Üretim Tesislerinde İstatistiksel Optimizasyon ile Maliyet Tahmini

Year 2024, Issue: 9, 1 - 18, 30.06.2024

Hatice Mine Saban , Hasan Şahin , Abdülkadir Atalan

https://doi.org/10.52693/jsas.1408523

Abstract

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.

Keywords

maliyet, üretim miktarı, istatistiksel optimizasyon, doğrusal regresyon

Cost Estimation with Statistical Optimization in Production Facilities

Abstract

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.

Keywords

cost, produce amount, statistical optimization, linear regression

References

• [1] F. Falahuddin, F. Fuadi, M. Munandar, R. Juanda, and R. N. Ilham, “Increasing Business Supporting Capacity In Msmes Business Group Tempe Bungong Nanggroe Kerupuk In Syamtalira Aron District, Utara Aceh Regency,” Irpitage J., vol. 2, no. 2, pp. 65–68, 2022.
• [2] Y. Liu, X. Ma, L. Shu, G. P. Hancke, and A. M. Abu-Mahfouz, “From Industry 4.0 to Agriculture 4.0: Current status, enabling technologies, and research challenges,” IEEE Trans. Ind. Informatics, vol. 17, no. 6, pp. 4322–4334, 2020
• [3] V. Sima, I. G. Gheorghe, J. Subić, and D. Nancu, “Influences of the industry 4.0 revolution on the human capital development and consumer behavior: A systematic review,” Sustainability, vol. 12, no. 10, p. 4035, 2020.
• [4] S. Wang et al., “Urbanization can benefit agricultural production with large-scale farming in China,” Nat. Food, vol. 2, no. 3, pp. 183–191, 2021.
• [5] A. Vadas and L. Ferenczi, “Small urban waters and environmental pressure before industrialization: The case of Hungary,” J. Hist. Geogr., vol. 82, pp. 98–109, 2023.
• [6] D. Tanasi, S. Hassam, K. Kingsland, P. Trapani, M. King, and D. Cali, “Melite civitas Romana in 3D: Virtualization project of the archaeological park and museum of the Domus Romana of Rabat, Malta,” Open Archaeol., vol. 7, no. 1, pp. 51–83, 2021.
• [7] G. N. Şarlıoğlu, E. Boyacı, and M. Akca, “Information and Communication Technologies in Logistics and Supply Chain Management in Turkey: Human Resource Practices and New Challenges,” in Managing Technology Integration for Human Resources in Industry 5.0, IGI Global, 2023, pp. 174–197.
• [8] S. Phuyal, D. Bista, and R. Bista, “Challenges, opportunities and future directions of smart manufacturing: a state of art review,” Sustain. Futur., vol. 2, p. 100023, 2020.
• [9] K. Valaskova, M. Nagy, S. Zabojnik, and G. Lăzăroiu, “Industry 4.0 wireless networks and cyber-physical smart manufacturing systems as accelerators of value-added growth in Slovak exports,” Mathematics, vol. 10, no. 14, p. 2452, 2022.
• [10] Y. Liu, J. Zhu, E. Y. Li, Z. Meng, and Y. Song, “Environmental regulation, green technological innovation, and eco-efficiency: The case of Yangtze river economic belt in China,” Technol. Forecast. Soc. Change, vol. 155, p. 119993, 2020.
• [11] I. Kim, J. Kim, and J. Lee, “Dynamic analysis of well-to-wheel electric and hydrogen vehicles greenhouse gas emissions: Focusing on consumer preferences and power mix changes in South Korea,” Appl. Energy, vol. 260, p. 114281, 2020.
• [12] S. P. Nunes et al., “Thinking the future of membranes: Perspectives for advanced and new membrane materials and manufacturing processes,” J. Memb. Sci., vol. 598, p. 117761, 2020.
• [13] N. Amirova, L. Sargina, and A. Khasanova, “Natural resource potential as a factor in the formation of the region’s natural-economic system,” in E3S Web of Conferences, EDP Sciences, 2020, p. 2011.
• [14] B. Yang, B. Liu, J. Peng, and X. Liu, “The impact of the embedded global value chain position on energy-biased technology progress: Evidence from chinas manufacturing,” Technol. Soc., vol. 71, p. 102065, 2022.
• [15] P. F. Borowski, “Digitization, digital twins, blockchain, and industry 4.0 as elements of management process in enterprises in the energy sector,” Energies, vol. 14, no. 7, p. 1885, 2021.
• [16] M. A. Hossain, A. Zhumabekova, S. C. Paul, and J. R. Kim, “A review of 3D printing in construction and its impact on the labor market,” Sustainability, vol. 12, no. 20, p. 8492, 2020.
• [17] J. Santillán‐Saldivar et al., “Design of an endpoint indicator for mineral resource supply risks in life cycle sustainability assessment: The case of Li‐ion batteries,” J. Ind. Ecol., vol. 25, no. 4, pp. 1051–1062, 2021.
• [18] I. J. Agabi and J. S. Ibrahim, “Energy Evaluation and Processing Cost Reduction in Agudu Maize Processing Industry,” Int. J. Eng. Manag. Res., vol. 11, 2021.
• [19] P. T. Diem, N. T. Vu, H. T. Dung, and N. V Dat, “The process of CRM system implementation at Dien May Xanh in Vietnam,” Int. J. Multidiscip. Res. growth Eval., vol. 2, no. 4, pp. 761–768, 2021.
• [20]C.-D. Hategan, R.-I. Pitorac, V.-P. Hategan, and C. M. Imbrescu, “Opportunities and challenges of companies from the Romanian e-commerce market for sustainable competitiveness,” Sustainability, vol. 13, no. 23, p. 13358, 2021.
• [21] M. Kim, X. Yin, and G. Lee, “The effect of CSR on corporate image, customer citizenship behaviors, and customers’ long-term relationship orientation,” Int. J. Hosp. Manag., vol. 88, p. 102520, 2020.
• [22] R. S. Ebrahim, “The role of trust in understanding the impact of social media marketing on brand equity and brand loyalty,” J. Relatsh. Mark., vol. 19, no. 4, pp. 287–308, 2020.
• [23]M. M. Rounaghi, H. Jarrar, and L.-P. Dana, “Implementation of strategic cost management in manufacturing companies: overcoming costs stickiness and increasing corporate sustainability,” Futur. Bus. J., vol. 7, no. 1, pp. 1–8, 2021.
• [24]A. Belhadi, K. Zkik, A. Cherrafi, and M. Y. Sha’ri, “Understanding big data analytics for manufacturing processes: insights from literature review and multiple case studies,” Comput. Ind. Eng., vol. 137, p. 106099, 2019.
• [25]Y. A. Atalan and A. Atalan, “Development of design of experiment optimization to obtain high-quality sugar,” İstatistik ve Uygulamalı Bilim. Derg., vol. 2, no. 1, pp. 1–7, 2021.
• [26]A. Atalan, “Türkiye Sağlık Ekonomisi için İstatistiksel Çok Amaçlı Optimizasyon Modelinin Uygulanması,” İşletme Ekon. ve Yönetim Araştırmaları Derg., vol. 1, no. 1, pp. 34–51, 2018, [Online]. Available: http://dergipark.gov.tr/download/article-file/414076
• [27] M. Sarkar and B. Sarkar, “How does an industry reduce waste and consumed energy within a multi-stage smart sustainable biofuel production system?,” J. Clean. Prod., vol. 262, p. 121200, 2020.
• [28]M.-L. Tseng, T. P. T. Tran, H. M. Ha, T.-D. Bui, and M. K. Lim, “Sustainable industrial and operation engineering trends and challenges Toward Industry 4.0: A data driven analysis,” J. Ind. Prod. Eng., vol. 38, no. 8, pp. 581–598, 2021.
• [29]E. Guzman, B. Andres, and R. Poler, “Models and algorithms for production planning, scheduling and sequencing problems: A holistic framework and a systematic review,” J. Ind. Inf. Integr., vol. 27, p. 100287, 2022.
• [30]C. Ç. Dönmez and A. Atalan, “Developing Statistical Optimization Models for Urban Competitiveness Index: Under the Boundaries of Econophysics Approach,” Complexity, vol. 2019, pp. 1–11, Nov. 2019, doi: 10.1155/2019/4053970.
• [31] Y. Ayaz Atalan and A. Atalan, “A Statistical Analysis of the Relationship Between Meteorological Parameters and the Spread of COVID-19 Cases: Comparison Between Turkey and Italy,” J. Stat. Appl. Sci., vol. 1, no. 2, pp. 76–84, 2020.
• [32]D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to Linear Regression Analysis, 5th ed. Wiley, 2012.
• [33] W. T. Hoyt, S. J. Leierer, and M. Millington, “Analysis and Interpretation of FindingsUsing Multiple Regression Techniques,” Rehabil. Couns. Bull., vol. 49, no. 4, pp. 223–233, 2014.
• [34]N. Günöz and A. Atalan, “Sağlık Kuruluşlarına ait Sağlık Kaynaklarının Bilgisayar Ortamında Verimliliklerinin Analiz Edilmesi ve Optimum Değerlerin Hesaplanması,” İstatistik ve Uygulamalı Bilim. Derg., no. 7, pp. 43–63, Jul. 2023, doi: 10.52693/jsas.1297504.
• [35]M. P. Jenarthanan and R. Jeyapaul, “Optimisation of machining parameters on milling of GFRP composites by desirability function analysis using Taguchi method,” Int. J. Eng. Sci. Technol., vol. 5, no. 4, pp. 22–36, Mar. 2018, doi: 10.4314/ijest.v5i4.3.
• [36]Y. Ayaz Atalan, M. Tayanç, K. Erkan, and A. Atalan, “Development of Nonlinear Optimization Models for Wind Power Plants Using Box-Behnken Design of Experiment: A Case Study for Turkey,” Sustainability, vol. 12, no. 15, p. 6017, Jul. 2020, doi: 10.3390/su12156017.