ATAMA PROBLEMLERİNDE KARDİNALİTE SORUNU

Year 2004, Volume: 6 Issue: 22, 323 - 335, 10.06.2004

Mustafa M. Özkan

https://doi.org/10.14783/maruoneri.678962

Abstract

Bu makalenin amacı atama problemlerindeki kardina- lite sorununu incelemek ve bu sorunu giderecek alternatif formiilasyonlar geliştirmektir. Bu amaç doğrultusunda yazılan makale, giriş ve sonuç dışında temel olarak beş bölümden oluşmaktadır. İlk üç bölümde atama problemlerinin temel varsayımları eleştirisel bir açıdan ele alınarak, iki boyutlu atama problemlerinde kardinalite sorununun görmezden gelinmesini sağlayan alternatif formülasyoıılar geliştirilmiştir. Dördüncü bölümde, üç boyutlu atama problemlerinde kardinalite sorununa rağmen optimal çözümler veren bir atama modeli önerilmiştir. Bu bölümde, uygun bir çözümü garantilemek için üç boyutlu atama problemlerinin hedef programlama yöntemiyle nasıl çözümlenebileceği de açıklanmıştır. Beşinci bölümde, önceki bölümlerde geliştirilen modeller ile üç boyutlu bir atama problemi çözümlenmiştir.

Keywords

Atama Problemi, Kardinalite, Çok Amaçlı Programlama, Hedef Programlama

References

• ABOUDI, RONNY AND GEORGE L. NEMHAUSER (1991), “Some Facets for an Assignment Problem with Side Constraints”, Operations Research, Volüme 39 (2), 244-250.
• AMİNİ, MOHAMMAD M. AND MICHAEL RACER (1994), “A Rigorous Computational Comparison of Alternative Solution Methods for the Generalized Assignment Problem”, Management Science, Volüme 40, Issue 7, 868-890.
• BALAS, EGON AND MATTHEW J. SALTZMAN (1991), “An Algorithm for the Three-Index Assignment Problem”, Operations Research, Volüme 39 (1), 150-161.
• CARON G AET AN, PIERRI HANSEN AND BRIGITTE JAUMARD (1999), “The Assignment Problem with Seniority and Job Priority Constraints”, Operations Research, Volüme 37 (3), 449-453.
• CHARNES A., W. W. COOPER, R. J. NIEHAUS AND A. STEDRY (1969), “Static and Dynamic Assignment Models with Multiple Objectives, and Some Remarks on Organization Design”, Management Science, Volüme 15, No 8, 365-375.
• FEIRING, B. R. (1993), “A Model Generation Approach to the Personel Assignment Problem”, The Journal of the Operational Research Society, Volüme 44 (5), 503-512.
• FRANZI LORI S. AND JANIS L. MİLLER (1993), “Scheduling Medical Residents to Rotations: Solving the Large-Scale Multiperiod Staff Assignment Problem”, Operations Research, Volüme 41 (2), 269-279.
• FRIEZE, A.M. (1974), “A Bilinear Programming Formulation of the 3-Dimensional Assignment Problem”, Mathematical Programming 7, 376-379.
• GEETHA, S. AND M. N. VARTAK (1989), “Time-Cost Trade-Off Analysis in Some Constrained Assignment Problems”, The Journal of the Operational Research Society, Volüme 40 (1), 97- 101.
• GEOFFRION, A. M. AND G. W. GRAVES (1976), “Scheduling Parallel Production Lines with Changeover Costs: Practical Application of a Quadratic Assignment / LP Approach”, Operations Research, Volüme 24 (4), 595-610.
• HAHN, PETER AND THOMAS GRANT (1998), “Lower Bounds for the Quadratic Assignment Problem Based upon a Dual Formulation”, Operations Research, Volüme 46 (6), 912- 922.
• HANAN, MAURICE AND JEROME M. KURTZBERG (1972), “ A Review of the Placement and Quadratic Assignment Problems”, SIAM Review, Volüme 14 (2), 324-342.
• HOWTON, F. WILLIAM (1963), “Work Assignment and Interpersonal Relations in a Research Organizations: Some Participant Observations”, Administrative Science Quarterly, Volüme 7 (4), 502-520.
• LASHKARI R. S. AND S.C. JAISINGH (1980), “A Heuristic Approach to Quadratic Assignment Problem”, The Journal of the Operational Research Society, Volüme 31 (9), 845-850.
• LEE, SANG M. AND MARC J. SCHNIEDERJANS (1983), “A Multicriteria Assignment Problem: A Goal Programming Approach”, Interfaces 13, 75-81.
• MAZZOLA, JOSEPH B„ AND ALAN W. NEEBE (1986), “Resource-Constraint Assignment Scheduling”, Operations Research, Volüme 34 (4), 560-572.
• PASSY, URRY (1971), “Nonlinear Assignment Problems Treated by Geometric Programming”, Operations Research, Volüme 19 (7), 1675-1690.
• PIERSKALLA, WILLIAM P. (1968), “The Multidimensional Assignment Problem”, Operations Research, Volüme 16 (2), 422-431.
• RITZMAN LARRY, JOHN BRADFORD AND ROBERT JACOBS (1979), “A Multiple Objective Approach to Space Planning for Academic Facilities”, Management Science, Volüme 25 (9), 895-906.
• ROSS, G. TERRY AND ANDRIS A ZOLTNERS (1979), “Weighted Assignment Models and their Applications”, Management Science, Volüme 25 (7), 683-696.
• SAATÇIOĞLU, ÖMER (1987), “A Multi-Attribute Assignment Goal-Programming Model with Incentives”, The Journal of the Operational Research Society, Volüme 38 (4), 361-365.
• SARKAR, ABHIRUP (1984), “A Dynamic Assignment Problem”, International Economic Review, Volüme 25 (3), 663-670.
• SESHAN, C. R. (1981), “Some Generalizations of the Time Minimizing Assignment Problem”, The Journal of the Operational Research Society, Volüme 32 (6), 489-494.
• SRINIVASAN, V. AND G.L. THOMPSON (1973), “Alternate Formulations for Static Multi-Attribute Assignment Models”, Management Science, Volüme 20 (2), 154-158.
• VARTAK, M. N. AND S. GEETHA (1990), “Specially Structured Precedence Constraints in Three-Dimensional Bottleneck Assignment Problems, The Journal of the Operational Research Society, Volüme 41 (4), 339-344.
• WHITE, D.J. (1984), “A Special Multi-Objective Assignment Problem”, The Journal of the Operational Research Society, Volüme 35 (8), 759-767.
• ZAN AKI S, STELIOS H. (1983), “A Staff to Job Assignment (Partitioning) Problem with Multiple Objectives”, Computers and Operations Research, Volüme 10, No 4, 357-363.