Tamamen belirsiz kaynak kısıtlı proje çizelgeleme problemi için proje yöneticisinin riske karşı tutumunu dikkate alan aralık programlama tabanlı bir yaklaşım

Son yıllarda, belirsizlik altında kaynak kısıtlı proje çizelgeleme problemlerinin modellenmesi ve çözümüne, giderek artan bir ilgi olduğu görülmektedir. Gerçek hayat uygulamalarının birçoğunda, proje yöneticileri, aktivite süreleri, kaynak kapasiteleri, aktivitelerin kaynak gereksinimleri ve en erken/en geç bitiş zamanlarının kesin ve net bir şekilde belirlenememesinden ötürü, birçok belirsizlik ile karşı karşıya kalmaktadır. Tüm bu parametrelerin belirsizlik içerdiği ortamlarda, aktivitelerin başlangıç veya bitiş zamanları olarak tanımlanan karar değişkenleri de kesin ve net bir şekilde belirlenememekte olup belirsizlik içerecektir. Bu araştırma motivasyonu ile bu çalışmada, aralık programlama tabanlı bir yaklaşım önerilerek, tamamen belirsiz ortamlarda problemin çözümü gerçekleştirilmiştir. Daha ayrıntılı olarak, probleme ait klasik kesikli zamanlı ikili tamsayılı programlama modeli, aralık sayılar ile ifade edilen parametre ve karar değişkenleri kullanılarak genişletilmiştir. Daha sonra, tamamen belirsiz kaynak kısıtlı proje çizelgeleme problemine ait matematiksel formülasyon, aralık programlama, aralık sıralama ve aralık aritmetik operasyonlar yardımıyla, belirlilik altındaki klasik eşdeğer forma dönüştürülmüştür. Önerilen yaklaşımda, aralık aritmetik operasyonlar, proje yöneticisinden elde edilen ek bilgiler yardımıyla gerçekleştirilmiştir. Bu sayede, proje yöneticilerinin riske karşı tutumları dikkate alınabilmekte ve riskten bağımsız, kabul edilebilir çözümler elde edilebilmektedir. Son olarak, önerilen yaklaşımın geçerliliğinin ve uygulanabilirliğinin test edilebilmesi için, bir petrol rafinerisindeki sıvılaştırılmış doğal gaz tankına ait inşaat projesine yer verilmiştir. Elde edilen sonuçlar göstermektedir ki, önerilen yaklaşım ile proje yöneticisinin riske karşı tutumu doğrultusunda, uygulanabilir ve bilgi etkin çözümler üretilebilmektedir.

Anahtar Kelimeler:

Kaynak kısıtlı proje çizelgeleme, Aralık programlama, Riske karşı tutum

An interval programming based approach for fully uncertain resource-constrained project scheduling problem considering project manager’s attitude toward risk

In recent years, there has been a growing attention to model and solve resource-constrained project scheduling problem (RCPSP) under uncertain environments. In most of the real-life cases, project managers may face with many uncertainties in activity durations, resource availabilities, resource requirements of the activities, the earliest and latest finishing times of the activities etc. In addition to these input parameters, project schedule which represents the starting and/or completion times of the activities should also be considered as uncertain variables in such a fully uncertain environments where all of the project data are imprecise. Based on this motivation, this paper presents an interval programming based transformation approach to overcome fully uncertain nature of the problem. In detail, classical discrete-time binary integer programming model of the deterministic problem was extended by incorporating interval-valued parameters and decision variables. Then, fully uncertain RCPSP was transformed into the crisp equivalent form by making use of interval programming, interval ranking and interval arithmetic operations. In the proposed approach, interval arithmetic operations are performed by using supplementary information obtained from the project manager. Thus, the proposed approach is also able to take into account the project managers’ attitude toward risk and produces more acceptable and risk-free solutions. Finally, a real-life liquefied natural gas (LNG) storage tank construction project in a petroleum refinery is presented for testing its validity and practicality. The computational results have shown that more applicable and information efficient project schedules can be derived via the proposed approach according to the project manager’s attitude toward risk.

Keywords:

Resource-Constrained project scheduling, Interval programming, Risk attitude,

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