بهینه‌سازی سفارش و تخصیص چند تأمین با تصمیم‌گیری مارکوف

حسینی, لیلا; فلاح نژاد, محمد صابر; درهمی, ولی; اولیا, محمد صالح

فراخوان حمایت از طرحهای فناورانه: جوش اتوماتیک به کمک ربات پرتابل

تعداد نشریات	34
تعداد شماره‌ها	1,331
تعداد مقالات	9,557
تعداد مشاهده مقاله	9,756,134
تعداد دریافت فایل اصل مقاله	5,960,679

	بهینه‌سازی سفارش و تخصیص چند تأمین با تصمیم‌گیری مارکوف
مدیریت زنجیره تأمین
دوره 27، شماره 87، شهریور 1404، صفحه 39-50
نوع مقاله: پژوهشی
نویسندگان
لیلا حسینی¹؛ محمد صابر فلاح نژاد^* ²؛ ولی درهمی³؛ محمد صالح اولیا⁴
¹دانشجوی دکتری، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه یزد، یزد، ایران
²استاد، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه یزد، یزد، ایران،
³استاد، گروه مهندسی کامپیوتر، دانشکده مهندسی، دانشگاه یزد، یزد، ایران
⁴استاد، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه یزد، یزد، ایران
تاریخ دریافت: 16 دی 1403، تاریخ بازنگری: 31 اردیبهشت 1404، تاریخ پذیرش: 08 شهریور 1404
چکیده
در این مقاله، یک مدل مدیریت موجودی مبتنی بر چارچوب تصمیم‌گیری مارکوف برای افق زمانی محدود و دوره‌های گسسته توسعه ‌یافته است. هدف اصلی این مدل، کاهش هزینه‌های کلی مدیریت موجودی از طریق تعیین مقادیر بهینه سفارش‌دهی و تخصیص آن‌ها به تأمین‌کنندگان است. هزینه‌های سفارش‌دهی به‌عنوان متغیرهای تصادفی و هزینه‌های نگهداری به‌صورت تابعی خطی مدل‌سازی شده‌اند. با استفاده از روش برنامه‌ریزی پویای برگشت به عقب، سیاست‌های بهینه‌ای طراحی‌شده‌اند که هزینه‌های مرتبط با سفارش‌دهی و نگهداری را به حداقل می‌رسانند. برای ارزیابی مدل، یک مطالعه موردی در یک شرکت تولیدی انجام‌شده است که ماده اولیه پلی‌پروپیلن خود را از دو تأمین‌کننده دریافت می‌کند. نتایج نشان می‌دهد که تخصیص بهینه سفارش‌ها می‌تواند هزینه‌های کلی زنجیره تأمین را تا پایان دوره برنامه‌ریزی به میزان قابل‌توجهی کاهش دهد. این کاهش هزینه ناشی از بهینه‌سازی در مقادیر سفارش‌دهی و انتخاب مناسب تأمین‌کنندگان بر اساس سیاست‌های ارائه‌شده توسط مدل است. مدل پیشنهادی با در نظر گرفتن عدم قطعیت در هزینه‌های سفارش‌دهی، قابلیت کاربرد در محیط‌های واقعی را دارد. این مدل ابزارهای مؤثری برای بهبود تصمیم‌گیری و کاهش هزینه‌ها در زنجیره تأمین فراهم می‌کند و می‌تواند به‌عنوان رویکردی عملی برای شرکت‌های تولیدی با تأمین‌کنندگان متعدد استفاده شود.
کلیدواژه‌ها
میزان سفارش‌دهی کالا؛ تخصیص به تأمین‌کننده؛ فرایند تصمیم‌گیری مارکوف؛ برنامه‌ریزی پویای برگشت به عقب
عنوان مقاله [English]
Multi-Supply Order Optimization and Allocation with Markov Decision Making
نویسندگان [English]
Leila Hosseini¹؛ Mohammad Saber Fallah Nezhad²؛ Vali Derhami³؛ Mohammad Saleh Owlia⁴
¹Student
²Department of Industrial Engineering, Yazd University, P.O. BOX 89195-741, Pejoohesh Street, Safa-ieh, Yazd, Iran
³Technical and Engineering Campus Building 1, Room 223. Yazd University. Yazd, Iran
⁴Department of Industrial Engineering, Yazd University,, Pejoohesh Street, Safa-ieh, Yazd, Iran
چکیده [English]
In this study, an inventory management model based on a Markov decision process (MDP) framework is developed for a finite planning horizon with discrete time periods. The primary objective of the model is to minimize the total inventory management costs by determining the optimal order quantities and their allocation to suppliers. Ordering costs are modeled as random variables, while In this paper, an inventory management model based on the Markov Decision Process (MDP) framework is developed for a finite horizon and discrete time periods. The primary objective of this model is to minimize the total inventory management costs by determining the optimal order quantities and their allocation to suppliers. Ordering costs are modeled as stochastic variables, while holding costs are represented as linear functions. Utilizing a backward dynamic programming approach, optimal policies have been derived to minimize costs associated with ordering and holding inventory.To evaluate the model, a case study was conducted in a manufacturing company that sources polypropylene raw material from two suppliers. The results indicate that optimal order allocation can significantly reduce the overall supply chain costs by the end of the planning horizon. This cost reduction stems from the optimization of order quantities and the appropriate selection of suppliers based on the policies provided by the model. The proposed model, by incorporating uncertainty in ordering costs, demonstrates applicability in real-world settings. It offers effective tools for improving decision-making and cost reduction in supply chain management and can serve as a practical approach for manufacturing firms with multiple suppliers.
کلیدواژه‌ها [English]
Order Quantity, Supplier Allocation, Markov Decision Process, Backward Dynamic Programming

مراجع
[1]Modares, Farimani, and Dehghanian, "Presentating a Model for the Vendor-Managed Inventory in a Two-Tier Supply Chain of Perishable Products Under Demand Uncertainty (In persian)," SCMJ, vol. 26, no. 82, pp. 1-16, 2024, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1402.25.81.1.9. [2]M. Layla, "Analisis persediaan bahan baku yang optimalmenggunakan rantai markov dipt. Papeteries de mauduitindonesia," Int. J. Disaster Risk Reduct, Unimed, 2013. [Online]. Available: https://digilib.unimed.ac.id/id/eprint/10672 [3]M. Layla, "Analisis persediaan bahan baku yang optimal menggunakan rantai Markov di PT. PDM Indonesia," J. Tek. Ind, vol. 20, no. 1, 2016, doi: https://doi.org/10.46306/lb.v4i1.259. [4]G. O. Ferreira, E. F. Arruda, and L. G. Marujo, "Inventory management of perishable items in long-term humanitarian operations using Markov Decision Processes," Int. J. Disaster Risk Reduct., vol. 31, pp. 460-469, 2018, doi: https://doi.org/10.1016/j.ijdrr.2018.05.010. [5]O. Oktaviyani, D. Dwijanto, and S. Supriyono, "Optimization of production scheduling and planning of raw materials supply using Markov chains (a case study of Kinken Cake & Bakery Kutoarjo)," Unnes J. Math., vol. 7, no. 2, pp. 165-180, 2018, doi: https://doi.org/10.15294/ujm.v7i2.13894. [6]G. O. Ferreira, E. F. Arruda, and L. G. Marujo, "Inventory management of perishable items in long-term humanitarian operations using Markov Decision Processes," International Journal of Disaster Risk Reduction, vol. 31, pp. 460-469, 2018. [7]T. Noorida, "Analisa persediaan material pada fire tube boiler stock yang optimal dengan menggunakan Markov chain," J. Tek. Ind., vol. 4, no. 2, pp. 40-49, 2003, doi: https://doi.org/10.22219/JTIUMM.Vol4.No2.40-49. [8]H. Sarjono, E. Edwin, H. Sentosa, and F. Bong, "Analisis Markov chain terhadap persediaan: studi kasus pada CV Sinar Bahagia Group," Binus Bus. Rev., vol. 2, no. 2, pp. 1071-1076, 2011, doi: https://doi.org/10.21512/bbr.v2i2.1249. [9]A. Azaron, O. Tang, and R. Tavakkoli-Moghaddam, "Dynamic lot sizing problem with continuous-time Markovian production cost," Int. J. Prod. Econ., vol. 120, no. 2, pp. 607-612, 2009, doi: https://doi.org/10.1016/j.ijpe.2009.04.007. [10]D. Erlenkotter, "Ford Whitman Harris and the economic order quantity model," Operations Research, vol. 38, no. 6, pp. 937-946, 1990, doi: https://doi.org/10.1287/opre.38.6.937. [11]H. M. Wagner and T. M. Whitin, "Dynamic version of the economic lot size model," Manag. Sci., vol. 5, no. 1, pp. 89-96, 1958, doi: https://www.jstor.org/stable/30046142. [12]H. M. Wagner and T. M. Whitin, "Dynamic version of the economic lot size model," Manag. Sci., vol. 50, no. 12_supplement, pp. 1770-1774, 2004, doi: https://doi.org/10.1287/mnsc.5.1.89. [13]J. R. Evans, "An efficient implementation of the Wagner-Whitin algorithm for dynamic lot-sizing," J. Oper. Manag., vol. 5, no. 2, pp. 229-235, 1985, doi: https://doi.org/10.1016/0272-6963(85)90009-9. [14]Maghari, Ariyanejad, Ebrahimi, and Ghazimoghadam, "Dynamic planning for supplier selection and order quantity determination (In Persian)," SCMJ, vol. 13, no. 33, pp. -, 2011. [Online]. Available: https://scmj.ihu.ac.ir/article_203409_5dc272c63d1a18442e7d65da8bb912b5.pdf. [15]A. Wagelmans, S. Van Hoesel, and A. Kolen, "Economic lot sizing: An O (n log n) algorithm that runs in linear time in the Wagner-Whitin case," Oper. Res., vol. 40, no. 1-supplement-1, pp. S145-S156, 1992, doi: https://doi.org/10.1287/opre.40.1.S145. [16]A. Aggarwal and J. K. Park, "Improved algorithms for economic lot size problems," Oper. Res., vol. 41, no. 3, pp. 549-571, 1993, doi: https://doi.org/10.1287/opre.41.3.549. [17]A. Federgruen and M. Tzur, "A simple forward algorithm to solve general dynamic lot sizing models with n periods in 0 (n log n) or 0 (n) time," Manag. Sci., vol. 37, no. 8, pp. 909-925, 1991, doi: https://doi.org/10.1287/mnsc.37.8.909. [18]M. Mohammadi, M. Esmaelian, and A. Atighehchian, "A Profit-Maximizing Problem With Multi-Item Supplier Selection and Demand Packages," Int. J. Prod. Econ., vol. 27, no. 3, 2020, doi: https://doi.org/10.23055/ijietap.2020.27.3.5815. [19]J. Feng and Z. Gong, "Integrated linguistic entropy weight method and multi-objective programming model for supplier selection and order allocation in a circular economy: A case study," J. Clean. Prod. , vol. 277, p. 122597, 2020, doi: https://doi.org/10.1016/j.jclepro.2020.122597. [20]Z. Chen and R. Rossi, "A dynamic ordering policy for a stochastic inventory problem with cash constraints," Omega, vol. 102, p. 102378, 2021, doi: https://doi.org/10.1016/j.omega.2020.102378. [21]R. Zheng, Y. Zhou, L. Gu, and Z. Zhang, "Joint optimization of lot sizing and condition-based maintenance for a production system using the proportional hazards model," Comput. Ind. Eng., vol. 154, p. 107157, 2021, doi: https://doi.org/10.1016/j.cie.2021.107157. [22]H. Kaur and S. P. Singh, "Multi-stage hybrid model for supplier selection and order allocation considering disruption risks and disruptive technologies," Int. J. Prod. Econ., vol. 231, p. 107830, 2021, doi: https://doi.org/10.1016/j.ijpe.2020.107830. [23]S. Kharvi and T. Pakkala, "An optimal ordering inventory policy when the purchase price follows a discrete-time Markov chain," Commun. Stat. Simul. Comput., pp. 1-18, 2022, doi: https://doi.org/10.1080/03610918.2022.2158340. [24]I. Maulidi, R. Radhiah, C. Hayati, and V. Apriliani, "Optimal Raw Material Inventory Analysis Using Markov Decision Process with Policy Iteration Method," JTAM vol. 6, no. 3, pp. 638-650, 2022, doi: https://doi.org/10.31764/jtam.v6i3.8563. [25]Z. S. Hosseini, S. D. Flapper, and M. Pirayesh, "Sustainable supplier selection and order allocation under demand, supplier availability and supplier grading uncertainties," Comput. Ind. Eng., vol. 165, p. 107811, 2022, doi: https://doi.org/10.1016/j.cie.2021.107811. [26]A. t. Jalali and R. E. Rasi, "Sustainable Supplier Selection In The Clothing supply chain Whit Best-worst method(BWM) (In Persian)," SCMJ, vol. 20, no. 61, pp. 47-61, 2019, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1397.20.61.5.8. [27]Y. Sun, S. C. Guo, and X. Li, "An order-splitting model for supplier selection and order allocation in a multi-echelon supply chain," Comput. Oper. Res., vol. 137, p. 105515, 2022, doi: https://doi.org/10.1016/j.cor.2021.105515. [28]M. J. Kazemi, H. Dezfoulian, and P. Samouei, "Investigating and Selecting the Best Strategies in the Online Ordering System of the Agricultural Supply Chain Using SWOT, Crowdsourcing, and ARAS Methods (In Persian)," SCMJ, vol. 25, no. 81, pp. 67-76, 2024, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1402.25.81.4.2. [29]D. Feizollahi and V. Sharafi, "Development of a Closed-Loop Supply Chain Mathematical Model with Demand Constraints and Fuzzy Supplier Capacity and Solving it with Meta-Heuristic Algorithms( In Persian)," SCMJ, vol. 25, no. 79, pp. 17-38, 2023, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1402.25.79.2.6. [30]H. Thi Xuan Chi, Uyen My, H., & Huynh Tram, P. , "Sustainable Supplier Evaluations and Order Allocation with Multiple Products using Machine Learning.," In 4th Asia Pacific International Conference on Industrial Engineering and Operations Management, , 2023, September, doi: https://doi.org/10.46254/AP04.20230286. [31]M. A. Nafteh and M. SHAHROKHI, "Presenting Mathematical Programming Model for Sustainable Supplier Selection and Order Allocation Using the COPRAS Method (In Persian)," SCMJ, 2023, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1402.25.79.6.0. [32]M. D. Jeshvaghani, M. Amiri, K. Khalili-Damghani, and L. Olfat, "A robust possibilistic multi-echelon multi-product multi-period production-inventory-routing problem considering internal operations of cross-docks: Case study of FMCG supply chain," Comput. Ind. Eng., vol. 179, p. 109206, 2023, doi: https://doi.org/10.1016/j.cie.2023.109206. [33]P. naseri, m. abbasi, and k. atashgar, "Designing a Model for Supplier Strategy Selection with Monitoring of Unforeseen Costs (In Persian)," SCMJ, vol. 26, no. 83, pp. 17-34, 2024, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1403.26.83.2.1. [34]I. M. Coelho, "A multi-period stochastic location-inventory problem," Comput. Ind. Eng., Universidade de Lisboa (Portugal), 2023. [Online]. Available: http://hdl.handle.net/10451/60538 [35]S. Hamdan, A. Cheaitou, A. Shikhli, and I. Alsyouf, "Comprehensive quantity discount model for dynamic green supplier selection and order allocation," Comput. Oper. Res., vol. 160, p. 106372, 2023, doi: https://doi.org/10.1016/j.cor.2023.106372. [36]A. Modares, N. M. Farimani, and F. Dehghanian, "Presentating a Model for the Vendor-Managed Inventory in a Two-Tier Supply Chain of Perishable Products Under Demand Uncertainty (In Persian)," SCMJ, vol. 25, no. 81, pp. 1-15, 2024, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1402.25.81.1.9. [37]a. modares, N. M. Farimani, and V. B. Emroozi, "The Development of the Order Allocation Model based on the Reliability of Retailers (In Persian)," SCMJ, vol. 26, no. 82, pp. 1-16, 2024, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1403.26.82.1.8. [38]A. Vaezi, E. Rabbani, and S. A. Yazdian, "Blockchain-integrated sustainable supplier selection and order allocation: A hybrid BWM-MULTIMOORA and bi-objective programming approach," J. Clean. Prod., vol. 444, p. 141216, 2024, doi: https://doi.org/10.1016/j.jclepro.2024.141216. [39]M. Zheng, Z. Su, D. Wang, and E. Pan, "Joint maintenance and spare part ordering from multiple suppliers for multicomponent systems using a deep reinforcement learning algorithm," Reliab. Eng. Syst. Saf, vol. 241, p. 109628, 2024, doi: https://doi.org/10.1016/j.ress.2023.109628. [40]M. Mozafari and S. Sobhani-Manesh, "A Multi-Objective Possibilistic Model to Platelet Supply Chain Network Design Considering Uncertainty in Demand and Number of Donors (In Persian)," SCMJ, 2025, doi: https://dor.isc.ac/dor/20.1001.1.20089198.1403.26.85.5.8. [41]M. Jafari-Raddani, H. C. Asgarabad, A. Aghsami, and F. Jolai, "A hybrid approach to sustainable supplier selection and order allocation considering quality policies and demand forecasting: a real-life case study," Information Sciences, vol. 8, no. 1, pp. 39-69, 2024, doi: https://doi.org/10.1007/s41660-023-00350-x. [42] S. Nayeri, M. A. Khoei, M. R. Rouhani-Tazangi, M. GhanavatiNejad, M. Rahmani, and E. B. Tirkolaee, "A data-driven model for sustainable and resilient supplier selection and order allocation problem in a responsive supply chain: A case study of healthcare system," Eng. Appl. Artif. Intell., vol. 124, p. 106511, 2023, doi: https://doi.org/10.1016/j.engappai.2023.106511. [43]O. Abbaas and J. A. Ventura, "An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand," Mathematics, vol. 12, no. 14, p. 2228, 2024, doi: https://doi.org/10.3390/math12142228. [44]Y. Wang, W. Sun, M. Z. Abedin, P. Hajek, and W. Xue, "A multi-objective lot sizing procurement model for multi-period cold chain management including supplier and carrier selection," Omega, vol. 130, p. 103165, 2025, doi: https://doi.org/10.1016/j.omega.2024.103165. [45]H.-W. Lo, C.-J. Pai, and M. Deveci, "A multi-objective model for integrated supplier order allocation and supply chain network transportation planning decision-making," Inf. Sci., vol. 689, p. 121487, 2025, doi: https://doi.org/10.1016/j.ins.2024.121487. [46]L. A. Johnson and D. C. Montgomery, "Operations research in production planning, scheduling, and inventory control," (No Title), 1974, doi: https://ci.nii.ac.jp/ncid/BA0375727X?l=en. [47]L. Zurich, "Operations Research in Production Planning, Scheduling and Inventory Control," J. Clean. Prod., vol. 26, no. 3, pp. 568-569, 1975, doi: https://doi.org/10.1057/jors.1975.120.
آمار تعداد مشاهده مقاله: 28

اخبار و اعلانات

آمار

بهینه‌سازی سفارش و تخصیص چند تأمین با تصمیم‌گیری مارکوف