Cost Estimation with Statistical Optimization in Production Facilities

Öz

Production facilities aim to minimize production costs and maximize product sales volume. This study aimed to calculate the optimum values of decision variables and objective functions by developing a statistical optimization model that minimizes the cost of a product produced in a production facility and maximizes the product production amount. Seven independent variables (x_1,x_2,x_3,x_4,x_5,x_6,x_7) that has an impact on product cost and production quantity are defined as decision variables. In the method of the study, the effects of independent variables on dependent variables were examined by performing regression analysis. Additionally, the regression equations obtained by regression analysis were evaluated as objective functions in line with the limits of the independent variables, and the mathematical model created was analyzed. The desirability degree of the model was calculated to verify the validity of the optimum values obtained in the optimization model. For this study, it has been determined that only the independent variable x_4 has no effect on the dependent variable y_1 (minimum production cost) for the preferred product. It was analyzed that all independent variables were statistically effective on the dependent variable y_2 (maximum production amount). The desirability degree of y_1 was calculated as 0.96004 and the desirability degree of y_2 was calculated as 0.87392. The composite desirability degree combining y_1 and y_2 targets was obtained as 0.91600. Optimum values were calculated as 1568. 6 TL for y_1 and 1713 units for y_2, taking into account the 95% prediction (PI) and confidence (CI) intervals. The optimum values for the decision variables x_1,x_2,x_3,x_4,x_5,x_6,and x_7 were calculated as J2, F3, H2, 63, 8, 1 and 0, respectively, within the scope of 95% PI and CI. As a result, with the statistical optimization model developed in this study, an important method has been put forward to obtain optimum values within the limits of the factors affecting a product.

Anahtar Kelimeler

• cost
• produce amount
• statistical optimization
• linear regression

Üretim Tesislerinde İstatistiksel Optimizasyon ile Maliyet Tahmini

Öz

Üretim tesisleri üretim maliyetini minimize ve ürün satış miktarını maksimize etmeyi hedeflemektedirler. Bu çalışmada bir üretim tesisinden üretilen bir ürünün maliyetini minimize ve üretilen ürün miktarının maksimize olmasını sağlayan istatistiksel optimizasyon modeli geliştirilerek karar değişkenlerine ve amaç fonksiyonlarına ait optimum değerlerin hesaplanması amaçlamıştır. Ürün maliyeti ve üretim miktarı üzerinde etkili olan yedi bağımsız değişkenler (x_1,x_2,x_3,x_4,x_5,x_6,x_7) karar değişkenleri olarak tanımlanmıştır. Bu çalışmanın yönteminde regresyon analizi yapılarak bağımsız değişkenlerin bağımlı değişkenler üzerindeki etkileri incelenmiştir. Ayrıca, regresyon analizi ile elde edilen regresyon denklemleri bağımsız değişkenlerin sahip olduğu limitler doğrultusunda amaç fonksiyonu olarak değerlendirilerek oluşturulan matematiksel model çözümlenmiştir. Optimizasyon modelinde elde edilen optimum değerlerin geçerliliklerini doğrulamak adına modele ait arzu edilebilirlik dereceleri hesaplanmıştır. Bu çalışma için tercih edilen ürün için y_1 (minimum üretim maliyeti) bağımlı değişken üzerinde sadece x_4 bağımsız değişkenin etkisi olmadığı tespit edilmiştir. y_2 (maksimum üretim miktarı) bağımlı değişken üzerinde ise tüm bağımsız değişkenlerin istatistiksel olarak etkili olduğu analiz edilmiştir. y_1’in arzuedilebilirlik derecesi 0,96004 ve y_2’nin arzu edilebilirlik derecesi 0,87392 olarak hesaplanmıştır. y_1 ve y_2 hedeflerini birleştiren composite arzuedilebilirlik derecesi 0,91600 olarak elde edilmiştir. Optimum değerler %95 tahmin (PI) ve güven (CI) aralıkları dikkate alınarak y_1 için 1568, 6TL, y_2 için 1713 adet olarak hesaplanmıştır. Karar değişkenleri olan x_1,x_2,x_3,x_4,x_5,x_6,x_7 için optimum değerleri %95 tahmin ve güven aralıkları kapsamında sırasıyla J2, F3, H2, 63, 8, 1 ve 0 hesaplanmıştır. Sonuç olarak, bu çalışma ile geliştirilen istatistiksel optimizasyon modeli ile bir ürüne etki eden faktörlerin limitleri kapsamında optimum değerlerin elde edilmesi sağlayan önemli bir yöntem ileri sürülmüştür.

Anahtar Kelimeler

• maliyet
• üretim miktarı
• istatistiksel optimizasyon
• doğrusal regresyon

Kaynakça

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