DETERMINISTIC EQUIVALENTS OF CHANCE CONSTRAINED STOCHASTIC PROGRAMMING PROBLEMS

Year 2010, Volume: 1 Issue: 1, 1 - 18, 29.07.2011

Kumru Atalay , Ayşen Apaydın

Abstract

Many real life problems which are modeled as linear programming problems where coefficients appear as random variables. In this case, such problems are called as stochastic programming problem. The basic approach in the stochastic programming is solving the problem with known methods by converting the problem from a probability structure to a deterministic structure. The chance constraints in this programming approach can be forced from being the random coefficients to deterministic one according to their specific levels.

In this study when the coefficients which are random variables have normal and Chi-square distributions, obtaining of deterministic models that are equivalent to chance constrained stochastic programming models are examined. The importance of choosing the correct distributions of coefficients is explained by a numeric example.

Keywords

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ŞANS KISITLI STOKASTİK PROGRAMLAMA PROBLEMLERİNİN DETERMİNİSTİK EŞİTLİKLERİ

Abstract

Doğrusal programlama problemi olarak modellenen birçok gerçek hayat probleminde katsayılar rasgele değişken olarak ortaya çıkar. Bu durumda kurulan probleme stokastik programlama problemi adı verilmektedir. Stokastik programlamanın çözümünde temel yaklaşım, problemin olasılıksal bir yapıdan deterministik bir yapıya dönüştürülerek bilinen yöntemlerle çözülmesidir. Stokastik programlama tekniklerinden biri olan şans kısıtlı programlama yaklaşımı, rasgele kısıtları belirli seviyelerine göre deterministik duruma getirmeyi amaçlar. Bu çalışmada rasgele değişken olan katsayıların normal dağılıma ve Ki-kare dağılımına sahip olması durumunda ortaya çıkan şans kısıtlı stokastik programlama modelleri kullanılarak deterministik modellerin oluşturulması süreci incelenmiştir. Katsayıların dağılımının doğru olarak seçilmesinin önemliliği sayısal bir örnekle açıklanmış ve irdelenmiştir.

Keywords

Şans kısıtlı stokastik programlama, Normal dağılım, Ki-Kare dağılımı

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