An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice

Frieze, Alan; Yadegar, Jacob

doi:10.1057/jors.1981.207

Cited by 75 publications

(37 citation statements)

References 7 publications

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“…Steps 4 and 5. Integer costs uniform in [1,10] are applied to nodes at level 3 such that the lower bound path cost of the optimal path node at level 2 is not reduced. Step 6.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…The first category of problems as used by [2] and [16] draws integer costs from a uniform distribution. A second category of test problems as by [10] used cost coefficients c i jk = a i j + a ik + a jk where a i j , a ik , and a jk are randomly generated integers from a uniform distribution. The last category of test problems includes problems generated for a specific MAP application such as for multitarget multisensor data association [14] or for some special cost structure such as decomposable costs as examined by [7].…”

Section: Introductionmentioning

confidence: 99%

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Test Problem Generator for the Multidimensional Assignment Problem

Grundel

Pardalos

2005

Comput Optim Applic

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“…Steps 4 and 5. Integer costs uniform in [1,10] are applied to nodes at level 3 such that the lower bound path cost of the optimal path node at level 2 is not reduced. Step 6.…”

Section: Proposed Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Test Problem Generator for the Multidimensional Assignment Problem

Grundel

Pardalos

2005

Comput Optim Applic

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“…Another subgradient procedure for solving a Lagrangean relaxation of the 3-DAP together with computational considerations has been described by Frieze and Yadegar [83]. Burkard and Rudolf [44] report on satisfactory computational results obtained by an algorithm which uses the classical branching rule combined with a reduction step in every node of the search tree.…”

Section: Axial 3-dimensional Assignment Problemsmentioning

confidence: 99%

Linear Assignment Problems and Extensions

Burkard

Çela

1999

Handbook of Combinatorial Optimization

252

150

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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 three-dimensional 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 by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.

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“…In Pierskalla (1968), the SAP was proposed and solved using the branch and bound method. Frieze and Yadegar (1981) developed an algorithm for solving three-dimensional APs with application in scheduling. Recently, Anuradha and Pandian (2012) proposed a method for solving a SAP.…”

Section: Introductionmentioning

confidence: 99%

Type II Sensitivity Analysis in Solid Assignment Problems

Kavitha¹,

Pandian

2012

MAS

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Type II sensitivity of the solid assignment problem is discussed in this paper. Parametric-bound method is proposed that determines the Type II sensitivity ranges of cost coefficients in the solid assignment problem. The procedure of the parametric-bound method is demonstrated with a numerical example. The result obtained by the proposed method will help the decision makers to take an appropriate action while handling various types of assignment problems having three parameters.

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An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice

Cited by 75 publications

References 7 publications

Test Problem Generator for the Multidimensional Assignment Problem

Test Problem Generator for the Multidimensional Assignment Problem

Linear Assignment Problems and Extensions

Type II Sensitivity Analysis in Solid Assignment Problems

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