Öz
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.
Anahtar Kelimeler
Kaynakça
- Charnes, A. ve Cooper, W.W. (1959). Chance Constrained Programming. Management Science 6, 73- 79.
- Déak, I. (1998). Linear Regression Estimators for Multinormal Distributions in Optimization of Stochastic Programming Problems. European Journal of Operational Research 111, 555-568.
- Hillier, F.S. ve Lieberman, G.J. (1990). Introduction to Mathematical Programming. Hill Publishing Company, New York.
- Hulsurkar, S., Biswal, M.P. ve Sinha, S.B. (1997). Fuzzy Programming Approach to Multi-Objective Stochastic Linear Programming Problems. Fuzzy Sets and Systems 88,173-181.
- Jana, R.K. ve Biswal, M.P. (2004). Stochastic Simulation-Based Genetic Algorıthm for Chance Constraint Programming Problems with Continuous Random Variables. International Journal of Computer Mathematics 81(9), 1069-1076.
- Kampas, A. ve White, B. (2003). Probabilistic Programming for Nitrate Pollution Control: Comparing Different Probabilistic Constraint Approximations. European Journal of Operational Research 147, 217-228.
- Kolbin, V.V. (1977). Stochastic Programming. D. Reidel Publishing Company, Boston.
- Patnaik, P.B. (1949). The Non-Central 2 χ and F- Distributions and Their Applications. Biometrika 36,202-232.
- Resh, M. (1970). Chance Constrained Programming of the Machine Loading Problem with Stochastic Proccessing Times. Management Science 17,48-65.
- Sengupta, J.K. (1970). A Generalization of Some Distribution Aspects of Chance Constrained Linear Programming. International Economic Review 11, 287-304.
- Sengupta, J.K. (1972). Stochastic Programming: Methods and Applications. North-Holland Publishing Company, Amsterdam.
- Symonds, G.H. (1967). Deterministic Solutions for A Class of Chance Constrained Programming Problems. Operations Research 15, 495-512.
Öz
Kaynakça
- Charnes, A. ve Cooper, W.W. (1959). Chance Constrained Programming. Management Science 6, 73- 79.
- Déak, I. (1998). Linear Regression Estimators for Multinormal Distributions in Optimization of Stochastic Programming Problems. European Journal of Operational Research 111, 555-568.
- Hillier, F.S. ve Lieberman, G.J. (1990). Introduction to Mathematical Programming. Hill Publishing Company, New York.
- Hulsurkar, S., Biswal, M.P. ve Sinha, S.B. (1997). Fuzzy Programming Approach to Multi-Objective Stochastic Linear Programming Problems. Fuzzy Sets and Systems 88,173-181.
- Jana, R.K. ve Biswal, M.P. (2004). Stochastic Simulation-Based Genetic Algorıthm for Chance Constraint Programming Problems with Continuous Random Variables. International Journal of Computer Mathematics 81(9), 1069-1076.
- Kampas, A. ve White, B. (2003). Probabilistic Programming for Nitrate Pollution Control: Comparing Different Probabilistic Constraint Approximations. European Journal of Operational Research 147, 217-228.
- Kolbin, V.V. (1977). Stochastic Programming. D. Reidel Publishing Company, Boston.
- Patnaik, P.B. (1949). The Non-Central 2 χ and F- Distributions and Their Applications. Biometrika 36,202-232.
- Resh, M. (1970). Chance Constrained Programming of the Machine Loading Problem with Stochastic Proccessing Times. Management Science 17,48-65.
- Sengupta, J.K. (1970). A Generalization of Some Distribution Aspects of Chance Constrained Linear Programming. International Economic Review 11, 287-304.
- Sengupta, J.K. (1972). Stochastic Programming: Methods and Applications. North-Holland Publishing Company, Amsterdam.
- Symonds, G.H. (1967). Deterministic Solutions for A Class of Chance Constrained Programming Problems. Operations Research 15, 495-512.
Öz
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.
Anahtar Kelimeler
Şans kısıtlı stokastik programlama Normal dağılım Ki-Kare dağılımı
Kaynakça
- Charnes, A. ve Cooper, W.W. (1959). Chance Constrained Programming. Management Science 6, 73- 79.
- Déak, I. (1998). Linear Regression Estimators for Multinormal Distributions in Optimization of Stochastic Programming Problems. European Journal of Operational Research 111, 555-568.
- Hillier, F.S. ve Lieberman, G.J. (1990). Introduction to Mathematical Programming. Hill Publishing Company, New York.
- Hulsurkar, S., Biswal, M.P. ve Sinha, S.B. (1997). Fuzzy Programming Approach to Multi-Objective Stochastic Linear Programming Problems. Fuzzy Sets and Systems 88,173-181.
- Jana, R.K. ve Biswal, M.P. (2004). Stochastic Simulation-Based Genetic Algorıthm for Chance Constraint Programming Problems with Continuous Random Variables. International Journal of Computer Mathematics 81(9), 1069-1076.
- Kampas, A. ve White, B. (2003). Probabilistic Programming for Nitrate Pollution Control: Comparing Different Probabilistic Constraint Approximations. European Journal of Operational Research 147, 217-228.
- Kolbin, V.V. (1977). Stochastic Programming. D. Reidel Publishing Company, Boston.
- Patnaik, P.B. (1949). The Non-Central 2 χ and F- Distributions and Their Applications. Biometrika 36,202-232.
- Resh, M. (1970). Chance Constrained Programming of the Machine Loading Problem with Stochastic Proccessing Times. Management Science 17,48-65.
- Sengupta, J.K. (1970). A Generalization of Some Distribution Aspects of Chance Constrained Linear Programming. International Economic Review 11, 287-304.
- Sengupta, J.K. (1972). Stochastic Programming: Methods and Applications. North-Holland Publishing Company, Amsterdam.
- Symonds, G.H. (1967). Deterministic Solutions for A Class of Chance Constrained Programming Problems. Operations Research 15, 495-512.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Temmuz 2011 |
| Yayımlandığı Sayı | Yıl 2010 Cilt: 1 Sayı: 1 |
