0-1 Hedef Programlama ve ANP Yöntemi ile Hemşire Çizelgeleme Problemi Çözümü

Yıl 2012, Cilt: 4 Sayı: 1, 2 - 6, 15.01.2012

Nurgül Bağ N. Merve Özdemir Tamer Eren

Öz

Hastaneler 24 saat hizmet vermeleri nedeniyle vardiya sistemi ile çalışan yerlerdir. Vardiyalı çalışma biçimi çalışanları fiziksel ve psikolojik açıdan olumsuz etkileyebilen ve bu yüzden yönetimi zor bir sistemdir. Ancak sağlık hizmeti gibi kesintisiz hizmet veren veya üretimi aralıksız devam ettirmek zorunda olan işletmeler vardiyalı sistem ile çalışmak zorundadırlar. Sağlık hizmeti veren çalışanların dikkatinin ve verimliliklerinin hayati önemi vardır. Yapılacak hatalar telafisi mümkün olmayan sonuçlara sebep olabilirler. Vardiyalı sistemin olumsuzluklarını azaltmanın bir yolu vardiyalı çalışma çizelgesinin çalışma kalitesini ve verimliliği olumsuz etkilemeyecek şekilde düzenlenmesidir. Hastanelerde çalışma saatleri çizelgeleme işlemi genellikle sorumlu hemşire tarafından yapılmaktadır.
Bu çalışmada hemşire çizelgeleme problemi ele alınmıştır. Problemi çözmek için 0-1 hedef programlama yöntemi kullanılmıştır. Hedef programlamanın ağırlıklarını belirlemek için analitik ağ prosesi (ANP) kullanılmıştır. Kurulan model Kırıkkale’de bir devlet hastanesinde uygulanmıştır.

Anahtar Kelimeler

Hemşire çizelgeleme, 0-1 hedef programlama, ANP yöntemi

Solving A 0-1 Goal Programming and ANP Methods with Nurse Scheduling Problem

Öz

Hospitals are the places that work with shift system since they give 24 hours of service. Shift system is a hard system which can negatively affect workers physically and psychologically. But, the institutions which have to give continuous service such as health services and the continuous production facilities have to work with shift system. Attention and efficiency of the employees that give health services are vital. Any mistakes can result in nonreparable consequences. One way to decrease the disadvantages of the shift system is to organize the shift schedule in order not to affect the quality of the service and efficiency. In hospitals, shift schedule is mostly organized by the nurses in charge.
In this study, a computerized nurse-scheduling model is developed. The model is approached through a 0-1 goal program. In this study the relative importance values of the constraints have been computed by the analytic network process (ANP), which are used as coefficients of the deviations from the constraints in the objective function. It is adapted to Kirikkale State Hospital (in Turkey) to improve the current manual-made schedules.

Anahtar Kelimeler

Nurse scheduling, 0-1 goal programming, ANP method

Kaynakça

• [1] M. Karaatlı, İ. Güngör, “Hemşire çizelgeleme sorununa bir çözüm önerisi ve bir uygulama”, Alanya İşletme Fakültesi Dergisi, 2 (1), 22-52, 2010. [2] İ. Güngör, “Hemşire görevlendirme ve çizelgeleme sorununa bir model önerisi”, SDÜ İktisadi ve İdari Bilimler Fakültesi Dergisi, 7 (2), 77-94, 2002. [3] M.N. Azaiez, S.S. Al Sharif, “A 0-1 goal programming model for nurse scheduling”, Computers & Operations Research, 32 (3), 491-507, 2005. [4] I. Ozkarahan, “A Disaggregation Model of A Flexible Nurse Scheduling Support System”, Journal of Socio-Economic Planning Sciences, 25 (1), 9-26, 1991. [5] I. Ozkarahan, “Integrated Nurse Scheduling Model”, IEEE Journal of the Society for Health Systems, 3 (2), 79-101, 1992. [6] M. Narlı, “Hemşirelerin çalışma vardiyalarının değerlendirilmesi ve çizelgelenmesi”, Çukurova Üniversitesi Fen Bilimleri Enstitüsü, Yüksel Lisans Tezi, 2007. [7] B. Cheang, H. Li, A. Lim, B. Rodrigues, “Nurse rostering problems-a bibliographic survey”, European Journal of Operational Research, 151, 447-460, 2003. [8] A. Ernst, H. Jiang, M. Krishnamoorthy, D. Sier, “Staff scheduling and rostering: A review of applications, methods, and models”, European Journal of Operations Research, 153, 3–27, 2004. [9] A. Ernst, H. Jiang, M.K.B. Owens, D. Sier, “An annotated bibliography of personnel scheduling and rostering”, Annals of Operations Research, 127, 21–144. 2004. [10] E.K. Burke, P. De Causmaecker, G. Vanden Berghe, H. Van Landeghem, “The state of the art of nurse rostering”, Journal of Scheduling, 7 (6), 441–499, 2004. [11] A.G. Celia, A.K. Roger, “The nurse rostering problem: a critical appraisal of the problem structure”, European Journal of Operational Research, 202 (2), 379-389, 2010. [12] W.J. Abernathy, N. Baloff, J.C. Hershey, S. Wandel, “A three-stage manpower planning and scheduling model—A service-sector example,” Operations Research, 22, 693–711, 1973. [13] J. Bailey, J. Field, “Personnel scheduling with flexshift models,” Journal of Operations Management, 5, 327–338, 1985. [14] M. Isken, “An implicit tour scheduling model with applications in healthcare,” Annals of Operations Research, 128, 91–109, 2004. [15] B. Jaumard, F. Semet, T. Vovor, “A generalized linear programming model for nurse scheduling,” European Journal of Operational Research, 107, 1–18, 1998. [16] H. H. Millar, M. Kiragu, “Cyclic and non-cylcic scheduling of 12h shift nurses by network programming,” European Journal of Operational Research, 104 (3), 582–592, 1998. [17] H.E. Miller, W. Pierskalla, G. Rath, “Nurse scheduling using mathematical programming,”, Operations Research, 24, 857–870, 1976. [18] M. Moz, M. Pato, “Solving the problem of rerostering Nurse schedules with hard constraints: New multicommodity flow models”, Annals of Operations Research, 128, 179–197, 2004. [19] E.S. Rosenbloom, N.F. Goertzen, “Cyclic Nurse scheduling”, European Journal of Operational Research, 31, 19–23, 1987. [20] V.M. Trivedi, M. Warner, “A branch and bound algorithm for optimum allocation of float nurses”, Management Science, 22 (9), 972-981, 1976. [21] M. Warner, “Scheduling Nursing personnel according to Nursing preference: A mathematical programming approach”, Operations Research, 24, 842–856, 1976. [22] M. Warner, J. Prawda, “A mathematical programming model for scheduling Nursing personnel in a hospital”, Management Science, 19, 411–422, 1972. [23] J. Arthur, A. Ravindran, “A multiple objective nurse scheduling model”, AIIE Transactions, 13 (1), 55–60, 1981. [24] I. Berrada, J. Ferland, P. Michelon, “A multi-objective approach to nurse scheduling with both hard and soft constraints”, Socio-Economic Planning Science, 30, 183–193, 1996. [25] J.G. Chen, T. Yeung, “Hybrid expert system approach to Nurse scheduling”, Computers in Nursing, 11 (4), 183–192 1993. [26] L.S. Franz, H.M. Baker, G.K. Leong, T.R. Rakes, “Mathematical model for scheduling and staffing multiclinic health regions”, European Journal of Operational Research, 41 (3), 277–289, 1989. [27] A. Jaszkiewicz, “Ametaheuristic approach tomultiple objective nurse scheduling”, Foundations of Computing and Decision Sciences, 22 (3), 169–184, 1997. [28] I. Ozkarahan, “An integrated Nurse scheduling model”, Journal of the Society for Health Systems, 3 (2), 79–101, 1991. [29] I. Ozkarahan, J.E. Bailey, “Goal programming model subsystem of a flexible nurse scheduling support system”, IEEE Transactions, 16, 306–316, 1988. [30] P.C. Bell, G. Hay, Y. Liang, “A visual interactive decision support system for workforce (Nurse) scheduling”, Information Systems and Operational Research, 24 (2), 133–144, 1986. [31] J.G. Chen, T. Yeung, “Development of a hybrid expert system for Nurse shift scheduling”, Journal of Industrial Ergonomics, 9 (4), 315–328, 1992. [32] B.M.W. Cheng, J.H.M. Lee, J.C.K. Wu, “A nurse rostering system using constraint programming and redundant modeling”, IEEE Transactions in Information Technology in Biomedicine, 1 (1), 44–54, 1997. [33] S.J. Darmoni, A. Fajner, N. Mahe, A. Leforestier, O. Stelian, M. Vondracek, M. Baldenweck, “Horoplan: Computerassisted nurse scheduling using constraint based programming”, Journal of the Society for Health Systems, 5, 41–54, 1995. [34] H. Li, A. Lim, B. Rodrigues, “A hybrid AI approach for Nurse rostering problem,” in Proceedings of the 2003 ACM Symposium on Applied Computing, 730–735, 2003. [35] A. Meisels, E. Gudes, G. Solotorevski, “Employee timetabling, constraint networks and knowledge-based rules: A mixed approach,” in E. K. Burke and P. Ross (eds.), Practice and Theory of Automated Timetabling, First International Conference, Edinburgh, Springer, Lecture Notes in Computer Science, 1153, 93–105, 1996. [36] M. Okada, M. Okada, “Prolog-based system for Nursing staff scheduling implemented on a personal computer,” Computers and Biomedical Research, 21, 53–63, 1988. [37] L.D. Smith, D. Bird, A. Wiggins, “A computerised system to schedule nurses that recognises staff preferences”, Hospital & Health Service Administration, 19–35, 1979. [38] L.D. Smith, A.Wiggins, D. Bird, “Post implementation experience with computer-assisted nurse scheduling in a large hospital”, Information Systems and Operational Research, 17, 309–321, 1979. [39] G. Weil, K. Heus, P. Francois, M. Poujade, “Constraint programming for Nurse scheduling”, in IEEE Engineering in Medicine and Biology, 417–422, 1995. [40] M. Kostreva, K. Jennings, “Nurse scheduling on a microcomputer”, Computers and Operations Research, 18, 731–739, 1991. [41] L.D. Smith, “The application of an interactive algorithm to develop cyclical rotational schedules for Nursing personnel,” INFOR, 14, 53–70, 1976. [42] M. Anzai, Y. Miura, “Computer program for quick work scheduling of nursing staff”, Medical Informatics, 12, 43–52, 1987. [43] R. Blau, A. Sear, “Nurse scheduling with a microcomputer”, Journal of Ambulance Care Management, 1–13, 1983. [44] M.J. Brusco, L.W. Jacobs, “Cost analysis of alternative formulations for personnel scheduling in continuously operating organisations,” European Journal of Operational Research, 86, 249–261, 1995. [45] M.W. Isken, W. Hancock, “A heuristic approach to Nurse scheduling in hospital units with non-stationary, urgent demand, and a fixed staff size”, Journal of the Society for Health Systems, 2 (2), 24–41, 1991. [46] U. Aickelin, P. White, “Building better nurse scheduling algorithms”, Annals of Operations Research, 128, 159–177, 2004. [47] F. Bellanti, G. Carello, F. Della Croce, R. Tadei, “A greedy-based neighborhood search approach to a nurse rostering problem”, European Journal of Operational Research, 153 (1), 28–40, 2004. [48] E.K. Burke, P. De Causmaecker, G.V. Berghe, “A hybrid tabu search algorithm for the Nurse rostering problem,” in B. McKay et al. (eds.), Simulated Evolution and Learning, Springer, Lecture Notes in Artificial Intelligence, 1585, 187–194, 1999. [49] K. Dowsland, “Nurse scheduling with Tabu search and strategic oscillation”, European Journal of Operations Research, 106, 393–407, 1998. [50] K.A. Dowsland, J.M. Thompson, “Solving a nurse scheduling problem with knapsacks, networks and tabu search,” Journal of the Operational Research Society, 51, 825–833, 2000. [51] A. Ikegami, A. Niwa, “A subproblem-centric model and approach to the Nurse scheduling problem”, Mathematical Programming, 97 (3), 517–541, 2003. [52] C. Valouxis, E. Housos, “Hybrid optimisation techniques for the workshift and rest assignment of nursing personnel”, Artificial Intelligence in Medicine, 20, 155–175, 2000. [53] U. Aickelinand, K. Dowsland, “An indirect genetic algorithm for a nurse scheduling problem,” Computers and Operations Research, 31 (5), 761–778,2004. [54] U. Aickelin, K. Dowsland, “Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem”, Journal of Scheduling, 3 (3), 139–153, 2000. [55] F. Easton, N. Mansour, “A distributed genetic algorithm for employee staffing and scheduling problems,” in International Conference on Genetic Algorithms, San Mateo, 360–367, 1993. [56] A. Jan, M. Yamamoto, A. Ohuchi, “Evolutionary algorithms for Nurse scheduling problem,” in Proceedings of the 2000 Congress on Evolutionary Computation, CEC00, San Diego, 196–203, 2000. [57] H. Kawanaka, K. Yamamoto, T. Yoshikawa, T. Shinogi, S. Tsuruoka, “Genetic algorithm with the constraints for Nurse scheduling problem,” in Proceedings of Congress on Evolutionary Computation, Seoul, IEEE Press, 1123–1130, 2001. [58] J. Tanomaru, “Staff scheduling by a genetic algorithm with heuristic operators,” in Proceedings of the IEEE Conference on Evolutionary Computation, 456–461, 1995. [59] E. K. Burke, P. Cowling, P. De Causmaecker, G.V. Berghe, “A memetic approach to the nurse rostering problem”, Applied Intelligence, 15 (3), 199–214, 2001. [60] A. Charnes, W.W. Cooper, R. Ferguson, “Optimal Estimation of Executive Compensation by Linear Programming”, Management Science, 1, 138-151, 1955. [61] A. Charnes, W.W. Cooper, “Management Models and Industrial Applications of Linear Programming”, Wiley, New York, 1961. [62] S.M. Lee, “Goal Programming for Decision Analysis”, Auerbach, Philadelphia, 1972. [63] J.P. Ignizio, “Goal Programming and Extensions”, Lexington Mass: Heath, Lexington Books, Lexington, MA, 1976. [64] C. Romero, “Handbook of Critical Issues in Goal Programming”, Pergamon Press, Oxford, 1991. [65] C. Romero, “A Survey of Generalised Goal Programming”, European Journal of Operational Research, 25, 183-191, 1986. [66] M.J. Schniederjans, “The Life Cycle of Goal Programming Research as Recorded in Journal Articles”, Operations Research, 43, 551-557, 1995. [67] M, Tamiz, D.F. Jones., E.El-Darzi, “A Review of Goal Programming and Its Applications”, Annals of Operations Research, 58, 39-53, 1993. [68] M. Tamiz, D. Jones, C. Romero, “Goal Programming For Decision Making: An Overview of The Current State-of-The-Art”, European Journal of Operational Research, 111 (3), 569-581, 1998. [69] M. Dağdeviren, T. Eren, “Tedarikçi firma seçiminde analitik hiyerarşi prosesi ve 0-1 hedef programlama yöntemlerinin kullanılması”, Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 16 (1-2), 41-52, 2001. [70] T.L. Saaty, “The Analytic Hierarchy Process”, McGraw-Hill, New York. 1980. [71] T.L. Saaty, “Decision Making with Dependence and Feedback: The Analytic Network Process”, RWS Publications, Pittsburgh, 1996. [72] http://www.superdecisions.com