Belirsiz Taleplerle Hemşire Çizelgeleme Problemi için Stokastik Hedef Programlama

Year 2023, Volume: 9 Issue: 3, 490 - 507, 01.01.2024

Seyit Hamza Çavga , Nezir Aydin

Abstract

İşletmelerin verimliliklerine direkt etkili olan vardiya çizelgeleme daima göz önünde bulundurulması gereken bir problemdir. Problemin temelinde kişilerin yetkinliklerine göre vardiyalara atanması, kişilerden beklenen mesailerin birbirinden minimum sapmada olması ve adil bir dağıtım olması amaçlanmaktadır. Bu çalışmada vardiya çizelgeleme probleminin modellenmesi için atama problemi türlerinden sıklıkla kullanılan hemşire çizelgeleme alanı seçilmiştir. Kısıtların belirlenmesinde yasaların belirlediği zorunlu durumlar, hastanenin belirlediği ihtiyaçlar, çalışanların yetkinlik/sorumlulukları ve izin durumları göz önünde bulundurulmuştur. Bunun yanında adil bir çizelgeleme olması için personellerin vardiyalara eşit dağıtımın sağlanması ve izin günlerinin mümkün olduğunda art arda olması hedeflenmiştir. Tüm kısıtların sağlandığı ve birden fazla sayıdaki birbiriyle çelişebilecek hedeflerin minimum sapma ile gerçekleştirebilmesi için hedef programlamadan yararlanılmıştır. Bunların yanında gerçek hayat verileri içeren olasılık temelli farklı senaryolardaki taleplere cevap verilebilmesi için stokastik parametreler de modele eklenmiştir. Seçilen problemin içeriğinde iki farklı birimde çalışan farklı yetkinlikteki yirmi sekiz hemşire için gerekli kısıtları sağlayarak adil dağıtımı sağlayan ve belirsizlik durumlarına uygun cevabı verebilecek bir modelleme yapılmıştır. Kurulan model, GAMS programı ile stokastik karma tamsayılı hedef programlama (MIP) kullanılarak çözüm aranmıştır.

Keywords

Vardiya çizelgeleme, hedef programlama, stokastik modelleme

Stochastic Goal Programming for the Nurse Scheduling Problem with Uncertain Demand

Abstract

Shift scheduling, which has a direct impact on the productivity of enterprises, is a problem that should always be considered. On the basis of the problem, it is aimed to assign people to shifts according to their competencies, to have a fair distribution of overtime expected from each other and to have minimum deviation from each other. In this study, nurse scheduling chose for the assignment problem. In determining the constraints, the mandatory situations determined by the law, the needs determined by the hospital, the competencies/responsibilities of the employees and annual leave situations taken into consideration. Goal programming has been used in order to achieve multiple goals that may conflict with each other, where all the constraints are met, with minimum deviation. In addition, stochastic parameters were added to the model in order to respond to the demands in different scenarios based on probabilistic real-life data. In the content of the selected problem, a modeling that provides fair distribution by providing the necessary constraints for twenty-eight nurses with different competencies working in two different units and can provide the appropriate response to uncertainty situations has been made. The model was solved by using mixed integer programming (MIP) with GAMS program.

Keywords

Shift scheduling, goal programming, stochastic modeling

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