems.- 1.4.3. Algorithm for determining a shortest simple path.- 1.5. The conception of network analysis.- 1.6. Bibliography.- 2. The linear transportation problem.- 2.1. Formulation of the problem.- 2.2. The solution according to Busacker and Gowen.- 2.3. The solution according to Klein.- 2.4. Proof of minimality.- 2.5. Conclusions.- 2.6. Bibliography.- 3. The cascade algorithm.- 3.1. Formulation of the problem.- 3.2. The standard method.- 3.3. The revised matrix algorithm.- 3.4. The cascade algorithm.- 3.5. Bibliography.- 4. Nonlinear transportation problems.- 4.1. Formulation of the problem.- 4.2. A convex transportation problem.- 4.3. A multi-flow problem.- 4.4. Bibliography.- 5. Communication and supply networks.- 5.1. Formulation of the problem.- 5.2. Networks without Steiner's points.- 5.3. Networks containing Steiner's points.- 5.4. Influence exerted by the cost function on the structure of the optimal network.- 5.5. Bibliography.- 6. The assignment and the travelling salesman problems.- 6.1. The assignment problem.- 6.1.1. Formulation of the problem.- 6.1.2. A solution algorithm for the assignment problem.- 6.2. The travelling salesman problem.- 6.2.1. Formulation of the problem.- 6.2.2. A branch-and-bound solution algorithm for the travelling salesman problem.- 6.2.3. A heuristic method for solving the travelling salesman problem.- 6.3. Final observations.- 6.4. Bibliography.- 7. Coding and decision graphs.- 7.1. Formulation of the problem.- 7.2. Algorithm for the generation of a cycle-free questionnaire.- 7.3. Optimal questionnaires.- 7.4. An example from coding.- 7.5. Bibliography.- 8. Signal flow graphs.- 8.1. Formulation of the problem.- 8.2. The algorithm of Mason for solving linear systems of equations.- 8.3. Bibliography.- 9. Minimum sets of feedback arcs.- 9.1. Formulation of the problem.- 9.2. The algorithm of Lempel and Cederbaum.- 9.3. The idea of Younger.- 9.4. Bibliography.- 10. Embedding of planar graphs in the plane.- 10.1. Formulation of the problem.- 10.2. Theorems of Kuratowski, MacLane and Whitney.- 10.3. The planarity algorithm of Dambitis.- 10.4. Planarity studies made by decomposing graphs.- 10.5. The embedding algorithm of Demoucron, Malgrange and Pertuiset.- 10.6. The planarity algorithm of Tutte.- 10.7. Bibliography.- Algorithms.- Author Index.

01 Jan 1984
TL;DR: The airport flight-to-gate assignment problem is solved using two methods: a linear programming relaxation of an integer program formulation and a heuristic, which indicates that the original assignment had a 32% higher average per passenger walking distance than the minimum possible distance given by the LP solution.
Abstract: The airport flight-to-gate assignment problem is solved using two methods: (1) a linear programming relaxation of an integer pro gram formulation and (2) a heuristic. The objective is to minimize passenger walking distances within the airport terminal area through a judicious gate assignment policy. An actual flight schedule for an average day at Toronto International Airport is used to compare existing walking distances, obtained from the original assignment, with results from the two methods. The results indicated that the original assignment had a 32% higher average per passenger walking distance than the minimum pos sible distance given by the LP solution. The heuristic fs perform ance was near optimal; it gave an average walking distance which was only 3.9% greater than the minimum. Computation times for the heuristic are 3.4 CPU seconds per run, while the linear program consumes 386 seconds per run on an IBM 370/168. In addition, if the heuristic is solved first and its solution is used as an initial feasible basis for the LP relaxation of the IP, the total CPU used to obtain optimality is reduced to 42 seconds.

Journal ArticleDOI
TL;DR: An experimental study of the distribution of the length of simplex paths for the Optimal Assignment Problem, where a version of the simplex method that with essentially equal probabilities introduces any variable with negative reduced cost into the basis turns out to be normally distributed and independent of the actual cost coefficients.
Abstract: This paper reports on an experimental study of the distribution of the length of simplex paths for the Optimal Assignment Problem. We study the distribution of the pivot counts for a version of the simplex method that with essentially equal probabilities introduces any variable with negative reduced cost into the basis. In this situation the distribution of the pivot counts turns out to be normally distributed and independent of the actual cost coefficients, provided these are sufficiently spread out. Further, the mean and standard deviation grow only moderately with the size of the problem, namely asd1.8, andd1.5 respectively for ad×d problem, implying in particular that the pivot counts concentrate around the mean with growingd. The usual simplex method on the other hand gives a growth ofd1.6. Hence a large part of the favourable polynomial growth experienced on practical problems may be attributed to the fact that the simplex paths are rather short on the average, at least for assignment problems.

Journal ArticleDOI
TL;DR: The multi-via assignment problem for multilayered printed circuit board routing is considered and an efficient approximation algorithm is presented of (low) polynomial time complexity and guarantees solutions with no more than 3 * OPT via columns.
Abstract: We consider the multi-via assignment problem for multilayered printed circuit board routing. An efficient approximation algorithm for this problem is presented. The algorithm is of (low) polynomial time complexity and guarantees solutions with no more than 3 * OPT via columns, where OPT is the number of via columns in an optimal solution. Several issues relating to the computational complexity of via and multi-via assignment problems are also discussed.

Journal ArticleDOI
TL;DR: A conversational optimization methodology is developed for solving the facility-layout planning problem, which utilizes a Lagrangean relaxation process to transform the original problem into a simpler combinatorial optimization problem.
Abstract: Facility-layout problems are well-known members of the class of wicked problems. Not only are these problems computationally intractable, they defy precise formulation which underscores their ‘wickedness’. A conversational optimization methodology is developed for solving the facility-layout planning problem, which utilizes a Lagrangean relaxation process to transform the original problem into a simpler combinatorial optimization problem. The original problem is a set-packing problem, whereas the transformed problem is a relaxed assignment problem. Along with the conversational optimization methodology an APL (a programming language) implementation of the process, a detailed example, and additional examples demonstrating the range and flexibility of the conversational models are presented.

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the income distribution theory inherent in the linear programming assignment problem and compared it with human capital and neoclassical and human capital theories, and showed that wage differences depend on both worker and machine properties.
Abstract: The income distribution theory inherent in the linear programming assignment problem i; analyzed. In a context in which workers are assigned to machines, dual prices correspond to worker wages and machine rents. The principle which guides the assignment is contrasted with comparative advantage. Using factor analysis, wage differences are shown to depend on both worker and machine properties. The determination of wage differences is illustrated in a numerical example. The assignment theory is then compared with neoclassical and human capital theories.


Book ChapterDOI
01 Jan 1984
TL;DR: In this paper, the determinantal assignment problem (DAP) is defined as a generalisation of the pole, zero assignment problems of linear multivariable theory, and the multilinear nature of DAP is reduced to a linear problem of zero assignment of polynomial combinants and a standard problem of decomposability of multivectors.
Abstract: The determinantal assignment problem (DAP) is defined as a generalisation of the pole, zero assignment problems of linear multivariable theory. The multilinear nature of DAP is reduced to a linear problem of zero assignment of polynomial combinants and a standard problem of decomposability of multivectors. The characterisation of the system problems by decomposable polynomial multivectors leads to the definition of the various system Plucker matrices. Necessary conditions for the solvability of frequency assignment problems are given in terms of the new system invariants, the Plucker matrices. The multilinear problem of decomposability is characterised by a minimal set of algebraically independent quadratics, the Reduced Quadratic Plucker Relations (RQPR). The set of RQPRs is used for the study of linearising compensators (feedbacks), and a linearising family of feedbacks superior to that of dyadic feedbacks is defined. A new proof to the pole assignment theorem by state feedback is given. The approach unifies the various problems of frequency assignment, provides a common algebrogeometric framework for their study, and establishes the basis for the development of a common algorithmic procedure for the computation of solution.


Journal ArticleDOI
TL;DR: This note proves that, in the problem considered by White, no efficient solution can be dominated by a linear combination of efficient solutions.
Abstract: This note proves that, in the problem considered by White, no efficient solution can be dominated by a linear combination of efficient solutions. This provides an elementary proof of a result due to Hartley, presented at a seminar at the University of Manchester.

Journal ArticleDOI
TL;DR: In this paper, the authors developed techniques to solve two variants of the time minimization assignment problem, one of which is an extension of the first one in the sense that an additional constraint on the minimum number of jobs to be taken up by each establishment is introduced.
Abstract: The present paper develops techniques to solve two variants of the time minimization assignment problem In the first, there are n jobs to be assigned to m establishments (m < n) in such a way that the time taken to complete all the jobs is the minimum, it being assumed that all the jobs are commenced simultaneously The second variant is an extension of the first one in the sense that an additional constraint on the minimum number of jobs to be taken up by each establishment is introduced Numerical examples are included to illustrate the techniques



01 Apr 1984
TL;DR: In this paper, the facial structure of the 3-index assignment polytope is examined with the aid of the intersection graph of the coefficient matrix of the problem's constraint set.
Abstract: : Given three disjoint n-sets and the family of all weighted triplets that contain exactly one element of each set, the 3- index assignment (or 3-dimensional matching) problem asks for a minimum-weight subcollection of triplets that covers exactly (i.e., partitions) the union of the three sets. Unlike the common (2-index) assignment problem, the 3-index problem is NP-complete. In this paper we examine the facial structure of the 3-index assignment polytope (the convex hull of feasible solutions to the problem) with the aid of the intersection graph of the coefficient matrix of the problem's constraint set. In particular, we describe the cliques of the intersection graph as belonging to three distinct classes, and show that cliques in two of three classes induce inequalities that define facets of our polytope. Furthermore, we give an 0 (n to the 4th power) procedure (note that the number of variables is n cubed) for finding a facet-defining clique-inequality violated by a given noninteger solution to the linear programming relaxation of the 3-index assignment problem, or showing that no such inequality exists.

Journal ArticleDOI
TL;DR: This paper describes a heuristic algorithm for problems in an automatic routing for a gate array LSI, and experimental results of the algorithm are shown to reveal its performance.
Abstract: Problems occur in an automatic routing for a gate array LSI. These include the logically equivalent terminals to be used for a net to be connected to any one of such terminals, and the vertical track of a feed-through cell to be used for a net assigned to the feed-through cell. Since the routing area in such an LSI chip is predetermined, these problems are important in attaining 100% interconnection in each horizonal channel. This paper describes a heuristic algorithm for these problems, and experimental results of the algorithm are also shown to reveal its performance.

Journal Article
TL;DR: In this article, the problem of finite spectrum assignment with multiple commensurate delays in state variables has been studied 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.

Book ChapterDOI
01 Jan 1984
TL;DR: In this paper, sufficient conditions are given for existence of a solution to the eigenvalues assignment problem for three-dimensional linear systems with separable closed-loop characteristic polynomials.
Abstract: Sufficient conditions are given for existence of a solution to the eigenvalues assignment problem for three-dimensional (3-D) linear systems with separable closed-loop characteristic polynomials Three methods for finding the feedback gain matrix are presented The method 3 is an extension for 3-D systems of the method presented in [3] for 2-D systems

Book ChapterDOI
01 Jan 1984
TL;DR: In this chapter, this chapter wishes to treat two discrete optimization problems, and only a small insight into the solution methods can be given.
Abstract: In this chapter, we wish to treat two discrete optimization problems. However, we shall not conceal that only a small insight into the solution methods can be given, since today there already exist such a variety of different methods and algorithms based on them for solving especially the travelling salesman problem that it is impossible at present to make a final evaluation.