ارائه سیستم پشتیبان تصمیم قاعده پایه هیبریدی برای مسئله EOQ به فرم برنامه‎ریزی هندسی پوزینمیال با محدودیت خطی

نوع مقاله : مقاله علمی پژوهشی

نویسنده

استادیار گروه مدیریت صنعتی، دانشکده علوم اجتماعی، دانشگاه بین‎المللی امام خمینی (ره)، قزوین، ایران

چکیده

هدف: حل مسئله تعیین اندازه اقتصادی سفارش با فرم برنامه‎ریزی هندسی در فضای هیبریدی به کمک یک سیستم پشتیبان تصمیم قاعده پایه، هدف اصلی این مقاله است. دوری از پیچیدگی‎های اجرای مسائل بهینه‎سازی و استفاده از دانش بهینه برای ساخت یک سیستم استنتاج که درک آن برای تصمیم‎گیرنده راحت‎تر است، از ویژگی‎های اصلی این مقاله محسوب می‎شود.
روش: استفاده از متغیرهای تصمیم غیر قطعی، استخراج دانش بهینه از مسئله بهینه‎سازی هیبریدی و به کار بردن این دانش در طراحی سیستم استنتاج هیبریدی رویکرد اصلی این مقاله است.
یافته‎ها: سیستم استنتاج هیبریدی توسعه داده شده در 100 مسئله تصادفی استفاده شد و نتایج آن با مقادیر بهینه به دست آمده از حل مسئله برنامه‎ریزی هندسی مقایسه گردید. افزون بر 97 درصدِ انحرافات مقدار تابع هدف از جواب بهینه، کمتر از 2 درصد بود. این موضوع در خصوص متغیرهای تصمیم نیز صدق می‎کند. این نتایج نشان می‎دهد که سیستم استنتاج هیبریدی برای به کارگیری به عنوان یک سیستم پشتیبان تصمیم بهینه‎گرا، کارایی بالایی دارد و به نتایج آن می‎توان اعتماد کرد.
نتیجه‎گیری: مهم‎ترین ویژگی مدل ارائه شده این است که بر خلاف سایر مقالات در ادبیات موضوع، مسئله بهینه‎سازی را با یک پایگاه قواعدِ گرفته شده از خبرگان جایگزین نمی‎کند، بلکه رویکردی برای ساختن پایگاه قواعد بهینه از مدل بهینه‎سازی ارائه می‎دهد. در این رویکرد با جایگزینی توزیع هیبریدی بهینه به جای مقدار قطعی بهینه برای متغیرهای تصمیم، تمام تصمیمات بهینه‎ای که ممکن است در آینده لازم باشد را به تصمیم‎گیرندگان ارائه می‎دهد.
 

کلیدواژه‌ها

عنوان مقاله [English]

Hybrid Rule-Based Decision Support System to the EOQ Problem in the Form of Posynomial Geometric Programming Formulation with Linear Constraints

نویسنده [English]

  • Amir Yousefli
Assistant Prof. of Industrial Management, Social Science Department, Imam Khomeini International University, Qazvin, Iran
چکیده [English]

Objective: The main objective of this paper is to solve theeconomic order quantity problem, which is formulated as a hybrid posynomial geometric programming, using a rule-based decision support system. Avoiding the complexities of the optimization process problems and using the optimum knowledge to build an inference system, which is easier to understand for the decision makers, are the main features of this article.
Methods: The main approach taken in this paper is to use uncertain decision variables, extracting the optimal knowledge through the hybrid optimization problem and applying this knowledge to design a hybrid inference system.
Results: The developed hybrid inference system was applied to 100 random problems and inferred values of the objective function as well as decision variables were compared to the obtained optimum values. Alike decision variables, more than 97% of the deviations between inferred and optimum values for objective function are less than 2%. These results indicated that the developed hybrid inference system is highly efficient to be implemented as an optimized decision support system and its results are quite reliable.
Conclusion: Unlike other works in the literature, in this paper, the optimization problem is not replaced with a rule-base which is presented by group of experts. But, an approach is provided to build the optimal rule-based decision support system in which the optimum knowledge is obtained through an optimization problem. This approach will provide decision makers with all optimal decisions that may be needed in the future by replacing the optimal deterministic values for decision variables with the optimal hybrid distribution.

کلیدواژه‌ها [English]

  • Economic order quantity
  • Hybrid geometric programming
  • Rule- based inference system
  • Uncertain decision variable
  • Hybrid rule base

مراجع

علامه، غزاله؛ اسمعیلی، مریم؛ تجویدی، ترانه (1393). توسعه چندین مدل قیمت‎گذاری در زنجیره تأمین سبز تحت ریسک با رویکرد نظریه بازی‎ها. فصلنامه مدیریت صنعتی، 6 (4)، 767-789.
فارسیجانی، حسن؛ عبدوس، محمدرضا (1390). استفاده از مدل‎های فازی در سیستم‎های سفارش‎دهی کنترل موجودی. فصلنامه مدیریت صنعتی، 6 (14)، 99-112.

جعفرنژاد، احمد؛ آذر، عادل؛ ابراهیمی، سید عباس (1395). طراحی مدل ریاضی مدیریت سفارشات زنجیرۀ تأمین با تکیه بر رویکرد بهینه‎سازی استوار و ساختار هزینه‎یابی بر مبنای فعالیت. فصلنامه مدیریت صنعتی، 8 (3)، 333-358.

 
References
Alinovi, A., Eleonora B., Roberto, M. (2012). Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies. International Journal of Production Research, 50 (5), 1243-1264.
Allameh, G., Esmaeili, M., Tajvidi, T. (2014). Developing several pricing models in green supply chain under risk by Game Theory Approach. Journal of Industrial Management, 6 (4), 767-789. (in Persian)
Beheshti, H. M. (2010). A decision support system for improving performance of inventory management in a supply chain network. International Journal of Productivity and Performance Management, 59(5), 452-467.
Bushuev, M. A., Guiffrida, A., Jaber, M. Y., Khan, M. (2015). A review of inventory lot sizing review papers. Management Research Review, 38(3), 283-298.
Carlsson, C., Fuller, R. (1994a). Fuzzy if-then rules for modeling interdependencies in FMOP problems, in: Proceedings of EUFIT’94 Conference, Aachen, Germany, Verlag der Augustinus Buchhandlung, 1504-1508.
Carlsson, C., Fuller, R. (1994b). Fuzzy reasoning for solving fuzzy multiple objective linear programs, in: R. Trappl ed., Cybernetics and Systems ’94, Proceedings of the Twelfth European Meeting on Cybernetics and Systems Research, World Scientific Publisher, London, 1: 295-301.
Carlsson, C., Fuller, R. (1998a). Multiobjective optimization with linguistic variables, in: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Aachen, Verlag Mainz, Aachen, 2, 1038-1042.
Carlsson, C., Fuller, R. (1998b). Optimization with linguistic values. TUCS Technical Reports, Turku Centre for Computer Science. Available in: http://uni-obuda.hu/users/fuller.robert/ TR157.pdf.
Carlsson, C., Fuller, R. (2000). Multi objective linguistic optimization, Fuzzy sets and systems, 115, 5-10.
De, L. N., Goswami, A. (2009). Probabilistic EOQ model for deteriorating items under trade credit financing. International Journal of Systems Science, 40(4), 335–346.
De, S. K., Sana, S. S. (2015). Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment. Pacific Science Review A: Natural Science and Engineering, 17(2), 61-68.
Dutta, P., Chakraborty, D., Roy, A. R. (2005). A single-period inventory model with fuzzy random variable demand. Mathematical and Computer Modelling, 41 (8-9), 915–922.
Dutta, P., Chakraborty, D., Roy, A. R. (2007). Continuous review inventory model in mixed fuzzy and stochastic environment. Applied Mathematics and Computation, 188 (1), 970–980.
Eynan, A., Kropp, D.H. (2007). Effective and simple EOQ-like solutions for stochastic demand periodic review systems. European Journal of Operational Research, 180(3), 1135-1143.
Farsijani, F., Abdoos, M.R. (2011), Using the Fuzzy Models for Ordering System in Inventory Control, Journal of Industrial Management, 3 (6), 99-112. (in Persian)
Friedman, M. F. (1984). On a stochastic extension of the EOQ formula. European Journal of Operational Research, 17 (1), 125–127.
Hayya, J. C., Harrison, T. P., Chatfield, D. C. (2009). A solution for the intractable inventory model when both demand and lead time are stochastic. International Journal of Production Economics, 122 (2), 595–605.
Jafanejad, A., Azar, A., Ebrahimi, S.A. (2016). Mathematical Model of Supply Chain Order Management Relying on Robust Optimization and Activity-Based Costing. Journal of Industrial Management, 8 (3), 333-358. (in Persian)
Kalantari, H., Yousefli, A., Ghazanfari, M., Shahanaghi, K. (2014). Fuzzy transfer point location problem: a possibilistic unconstrained nonlinear programming approach. The International Journal of Advanced Manufacturing Technology, 70 (5-8), 1043-1051.
Khan, M., Jaber, M. Y., Guiffrida, A. L., Zolfaghari, S. (2011). A review of the extensions of a modified EOQ model for imperfect quality items. International Journal of Production Economics, 132 (1), 1–12.
Lee, W. C., Wu, J. W. (2002). An EOQ model for items with Weibull distributed deterioration, shortages and power demand pattern, International Journal of Information and Management Sciences, 13 (2), 19–34.
Liu, B. (2008). Theory and practice of uncertain programming (second edition). Springer- Verlag.
Maddah, B., & Noueihed, N. (2017). EOQ holds under stochastic demand, a technical note. Applied Mathematical Modelling, 45, 205-208.
Mondal, S., Maiti, M. (2003), Multi-item fuzzy EOQ models using genetic algorithm. Computers and Industrial Engineering, 44 (1), 105–117.
Muriana, C. (2016). An EOQ model for perishable products with fixed shelf life under stochastic demand conditions. European Journal of Operational Research, 255(2), 388-396.
Omrani, H., Keshavarz, M. (2014). An interval programming approach for developing economic order quantity model with imprecise exponents and coefficients. Applied Mathematical Modelling, 38(15), 3917-3928.
Panda, D., Kar, S., Maiti, M. (2008). Multi-item EOQ model with hybrid cost parameters under fuzzy/fuzzy-stochastic resource constraints: a geometric programming approach. Computers and Mathematics with Applications, 56 (11), 2970–2985.
Park, K. S. (1987). Fuzzy-set theoretic interpretation of economic order quantity, IEEE Transactions on Systems, Man and Cybernetics, 17 (6), 1082–1084.
Pentico, D. W., Drake, M. J. (2011). A survey of deterministic models for the EOQ and EPQ with partial backordering. European Journal of Operational Research, 214 (2), 179–198.
Pereira, V., Costa, H. G. (2015). A literature review on lot size with quantity discounts: 1995-2013. Journal of Modelling in Management, 10 (3), 341-359.
Render, B., Stair Jr, R. M., & Hanna, M. E. (2009). Quantitative Analysis for management (10th ed.). Pearson Education, Upper Saddle River, NJ.
Roy, T. K., Maiti, M. (1997). A fuzzy EOQ model with demand dependent unit cost under limited storage capacity. European Journal of Operational Research, 99 (2), 425–432.
Sadjadi, S. J., Ghazanfari, M, Yousefli, A. (2010). Fuzzy pricing and marketing planning model: A possibility geometric programming approach. Expert Systems with Applications, 37 (4), 3392-3397.
Samanta, B., Al-Araimi, S. A. (2001). An inventory control model using fuzzy logic, International Journal of Production Economics, 73 (3), 217–226.
Sana, S. S. (2011). The stochastic EOQ model with random sales price, Applied Mathematics and Computation, 218 (2), 239–248.
Waliv, R. H., Hemant, P. U. (2016). Fuzzy stochastic inventory model for deteriorating item. Yugoslav Journal of Operations Research, 27(1), 91-97.
Wang, C. H. (2010). Some remarks on an optimal order quantity and reorder point when supply and demand are uncertain. Computers and Industrial Engineering, 58 (4), 809– 813.
Wang, X., Tang, W., Zhao, R. (2007). Random fuzzy EOQ model with imperfect quality items. Fuzzy Optimization and Decision Making, 6 (2), 139–153.
Yousefli, A., Ghazanfari, M., & Abiri, M. B. (2014). An Integrated Model for Optimization Oriented Decision Aiding and Rule Based Decision Making in Fuzzy Environment. Journal of Fuzzy Set Valued Analysis, 2014, 1-13.
Yousefli, A., Kalantari, H., & Ghazanfari, M. (2018). Stochastic transfer point location problem: A probabilistic rule-based approach. Uncertain Supply Chain Management, 6(1), 65-74.
Yu, G. (1997). Robust economic order quantity models. European Journal of Operational Research, 100 (3), 482-493.
 
علامه، غزاله؛ اسمعیلی، مریم؛ تجویدی، ترانه (1393). توسعه چندین مدل قیمت‎گذاری در زنجیره تأمین سبز تحت ریسک با رویکرد نظریه بازی‎ها.فصلنامه مدیریت صنعتی، 6 (4)، 767-789.
فارسیجانی، حسن؛ عبدوس، محمدرضا (1390). استفاده از مدل‎های فازی در سیستم‎های سفارش‎دهی کنترل موجودی. فصلنامه مدیریت صنعتی، 6 (14)، 99-112.

جعفرنژاد، احمد؛ آذر، عادل؛ ابراهیمی، سید عباس (1395). طراحی مدل ریاضی مدیریت سفارشات زنجیرۀ تأمین با تکیه بر رویکرد بهینه‎سازی استوار و ساختار هزینه‎یابی بر مبنای فعالیت. فصلنامه مدیریت صنعتی، 8 (3)، 333-358.

 
References
Alinovi, A., Eleonora B., Roberto, M. (2012). Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies. International Journal of Production Research, 50 (5), 1243-1264.
Allameh, G., Esmaeili, M., Tajvidi, T. (2014). Developing several pricing models in green supply chain under risk by Game Theory Approach. Journal of Industrial Management, 6 (4), 767-789. (in Persian)
Beheshti, H. M. (2010). A decision support system for improving performance of inventory management in a supply chain network.International Journal of Productivity and Performance Management,59(5), 452-467.
Bushuev, M. A., Guiffrida, A., Jaber, M. Y., Khan, M. (2015). A review of inventory lot sizing review papers.Management Research Review,38(3), 283-298.
Carlsson, C., Fuller, R. (1994a). Fuzzy if-then rules for modeling interdependencies in FMOP problems, in: Proceedings of EUFIT’94 Conference, Aachen, Germany, Verlag der Augustinus Buchhandlung, 1504-1508.
Carlsson, C., Fuller, R. (1994b). Fuzzy reasoning for solving fuzzy multiple objective linear programs, in: R. Trappl ed., Cybernetics and Systems ’94, Proceedings of the Twelfth European Meeting on Cybernetics and Systems Research, World Scientific Publisher, London, 1: 295-301.
Carlsson, C., Fuller, R. (1998a). Multiobjective optimization with linguistic variables, in: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Aachen, Verlag Mainz, Aachen, 2, 1038-1042.
Carlsson, C., Fuller, R. (1998b). Optimization with linguistic values. TUCS Technical Reports, Turku Centre for Computer Science. Available in: http://uni-obuda.hu/users/fuller.robert/ TR157.pdf.
Carlsson, C., Fuller, R. (2000). Multi objective linguistic optimization, Fuzzy sets and systems, 115, 5-10.
De, L. N., Goswami, A. (2009). Probabilistic EOQ model for deteriorating items under trade credit financing. International Journal of Systems Science, 40(4), 335–346.
De, S. K., Sana, S. S. (2015). Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment.Pacific Science Review A: Natural Science and Engineering,17(2), 61-68.
Dutta, P., Chakraborty, D., Roy, A. R. (2005). A single-period inventory model with fuzzy random variable demand. Mathematical and Computer Modelling, 41 (8-9), 915–922.
Dutta, P., Chakraborty, D., Roy, A. R. (2007). Continuous review inventory model in mixed fuzzy and stochastic environment. Applied Mathematics and Computation, 188 (1), 970–980.
Eynan, A., Kropp, D.H. (2007). Effective and simple EOQ-like solutions for stochastic demand periodic review systems. European Journal of Operational Research, 180(3), 1135-1143.
Farsijani, F., Abdoos, M.R. (2011), Using the Fuzzy Models for Ordering System in Inventory Control, Journal of Industrial Management, 3 (6), 99-112. (in Persian)
Friedman, M. F. (1984). On a stochastic extension of the EOQ formula. European Journal of Operational Research, 17 (1), 125–127.
Hayya, J. C., Harrison, T. P., Chatfield, D. C. (2009). A solution for the intractable inventory model when both demand and lead time are stochastic. International Journal of Production Economics, 122 (2), 595–605.
Jafanejad, A., Azar, A., Ebrahimi, S.A. (2016). Mathematical Model of Supply Chain Order Management Relying on Robust Optimization and Activity-Based Costing. Journal of Industrial Management, 8 (3), 333-358. (in Persian)
Kalantari, H., Yousefli, A., Ghazanfari, M., Shahanaghi, K. (2014). Fuzzy transfer point location problem: a possibilistic unconstrained nonlinear programming approach. The International Journal of Advanced Manufacturing Technology, 70 (5-8), 1043-1051.
Khan, M., Jaber, M. Y., Guiffrida, A. L., Zolfaghari, S. (2011). A review of the extensions of a modified EOQ model for imperfect quality items. International Journal of Production Economics, 132 (1), 1–12.
Lee, W. C., Wu, J. W. (2002). An EOQ model for items with Weibull distributed deterioration, shortages and power demand pattern, International Journal of Information and Management Sciences, 13 (2), 19–34.
Liu, B. (2008). Theory and practice of uncertain programming (second edition). Springer- Verlag.
Maddah, B., & Noueihed, N. (2017). EOQ holds under stochastic demand, a technical note. Applied Mathematical Modelling, 45, 205-208.
Mondal, S., Maiti, M. (2003), Multi-item fuzzy EOQ models using genetic algorithm. Computers and Industrial Engineering, 44 (1), 105–117.
Muriana, C. (2016). An EOQ model for perishable products with fixed shelf life under stochastic demand conditions. European Journal of Operational Research, 255(2), 388-396.
Omrani, H., Keshavarz, M. (2014). An interval programming approach for developing economic order quantity model with imprecise exponents and coefficients.Applied Mathematical Modelling,38(15), 3917-3928.
Panda, D., Kar, S., Maiti, M. (2008). Multi-item EOQ model with hybrid cost parameters under fuzzy/fuzzy-stochastic resource constraints: a geometric programming approach. Computers and Mathematics with Applications, 56 (11), 2970–2985.
Park, K. S. (1987). Fuzzy-set theoretic interpretation of economic order quantity, IEEE Transactions on Systems, Man and Cybernetics, 17 (6), 1082–1084.
Pentico, D. W., Drake, M. J. (2011). A survey of deterministic models for the EOQ and EPQ with partial backordering. European Journal of Operational Research, 214 (2), 179–198.
Pereira, V., Costa, H. G. (2015). A literature review on lot size with quantity discounts: 1995-2013.Journal of Modelling in Management,10 (3), 341-359.
Render, B., Stair Jr, R. M., & Hanna, M. E. (2009). Quantitative Analysis for management (10th ed.). Pearson Education, Upper Saddle River, NJ.
Roy, T. K., Maiti, M. (1997). A fuzzy EOQ model with demand dependent unit cost under limited storage capacity. European Journal of Operational Research, 99 (2), 425–432.
Sadjadi, S. J., Ghazanfari, M, Yousefli, A. (2010). Fuzzy pricing and marketing planning model: A possibility geometric programming approach. Expert Systems with Applications, 37 (4), 3392-3397.
Samanta, B., Al-Araimi, S. A. (2001). An inventory control model using fuzzy logic, International Journal of Production Economics, 73 (3), 217–226.
Sana, S. S. (2011). The stochastic EOQ model with random sales price, Applied Mathematics and Computation, 218 (2), 239–248.
Waliv, R. H., Hemant, P. U. (2016). Fuzzy stochastic inventory model for deteriorating item. Yugoslav Journal of Operations Research, 27(1), 91-97.
Wang, C. H. (2010). Some remarks on an optimal order quantity and reorder point when supply and demand are uncertain. Computers and Industrial Engineering, 58 (4), 809– 813.
Wang, X., Tang, W., Zhao, R. (2007). Random fuzzy EOQ model with imperfect quality items. Fuzzy Optimization and Decision Making, 6 (2), 139–153.
Yousefli, A., Ghazanfari, M., & Abiri, M. B. (2014). An Integrated Model for Optimization Oriented Decision Aiding and Rule Based Decision Making in Fuzzy Environment. Journal of Fuzzy Set Valued Analysis, 2014, 1-13.
Yousefli, A., Kalantari, H., & Ghazanfari, M. (2018). Stochastic transfer point location problem: A probabilistic rule-based approach. Uncertain Supply Chain Management, 6(1), 65-74.
Yu, G. (1997). Robust economic order quantity models. European Journal of Operational Research, 100 (3), 482-493.
 
 
مدیریت صنعتی
دوره 10، شماره 1
1397
صفحه 139-160

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