مدل اندازه انباشته پویای احتمالی در شبکه تولید و انتقال کالا با درنظرگرفتن سطح سرویس متفاوت

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار گروه مهندسی صنایع، دانشکدۀ مهندسی، دانشکدگان فارابی، دانشگاه تهران، تهران، ایران

2 کارشناسی ارشد مهندسی صنایع، گروه مهندسی صنایع، دانشکدۀ مهندسی، دانشکدگان فارابی، دانشگاه تهران، تهران، ایران

3 کارشناسی ارشد مدیریت صنعتی، گروه مدیریت صنعتی، دانشکدۀ مدیریت، دانشکدگان فارابی، دانشگاه تهران، تهران، ایران

4 دانشجوی کارشناسی ارشد مهندسی صنایع، گروه مهندسی صنایع، دانشکدۀ مهندسی، دانشکدگان فارابی، دانشگاه تهران، تهران، ایران

10.22084/ier.2024.5573

چکیده

در این پژوهش، یک مدل انباشته پویای احتمالی برای تولید یک محصول با تقاضای تصادفی و محدودیت ظرفیت در شبکه تولید و انتقال کالا توسعه داده شده است، با هدف کمینه‌سازی هزینه‌های نگهداری، راه‌اندازی و اضافه‌کاری. در این مدل پیشنهادی، قابلیت انتقال راه‌اندازی کالا به دوره‌های بعدی وجود دارد که نقش مهمی در کاهش هزینه‌های راه‌اندازی مجدد ایفا می‌کند. استراتژی عدم قطعیت ایستا و شاخص‌های عملکردی سطح سرویس مختلف برای محدود کردن مقدار تقاضا در مواجهه با پس‌افت درنظر گرفته شده است. مسأله به‌صورت یک مدل غیرخطی عدد صحیح مختلط فرموله شده است و برای حل آن از روش‌های حل ابتکاری و حل‌کننده‌های تجاری رایج استفاده شده است. آنالیز حساسیت و تحلیل نتایج مدل پیشنهادی در سطوح مختلف سرویس نشان می‌دهد که این مدل عملکرد و کارایی مناسبی دارد و چشم‌انداز واقع‌بینانه‌تری برای برنامه‌ریزی در شرایط عدم قطعیت ناشی از تقاضا را ارائه می‌دهد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

The Probabilistic Dynamic Lot Sizing Model in Production and Transportation Network with Service Levels

نویسندگان [English]

  • Babak Javadi 1
  • Sajad Hedayati 2
  • Mona Karimi 3
  • Mohammad Reza Abdali 4
1 Assistant Profssor, Department of Industrial Engineering, Faculty of Farabi, University of Tehran, Iran
2 M.A. in Industrial Engineering, Department of Industrial Engineering, Faculty of Farabi, University of Tehran, Iran
3 M.A. industrial Management, Department of Management and Accounting, Faculty of Farabi, University of Tehran, Iran
4 M.A. Student in Industrial Engineering, Department of Industrial Engineering, Faculty of Farabi, University of Tehran, Iran
چکیده [English]

In this research, a model of the possible dynamic cumulative size of a single product with random demand and capacity limitations in the production and transportation network has been developed to minimize the total costs of maintenance, start-up, and overtime. In the proposed model, there is a possibility of transferring the launch of goods to the next period, which plays a significant role in reducing the cost of restarting. Static uncertainty strategies and various service level performance indicators are considered to limit the amount of post-drop demand. Common commercial agents have been used. It is demonstrated by the sensitivity analysis of the proposed model and its analysis at the level of different services that it is performing and efficient, and it also provides a more realistic perspective for planning in the face of uncertain demand conditions.

کلیدواژه‌ها [English]

  • Production Planning
  • Lot Sizing
  • Probabilistic Demand
  • Static Uncertainty Strategy
  • Service Level

مراجع

  • Chen, H. (2015). Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems. Omega, 56, 25-36.
  • Harris, F. W. (1990). How many parts to make at once? Operations Research, 947-950.
  • Rogers, J. (1958). A computational approach to the economic lot scheduling problem. Management Science, 4(3), 264-291.
  • Wagner, H. M. and T. M. Whitin (1958)., “Dynamic version of the economic lot size model”, Management Science 5, 1, 89-96.
  • Aloulou MA, Dolgui A, Kovalyov MY (2014) A bibliography of non-deterministic lot-sizing models. Int J Prod Res 52:2293–2310.
  • Drexl A, Kimms A (1997) Lot sizing and scheduling: survey and extensions. Eur J Oper Res 99:221–235.
  • Karimi B, Fatemi Ghomi SMT, W ilson JM (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega; 31:365–78.
  • van Norden, L., & van de Velde, S. (2005). Multi-product lot-sizing with a transportation capacity reservation contract. European Journal of Operational Research, 165(1), 127-138.
  • Tempelmeier, H. (2011). A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint. Omega, 39(6), 627-633.Helber, S., & Sahling, F. (2010). A fix-and-optimize approach for the multi-level capacitated lot sizing problem. International Journal of Production Economics, 123(2), 247-256.
  • Pochet, Y., & Wolsey, L. A. (2006). Production planning by mixed integer programming. Springer Science & Business Media.
  • Tempelmeier, H., & Hilger, T. (2015). Linear programming models for a stochastic dynamic capacitated lot sizing problem. Computers & Operations Research, 59, 119-125.
  • Brahimi, N., Dauzere-Peres, S., Najid, N. M., & Nordli, A. (2006). Single item lot sizing problems. European Journal of Operational Research, 168(1), 1-16.
  • Jans, R., & Degraeve, Z. (2008). Modeling industrial lot sizing problems: a review. International Journal of Production Research, 46(6), 1619-1643.
  • Jans, R.; Degraeve, Z. (2007). Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches. European Journal of Operational Research, 177 (3), 1855- 1875.
  • Buschk¨uhl, L., F. Sahling, S. Helber and H. Tempelmeier (2010). “Dynamic capacitated lot-sizing problems: a classification and review of solution approach”, OR Spectrum 32, 2, 231– 261.
  • Florian, M., J. K. Lenstra and A. Rinno oy Kan (1980). “Deterministic production planning: Algorithms and complexity”, Management Science 26, 7, 669–679.
  • Trigeiro WW (1989) A simple heuristic for lot sizing with setup times. Decis Sci 20:294–303.
  • Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York.
  • Sox C, Jackson P, Bowman A, Muckstadt J. (1999). A review of the stochastic lot scheduling problem. Int J Prod Econ; 62:181–200.
  • Winands E, Adan I, van Houtum G. The stochastic economic lot scheduling problem: a survey. Eur J Oper Res 2011; 210:1 –9.
  • Tempelmeier, H. (2013). Stochastic lot sizing problems. In Handbook of Stochastic Models and Analysis of Manufacturing System Operations (pp. 313-344). Springer New York.
  • Raa, B. & Aghezzaf, E. J (2005). A robust dynamic planning strategy for lot-sizing problems with stochastic demands, Intell Manuf16: 207. doi:10.1007/s10845-004-5889-3.
  • Brandimarte P. (2006). Multi-item capacitated lot-sizing with demand uncertainty. Int J Prod Res;44(15):2997–3022.
  • Sox C, Muckstadt J. (1997). Optimization-based planning for the stochastic lot scheduling problem. IIE Trans;29(5):349–57.
  • Martel A, Diaby M, Boctor F. (1995). Multiple items procurement under stochastic nonstationary demands. European Journal of Operational Research;87(1):74–92.
  • Tempelmeier, H., & Herpers, S. (2011). Dynamic uncapacitated lot sizing with random demand under a fillrate constraint. European Journal of Operational Research, 212(3), 497-507.
  • Bookbinder, J. and J.-Y. Tan (1988). Strategies for the probabilistic lot-sizing problem with service-level constraints. Management Science 34, 1096–1108.
  • Tempelmeier, H. (2007). On the stochastic uncapacitated dynamic single-item lot sizing problem with service level constraints. European Journal of Operational Research, 181(1), 184-194.
  • Vargas, V. (2009). An optimal solution for the stochastic version of the WagnerWhitin dynamic lot-size model. European Journal of Operational Research 198,447–451.
  • Tarim, S. A., & Kingsman, B. G. (2006). Modeling and computing (R n, S n) policies for inventory systems with non-stationary stochastic demand. European Journal of Operational Research, 174(1), 581-599.
  • Tunc, H., O. Kilic, S. A. Tarim, and B. Eksioglu (2011). The cost of using stationary inventory policies when demand is non-stationary. Omega 39, 410–415.
  • Rossi, R., Kilic, O. A., & Tarim, S. A. (2015). Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing. Omega, 50, 126-140.
  • Helber S, Sahling F, Schimmelpfeng K. Dynamic capacitated lot sizing with random demand and dynamic safety stocks. OR Spectrum 2013;35(1):75 –105.
  • فخرزاد، محمدباقر؛ و علی‌نژاد، اسماعیل، (1392). «برنامه‌ریزی و زمان‌بندی پیشرفته با درنظر گرفتن اثر یادگیری در سیستم‌های ساخت کارگاهی انعطاف‌پذیر». نشریه پژوهش‌های مهندسی صنایع در سیستم‌های تولید، 1(1): 13-24. https://ier.basu.ac.ir/article_493_1.html
  • مختاری, قاسم, و ابوالفتحی, مینا. (1399). زمان‌بندی تولید کارگاهی انعطاف‌پذیر با منابع دوگانه‌ی محدود و اهداف لکزیکوگراف. نشریه پژوهش های مهندسی صنایع در سیستم های تولید, 8(17): 295-309. doi: 10.22084/ier.2021.22227.1978
  • Hilger, T. J. (2015). Stochastic Dynamic Lot-Sizing in Supply Chains. BoD–Books on Demand.
  • Haase K (1994) Lotsizing and scheduling for production planning. Lecture notes in economics and mathematical systems, vol 408. Springer, Berlin.
  • Suerie C, Stadtler H. The capacitated lot-sizing problem with linked lot sizes. Manag Sci 2003; 49:1039–54.
  • Swenseth, S.R., Godfrey, M.R., 2002. Incorporating transportation costs into inventory replenishment decisions. International Journal of Production Economics 77, 113–130.
  • Tersine, R.J., Barman, S., 1991. Lot size optimization with quantity and freight rate discounts. Logistics and Transportation Review 27(4), 319–332.
  • Carter, J.R., Ferrin, B.G., 1996. Transportation costs and inventory management: Why transportation costs matter. Production and Inventory Management Journal 37 (3), 58–62.
  • Burwell, T.H., Dave, D.S., Fitzpatrick, K.E., Roy, M.R., 1997. Economic lot size model for price dependent demand under quantity and freight discounts. International Journal of Production Economics 48, 141–155.
  • Bertazzi, L., Speranza, M.G., 1999. Models and algorithms for the minimization of inventory and transportation costs: A survey. In: Speranza, M.G., St€ahly, P. (Eds.), New Trends in Distribution Logistics. Springer.
  • Vroblefski, M., Ramesh, R., Zionts, S., 2000. Efficient lot-sizing under a differential transportation cost structure for serially distributed ware-houses. European Journal of Operational Research 127, 574–593.
  • Maes, J., & Van Wassenhove, L. N. (1986). A simple heuristic for the multi-item single-level capacitated lotsizing problem. Operations research letters, 4(6), 265-273.‏
  • De Smet, N., Minner, S., Aghezzaf, E. H., & Desmet, B. (2020). A linearisation approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers. International Journal of Production Research, 58(16), 4980-5005.
  • Tavaghof-Gigloo, D., & Minner, S. (2021). Planning approaches for stochastic capacitated lot-sizing with service level constraints. International Journal of Production Research, 59(17), 5087-5107.
  • Mohammadi, M. (2020). Designing an integrated reliable model for stochastic lot-sizing and scheduling problem in hazardous materials supply chain under disruption and demand uncertainty. Journal of Cleaner Production, 274, 122621.
  • Tirkolaee, E.B., Mardani, A., Dashtian, Z., Soltani, M., Weber, G.W., 2020. A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design. Clean. Prod. 250, 119517.
  • Gholizadeh, H., Fazlollahtabar, H., Khalilzadeh, M., 2020. A robust fuzzy stochastic programming for sustainable procurement and logistics under hybrid uncertainty using big data. J. Clean. Prod. 258, 120640.
  • Hasan, R. B. (2023). Improvement to an existing multi-level capacitated lot sizing problem with setup carryover, backlogging, and emission control(Doctoral dissertation, University of Windsor (Canada)).
  • Marco A. Duran and Ignacio E. Grossmann. An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming, 36(3):307–339, 1986.
  • Roger Fletcher and Sven Leyffer. Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming, 66(1-3):327–349, 1994.
  • Ignacio Quesada and Ignacio E. Grossmann. An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Computers & Chemical Engineering, 16(10-11):937–947, 1992.
  • Bonami, A. Wächter, L. T. Biegler, A. R. Conn, G. Cornuéjols, I. E. Grossmann, C. D. Laird, J. Lee, A. Lodi, F. Margot, and N. W. Sawaya. An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optimization, 5(2):186–204, 2008.
  • Abhishek, S. Leyffer, and J. T. Linderoth. FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs. INFORMS Journal on Computing, 22(4):555–567, 2010.
  • Bonami, G. Cornuéjols, A. Lodi, and F. Margot. A feasibility pump for mixed integer nonlinear programs. Mathematical Programming, 119(2):331–352, 2009.
نشریه پژوهش های مهندسی صنایع در سیستم های تولید
دوره 11، شماره 23
اسفند 1402
صفحه 199-215

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