Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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25 Jul 1989
TL;DR: In this paper, the authors present a generalization of the Simplex Algorithm for Maximum Basic Feasible Tableaus (MBF) algorithm for linear programming problems, which is based on the duality in Canonical Tableaus.
Abstract: 0 Introduction.- I: Linear Programming.- 1 Geometric Linear Programming.- 0. Introduction.- 1. Two Examples: Profit Maximization and Cost Minimization.- 2. Canonical Forms for Linear Programming Problems.- 3. Polyhedral Convex Sets.- 4. The Two Examples Revisited.- 5. A Geometric Method for Linear Programming.- 6. Concluding Remarks.- Exercises.- 2 The Simplex Algorithm.- 0. Introduction.- 1. Canonical Slack Forms for Linear Programming Problems Tucker Tableaus.- 2. An Example: Profit Maximization.- 3. The Pivot Transformation.- 4. An Example: Cost Minimization.- 5. The Simplex Algorithm for Maximum Basic Feasible Tableaus.- 6. The Simplex Algorithm for Maximum Tableaus.- 7. Negative Transposition The Simplex Algorithm for Minimum Tableaus.- 8. Cycling.- 9. Concluding Remarks.- Exercises.- 3 Noncanonical Linear Programming Problems.- 0. Introduction.- 1. Unconstrained Variables.- 2. Equations of Constraint.- 3. Concluding Remarks.- Exercises.- 4 Duality Theory.- 0. Introduction.- 1. Duality in Canonical Tableaus.- 2. The Dual Simplex Algorithm.- 3. Matrix Formulation of Canonical Tableaus.- 4. The Duality Equation.- 5. The Duality Theorem.- 6. Duality in Noncanonical Tableaus.- 7. Concluding Remarks.- Exercises.- II: Applications.- 5 Matrix Games.- 0. Introduction.- 1. An Example Two-Person Zero-Sum Matrix Games.- 2. Linear Programming Formulation of Matrix Games.- 3. The Von Neumann Minimax Theorem.- 4. The Example Revisited.- 5. Two More Examples.- 6. Concluding Remarks.- Exercises.- 6 Transportation and Assignment Problems.- 0. Introduction.- 1. An Example The Balanced Transportation Problem.- 2. The Vogel Advanced-Start Method (VAM).- 3. The Transportation Algorithm.- 4. Another Example.- 5. Unbalanced Transportation Problems.- 6. The Assignment Problem.- 7. Concluding Remarks.- Exercises.- 7 Network-Flow Problems.- 0. Introduction.- 1. Graph-Theoretic Preliminaries.- 2. The Maximal-Flow Network Problem.- 3. The Max-Flow Min-Cut Theorem The Maximal-Flow Algorithm.- 4. The Shortest-Path Network Problem.- 5. The Minimal-Cost-Flow Network Problem.- 6. Transportation and Assignment Problems Revisited.- 7. Concluding Remarks.- Exercises.- APPENDIX A Matrix Algebra.- APPENDIX B Probability.- Answers to Selected Exercises.
46 citations
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01 Jan 1980TL;DR: In this article, a binary branch and bound algorithm for the exact solution of the Koopmans-Beckmann quadratic assignment problem is described which exploits both the transformation and the greedily obtained approximate solution described in a previous paper by the author.
Abstract: In this paper a binary branch and bound algorithm for the exact solution of the Koopmans-Beckmann quadratic assignment problem is described which exploits both the transformation and the greedily obtained approximate solution described in a previous paper by the author. This branch and bound algorithm has the property that at each bound an associated solution is obtained simultaneously, thereby rendering any premature termination of the algorithm less wasteful.
46 citations
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TL;DR: General algorithms for the bottleneck or minimax criterion are described and (after modification) applied to the inverse minimum spanning tree problem, the inverse shortest path tree problem and the linear assignment problem.
46 citations
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TL;DR: This work extends a classical single-machine due-window assignment problem to the case of position-dependent processing times, and introduces an O(n3) solution algorithm, where n is the number of jobs.
Abstract: We extend a classical single-machine due-window assignment problem to the case of position-dependent processing times. In addition to the standard job scheduling decisions, one has to assign a time interval (due-window), such that jobs completed within this interval are assumed to be on time and not penalized. The cost components are: total earliness, total tardiness and due-window location and size. We introduce an O(n
3) solution algorithm, where n is the number of jobs. We also investigate several special cases, and examine numerically the sensitivity of the solution (schedule and due-window) to the different cost parameters.
46 citations
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TL;DR: It is shown that the CVM3 problem is NP-complete and a heuristic algorithm is proposed and the experimental results show that the proposed algorithm is efficient and generates fairly good solutions.
Abstract: The layer assignment problem for interconnect is the problem of determining which layers should be used for wiring the signal nets so that the number of vias is minimized. The problem is often referred to as the via minimization problem. The problem is considered for three-layer routing, concentrating on one version called the constrained via minimization (CVM3) problem. It is shown that the CVM3 problem is NP-complete and a heuristic algorithm is proposed. The experimental results show that the proposed algorithm is efficient and generates fairly good solutions. >
46 citations