Pembe GÜÇLÜ, Ali ÖZDEMİR

10383

Belirsizlik Altında Üretim Planlaması Problemi için Robust Eniyileme Modeli

İşletmelerin içinde bulundukları şartlar oldukça hızlı bir şekilde değişmektedir. Planlama yapılırken değişimin doğurduğu belirsizliği hesaba katmak adeta bir kural haline gelmiştir. Belirsizliği ele alma yöntemlerinden olan robust eniyileme teknikleri, değişen koşullara daha az duyarlı sonuçlar üreten modellerin oluşturulmasını sağlamaktadır. Üretim planlaması en basit anlamda hangi üründen, ne zaman, ne kadar üretileceğine karar verilmesidir. Üretim planlama problemlerinin modellenmesi ve çözümü üretim sürecinin, ele alınan parametrelerin ve değişkenlerin yapısına bağlı olarak farklılık göstermektedir. Bu çalışmada parametre ve talep belirsizliği altında, kapasite kısıtlı iki aşamalı, çok ürünlü üretim planlaması problemi için eniyileme modelinin oluşturulması ve çözülmesi amaçlanmıştır. Bu amaçla İzmir’de faaliyet gösteren bir tekstil firmasının üretim planlama problemi modellenerek çözülmüş, robust modelin sonuçları ile deterministik senaryoların sonuçları karşılaştırılmıştır. Robust yöntem, daha yüksek maliyetli ancak gelecekte karşılaşılabilecek farklı senaryoların çoğunluğunda büyük ölçüde olurlu ve optimale yakın sonuçlar verecek, sağlam bir üretim planı sunmuştur.
Anahtar Kelimeler:

Robust Eniyileme, Üretim Planlaması, Belirsizlik

Robust Optimization Model for Production Planning Problem under Uncertainty

Conditions of businesses change very quickly. To take into account the uncertainty engendered by changes has become almost a rule while planning. Robust optimization techniques that are methods of handling uncertainty ensure to produce less sensitive results to changing conditions. Production planning, is to decide from which product, when and how much will be produced, with a most basic definition. Modeling and solution of the Production planning problems changes depending on structure of the production processes, parameters and variables. In this paper, it is aimed to generate and apply scenario based robust optimization model for capacitated two-stage multi-product production planning problem under parameter and demand uncertainty. With this purpose, production planning problem of a textile company that operate in İzmir has been modeled and solved, then deterministic scenarios’ and robust method’s results have been compared. Robust method has provided a production plan that has higher cost but, will result close to feasible and optimal for most of the different scenarios in the future.
Keywords:

Robust Optimization, Production Planning, Uncertainty,

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  • Adasme, P., Lisser, A., ve Soto, I. (2011) “Robust Semidefinite Relaxations for a Quadratic OFDMA Resource Allocation Scheme”, Computers & Operations Research, 38(10): 1377-1399.
  • Adida, E., ve Joshi, P. (2009) “A Robust Optimisation Approach to Project Scheduling and Resource Allocation”, International Journal of Services Operations and Informatics, 4(2): 169-193.
  • Adida, E., ve Perakis, G. (2006) “A Robust Optimization Approach to Dynamic Pricing and İnventory Control with no Backorders”, Mathematical Programming, 107(1-2): 97-129.
  • Adida, E., ve Perakis, G. (2010) “Dynamic Pricing and İnventory Control: Robust vs. Stochastic Uncertainty ModelsA Computational Study” Annals of Operations Research, 181(1): 125-157.
  • Aghezzaf, E. (2005) “Capacity Planning and Warehouse Location in Supply Chains with Uncertain Demands”, Journal of the Operational Research Society, 56(4): 453-462.
  • Agra, A., Christiansen, M., Figueiredo, R., Hvattum, L. M., Poss, M. ve Requejo, C. (2013) “The Robust Vehicle Routing Problem with Time Windows”, Computers & Operations Research, 40(3): 856-866.
  • Ait-Alla, A., Teucke, M., Lütjen, M., Beheshti-Kashi, S. ve Karimi, H.R. (2014) “Robust Production Planning in Fashion Apparel Industry under Demand Uncertainty via Conditional Value at Risk”, Hindawi Publishing Corporation Mathematical Problems in Engineering, Cilt 2014.
  • Alem, D. J. ve Morabito, R. (2012) “Production Planning in Furniture Settings via Robust Optimization”, Computers&Operations Research, 30: 139-150.
  • Aloulou, M. A., Dolgui, A., & Kovalyov, M. Y. (2014). A Bibliography of Non-Deterministic Lot-Sizing Models. International Journal of Production Research. 52(8): 2293-2310.
  • Atamtürk, A., ve Zhang, M. (2007) “Two-Stage Robust Network Flow and Design under Demand Uncertainty”, Operations Research, 55(4): 662-673.
  • Ayuso, A. A., & Sánchez, M. T. O. (2007). On Modelling Planning Under Uncertainty in Manufacturing. SORT: Statistics and Operations Research Transactions. 31(2): 109-150.
  • Babonneau, F., Vial, J. P., Klopfenstein, O., ve Ouorou, A. (2013) “Robust Capacity Assignment Solutions for Telecommunications Networks with Uncertain Demands”, Networks. 62(4): 255-272.
  • Baghalian, A., Rezapour, S., ve Farahani, R. Z. (2013) “Robust Supply Chain Network Design with Service Level Against Disruptions and Demand Uncertainties: A Real-Life Case”, European Journal of Operational Research, 227(1): 199-215.
  • Barahona, F., Bermon, S., Günlük, O., ve Hood, S. (2005) “Robust Capacity Planning in Semiconductor Manufacturing”, Naval Research Logistics (NRL),52(5): 459-468.
  • Bel-Tal, A., El Ghaoui, L. ve Nemirowski, A. (2009) Robust Optimization, USA: Princeton University Press.
  • Ben-Tal, A., ve Nemirovski, A. (1998) “Robust Convex Optimization”, Mathematics of Operations Research, 23(4): 769-805.
  • Ben-Tal, A., ve Nemirovski, A. (1999) “Robust Solutions of Uncertain Linear Programs”, Operations Research Letters. 25(1): 1-13.
  • Ben-Tal, A., & Nemirovski, A. (2000) “Robust Solutions of Linear Programming Problems Contaminated with Uncertain Data”, Mathematical Programming, 88(3): 411-424.
  • Ben-Tal, A., ve Nemirovski, A. (2002) “Robust Optimization–Methodology and Applications”, Mathematical Programming, 92(3): 453-480.
  • Berglund, P. G., ve Kwon, C. (2014) “Robust Facility Location Problem for Hazardous Waste Transportation”, Networks and Spatial Economics, 14(1): 91-116.
  • Bertsimas, D., ve Sim, M. (2003) “Robust Discrete Optimization and Network Flows”, Mathematical Programming, 98(1-3): 49-71.
  • Bertsimas, D., ve Thiele, A. (2004) “A Robust Optimization Approach to Supply Chain Management”, Integer Programming and Combinatorial Optimization (ss. 86-100), Springer Berlin Heidelberg.
  • Bertsimas, D., ve Thiele, A. (2006) “A Robust Optimization Approach to Inventory Theory”, Operations Research, 54(1): 150-168.
  • Bertsimas, D., Brown, D. B., & Caramanis, C. (2011) “Theory and Applications of Robust Optimization”, SIAM Review, 53(3): 464-501.
  • Büsing, C. (2012) “Recoverable Robust Shortest Path Problems”, Networks, 59(1): 181-189.
  • Chen, W., Tan, S., ve Yang, D. (2011) “Worst-Case VaR and Robust Portfolio Optimization with Interval Random Uncertainty Set”, Expert Systems with Applications, 38(1): 64-70: 99.
  • Conde, E. (2009) “A Minmax Regret Approach to the Critical Path Method with Task Interval Times”, European Journal of Operational Research, 197(1): 235-242.
  • De Rosa, V., Gebhard, M., Hartmann, E., ve Wollenweber, J. (2013) “Robust Sustainable Bi-Directional Logistics Network Design under Uncertainty”, International Journal of Production Economics, 145(1): 184-198.
  • Dolgui, A., Grimaud, F., & Shchamialiova, K. (2010). Supply Chain Management Under Uncertainties: Lot-sizing and Scheduling Rules. In Artificial Intelligence Techniques for Networked Manufacturing Enterprises Management (ss. 181-220). London: Springer.
  • Fliege, J., ve Werner, R. (2014) “Robust Multiobjective Optimization & Applications in Portfolio Optimization”, European Journal of Operational Research, 234(2): 422-433.
  • Ghaoui, L. E., Oks, M., ve Oustry, F. (2003) “Worst-Case Value-at-Risk and Robust Portfolio Optimization: A Conic Programming Approach”, Operations Research, 51(4): 543-556.
  • Goldfarb, D., ve Iyengar, G. (2003) “Robust Portfolio Selection Problems”, Mathematics of Operations Research, 28(1): 1-38.
  • Gounaris, C. E., Wiesemann, W., ve Floudas, C. A. (2013) “The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty”, Operations Research, 61(3): 677-693.
  • Graves, S. C. (2011). Uncertainty and Production Planning. In Planning Production and Inventories in the Extended Enterprise (ss. 83-101). Springer US.
  • Gülpınar, N., Pachamanova, D., ve Çanakoğlu, E. (2013) “Robust Strategies for Facility Location under Uncertainty”, European Journal of Operational Research, 225(1): 21-35.
  • Herroelen, W., ve Leus, R. (2004) “Robust and Reactive Project Scheduling: A Review and Classification of Procedures”, International Journal of Production Research, 42(8): 1599-1620.
  • Huang, D., Zhu, S., Fabozzi, F. J., ve Fukushima, M. (2010) “Portfolio Selection under Distributional Uncertainty: A Relative Robust CVaR Approach”, European Journal of Operational Research, 203(1): 185-194.
  • Kang, D., ve Lansey, K. (2012) “Scenario-Based Robust Optimization of Regional Water and Wastewater Infrastructure”, Journal of Water Resources Planning and Management, 139(3): 325-338.
  • Kasperski, A., ve ZielińSki, P. (2006) “The Robust Shortest Path Problem in Series–Parallel Multidigraphs with Interval Data”, Operations Research Letters, 34(1): 69-76.
  • Klabjan, D., Simchi-Levi, D. ve Sang, M. (2013) “Robust Stochastic Lot-Sizing by Means of Histograms”, Production and Operations Management, 22 (3): 691–710.
  • Koster, A. M., Kutschka, M., ve Raack, C. (2013) “Robust Network Design: Formulations, Valid Inequalities, and Computations”, Networks, 61(2): 128-149.
  • Kouvelis, P. ve Yu, G. (1997) Robust Discrete Optimization and Its Applications, USA: Springer.
  • Lai, K. K., ve Ng, W. L. (2005) “A Stochastic Approach to Hotel Revenue Optimization”, Computers & Operations Research, 32(5): 1059-1072.
  • Lan, Y., Gao, H., Ball, M. O., ve Karaesmen, I. (2008) “Revenue Management with Limited Demand Information”, Management Science, 54(9): 1594-1609.
  • Latifoğlu, Ç., Belotti, P., ve Snyder, L. V. (2013) “Models for Production Planning under Power Interruptions”, Naval Research Logistics (NRL), 60(5): 413-431.
  • Lee, C., Lee, K., ve Park, S. (2012) “Robust Vehicle Routing Problem with Deadlines and Travel Time/Demand Uncertainty”, Journal of the Operational Research Society, 63(9): 1294-1306.
  • Leung, S.C. ve Wu, Y. (2004). “A Robust Optimization Model for Stochastic Aggregate Production Planning”, Production Planning&Control: The Management of Operations. 15(5): 502-514.
  • Leung, S.C. ve Wu, Y. (2007) “A Robust Optimization Model for Stochastic Aggregate Production Planning”, Production Planning&Control: The Management of Operation, 15(5): 502-514.
  • Leung, S.C.H, Tsang, S.O.S., Ng, W.L. Ve Wu, Y. (2007) “A Robust Optimization Model for Multi-Site Production Planning Problem in an Uncertain Environment”, European Journal of Operational Research, 181: 224-238.
  • Li, Z., Ding, R. ve Floudas, C.A. (2011) “A Comparative Theoritical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization”, Industrial & Engineering Chemistry Research, 50: 10567-10603.
  • Minoux, M. (2009) “Robust Linear Programming with Right-Hand-Side Uncertainty: Duality and Applications”, Encyclopedia of Optimization (ss. 3317-3327), Springer-Verlag.
  • Mirzapour Al-e Hashem, S.M.J., Maleky, H. Ve Aryanezhad, M.B. (2011) “A Multi Objective Robust Optimization Model for Multi Product Multi-Site Aggregate Production Planning in a Supply Chain Under Uncertainty”, International Journal of Production Economics, 134: 28-42.
  • Moazeni, S., Coleman, T. F., ve Li, Y. (2013) “Regularized Robust Optimization: the Optimal Portfolio Execution Case”, Computational Optimization and Applications, 55(2): 341-377.
  • Moon, Y., ve Yao, T. (2011) “A Robust Mean Absolute Deviation Model for Portfolio Optimization”, Computers & Operations Research, 38(9): 1251-1258.
  • Mula, J., Poler, R., Garcia-Sabater, J. P. ve lario, F. C. (2006). Models for Production Planning Under Uncertainty: A Review. International Journal of Production Economics. 103: 271–285.
  • Mulvey, J. M., Vanderbei, R. J. ve Zenios, S. A. (1995) “Robust Optimization of Large Scale Systems”, Operations Research, 43(2): 264-281.
  • Pascoal, M. M., ve Resende, M. (2014) “The Minmax Regret Robust Shortest Path Problem in a Finite Multi-Scenario Model”, Applied Mathematics and Computation, 241: 88-111.
  • Perakis, G., ve Sood, A. (2006) “Competitive Multi-Period Pricing for Perishable Products: A Robust Optimization Approach”, Mathematical Programming, 107(1-2): 295-335.
  • Raa, B., ve Aghezzaf, E. H. (2005) “A Robust Dynamic Planning Strategy for Lot-Sizing Problems with Stochastic Demands”, Journal of Intelligent Manufacturing, 16(2): 207-213.
  • Sim, M. (2004) Robust Optimization (Yayınlanmamış Doktora Tezi), Sloan School of Management Massachusetts Institute of Technology.
  • Sitompul, C., ve Aghezzaf, E. H. (2008) “Robust Production Planning: An Alternative to Scenario-Based Optimization Models”, Modelling, Computation and Optimization in Information Systems and Management Sciences (ss. 328-337), Springer Berlin Heidelberg.
  • Soyster, L.A. (1973) “Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming”, Operations Research, 21(5): 1154-1157.
  • Sungur, I., Ordónez, F., ve Dessouky, M. (2008) “A Robust Optimization Approach for the Capacitated Vehicle Routing Problem with Demand Uncertainty”, IIE Transactions, 40(5): 509-523.
  • Thiele, A. (2004) A Robust Optimization Approach to Supply Chains and Revenue Management. (Yayınlanmamış Doktora Tezi), Massachusetts Institute of Technology.
  • Wiesemann, W., Kuhn, D., ve Rustem, B. (2012) “Robust Resource Allocations in Temporal Networks”, Mathematical Programming, 135(1-2): 437-471.
  • Yamashita, D. S., Armentano, V. A., ve Laguna, M. (2007) “Robust Optimization Models for Project Scheduling with Resource Availability Cost”, Journal of Scheduling, 10(1): 67-76.
  • Yu, C-S. ve Li, H-L. (2000) “A Robust Optimization Model for Stochastic Logistic Problems”, International Journal of Production Economics, 64: 385-397.
  • Zanjani, M.K., Ait-Kadi, D. Ve Nourelfath, M.(2010) “Robust Production Planning in a Manufacturing Environment with Random Yield: A Case in Sawmill Production Planning”, European Journal of Operational Research, 201: 882-891.
  • Zhou, Zhili. (2010) “Multi-Stage Discrete Optimization under Uncertainty and Lot Sizing”, (Yayınlanmamış Doktora Tezi). Florida Üniversitesi.
Optimum Ekonomi ve Yönetim Bilimleri Dergisi-Cover
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2014
  • Yayıncı: -
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