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Linear Assignment Problems and Extensions
"... This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems ..."
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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial threedimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published
A Survey on Pivot Rules for Linear Programming
 ANNALS OF OPERATIONS RESEARCH. (SUBMITTED
, 1991
"... The purpose of this paper is to survey the various pivot rules of the simplex method or its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with the finiteness property of simplex type pivot rules. Th ..."
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Cited by 10 (1 self)
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The purpose of this paper is to survey the various pivot rules of the simplex method or its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with the finiteness property of simplex type pivot rules. There are some other important topics in linear programming, e.g. complexity theory or implementations, that are not included in the scope of this paper. We do not discuss ellipsoid methods nor interior point methods. Well known classical results concerning the simplex method are also not particularly discussed in this survey, but the connection between the new methods and the classical ones are discussed if there is any. In this paper we discuss three classes of recently developed pivot rules for linear programming. The first class (the largest one) of the pivot rules we discuss is the class of essentially combinatorial pivot rules. Namely these rules only use labeling and signs of the variab...
MANAGING COST UNCERTAINTIES IN TRANSPORTATION AND ASSIGNMENT PROBLEMS
"... Abstract. In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP). A time lag between the development and application of the model could cause cost parameters to assume di erent values when an op ..."
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Abstract. In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP). A time lag between the development and application of the model could cause cost parameters to assume di erent values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coe cients which ensures the stability of an optimal solution under such uncertainties. The widelyused methods of solving the TP and AP are the steppingstone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added di culty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading. We propose a uni ed pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, whichmaycause cycling, and does not require any extra variables such asslack, surplus, or arti cial variables used in dual and primal simplex. The algorithm permits higherorder assignment problems and sideconstraints. Computational results comparing the proposed algorithm to the closelyrelated pivotal solution algorithm, the simplex, via the widelyused package Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in reallife situations. Some illustrative numerical examples are also presented.
A PARAMETRIC VISUALIZATION SOFTWARE FOR THE ASSIGNMENT PROBLEM
, 2005
"... In this paper we present a parametric visualization software used to assist the teaching of the Network Primal Simplex Algorithm for the assignment problem (AP). The assignment problem is a special case of the balanced transportation problem. The main function of the algorithm and design technique ..."
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In this paper we present a parametric visualization software used to assist the teaching of the Network Primal Simplex Algorithm for the assignment problem (AP). The assignment problem is a special case of the balanced transportation problem. The main function of the algorithm and design techniques is also presented. Through this process, we aim to underlie the importance and necessity of using such educational methods in order to improve the teaching of Computer Algorithms.
Journal of Computer Science 1 (1): 1923, 2005
"... This study present a new learning tool developed for the visualization of an algorithm for the assignment problem. We show how the teaching of an algorithm can be greatly enhanced and the tutor's effort decreased with a visualization tool that provides an interactive and animated view of the ..."
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This study present a new learning tool developed for the visualization of an algorithm for the assignment problem. We show how the teaching of an algorithm can be greatly enhanced and the tutor's effort decreased with a visualization tool that provides an interactive and animated view of the subject being taught to the students. This tool makes use of the Java technology, therefore it is platform independed and can be used efficiently in Distance Education. The " Achatz, Kleinschmidt and Paparrizos" algorithm features significant tree modifications and furthermore, it is the first time that this visualization is being made. This tool has a friendly user interface, thus enabling the user  student to familiarize quickly. It can be used efficiently in courses like Graph Theory or Network Optimization. Benefits and drawbacks are thoroughly described in order to support the significance of this tool in computeraided education.
A NEW SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM KARAGIANNIS PANAGIOTIS
"... A new primal simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs ..."
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A new primal simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs