The Bi-level Programming Approach to Improve the Inventory Control System with a Practical Application
DOI:
https://doi.org/10.33095/gd8dy062Keywords:
The linear-quadratic bi-level programming (LQBP), Modified Simplex Algorithm, Karush-Kuhn-Tucker conditions (K.K.T), Multi-item production model (no shortage) With -Restriction ,The Classic method.Abstract
In this research, we investigated addressing the challenges associated with the seasonal allergic medical drug inventory system. The focus was on determining the optimal demand by calculating the Economic Order Quantity (EOQ) and achieving the lowest cost within the Pharmaceutical Industries and Medical Supplies company in Samarra. The primary objective was to efficiently meet the demand for seasonal allergy medications by identifying the optimal demand for medical drugs. The study encompassed two types of seasonal allergy medications, namely Samatifen drink and VALIAPAM 2 pills. The calculation of the lowest cost involved two methods: the multi-component production model without deficit, with restrictions, the solution was done using the classical method (normal) and mathematical analyses, utilizing tools such as QM and Win Qsb. Additionally, linear quadratic bilevel programming (LQBP) was employed. The LQBP model comprised an upper-level decision maker (leader) and a lower-level decision maker (follower). The transformation of the bilevel model into a single-level model was accomplished through the application of Karush-Kuhn-Tucker (KKT) conditions, and the solution was obtained using the modified simplex algorithm. The study's findings underscore the effectiveness of the LQBP method in identifying the optimal solution for the inventory problem by calculating the lowest cost. This approach significantly reduced medical drug inventory-related costs, with a value of 1,496,700,000 Iraqi Dinars (ID) and a production of 1200,700 ID. Notably, this cost was considerably lower than the total cost value obtained using the classical method, which was 1,719,166 ID/year, with a production of 2526,1773 ID. Therefore, bilevel programming (BLPP) demonstrates superior efficiency, providing more accurate and cost-effective solutions. This research emphasizes the potential of bilevel programming in optimizing medical drug inventory systems and contributes to the advancement of operational research in the healthcare sector.
Paper type: Research Paper
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References:
Achamrah, F.E., Riane, F. and Aghezzaf, E.H. (2022) ,"Bi-level programming for modeling inventory sharing in decentralized supply chains" ,Transportation Research Procedia.
Al Nuaimi, M.A.A (1999), operations Research ,Dar Wael for Printing and Publishing, Amman, Jordan.
Al-Obaidi, M.A.A. and Abbas, R.N.A(2019(,"Sggregate production planning using linear programming with a practical application.", Journal of Economic and Administrative Sciences, Vol. 25, No. 113, pp .526-542. https://search.emarefa.net/detail/BIM-888626
Al-Obeidi, M.A.A (2009),"Fuzzy Linear Programming Problems, FLPP ,Fuzzy Linear Programming Problems” ,Journal of Economic SciencesAnd administrative, Vol.15, No.56, pp.181-200.
https://search.emarefa.net/detail/BIM-334121
Al-Shamrati, H.S. and Harbi ,H. F(2020), "Comparing the branching and determining method with the penalty function method for solving nonlinear Bi-level programming (practical application)",Journal of Economic and Administrative Sciences.Vol.2 ,No.119,pp.444 - 457. ,https://doi.org/10.33095/jeas.v26i119.1893
Al-Shamrati, H.S.N (2010), Operations research concept and application , Althakra Library, Beirut.
Al-Shamrati, H.S.N and Al-Zubaidi, A. Kh (2007), Introduction to Operations Research, ed The first, Majd Lawi Publishing House, Kingdom of Jordan Hashemite.
Assadipour, G, Ke, G.Y and Verma, M. (2016) ",A toll-based bi-level programming approach to managing hazardous materials shipments over an intermodal transportation network", Transportation Research Part D-transport, and Environment, Vol.47,No.55,pp. 208-221. https://doi.org/10.1016/j.trd.2016.06.002
Bakheet, A. A. Kh (2010), "Planning major production schedules Buse Integer programming method with binary decisions," Journal of Economic and Administrative Sciences.Vo.16,No.57,pp.151. https://doi.org/10.33095/jeas.v16i57.1447
Bakhit, A.K, Batikh, A. H and Atta, K.W. (2012), "Using operations research in managerial decision-making," Journal of Management and Economics, Vol. 35, No. 93, pp. 121-132.
Balbas, K.M.A(2003), "Building the optimal model for controlling the multi-site storage of the General Company for Baghdad Electricity Distribution", master’s thesis, College of Administration and Economics, University of Baghdad.
Bard, J. F, Plummer, J and Sourie, J. C. (2000) ",A bilevel programming approach to determining tax credits for biofuel production ", European Journal of Operational Research,Vol.120.No.2, pp.30-46. https://doi.org/10.1016/S0377-2217(98)00373-7
Bard, J. F. (2013), Practical bilevel optimization: algorithms and applications , Springer Science and Business Media. Vol. 30,No.20,pp.12-18.
Bracken, J and McGill, J. T (1973) , "Mathematical programs with optimization problems in the constraints", Operations research,Vol.21,No.1, pp.37-44. https://doi.org/10.1287/opre.21.1.37
Calvete, C. (2004), "A Penalty Method for Solving Bi-level Linear-fractional Linear Programming Problems", Asia-Pacific Journal of Operational Research, Vol .52,No.30,PP. 207-224.
Chu, Y. and You, F. (2014), "integrated scheduling and dynamic optimization by Stackelberg game: bilevel model formulation and efficient solution algorithm, Industrial and Amp", Engineering Chemistry Research, Vol. 53,No.13,pp. 5564-5581. https://doi.org/10.1021/ie404272t
Colson, B, Marcotte, P and Savard, G. (2007) ,"An overview of bilevel optimization", Annals of operations research, Vol.153,No.1,pp.235-256. https://doi.org/10.1007/s10479-007-0176-2
Dempe, S. and Zemkoho, A. B. (2012) ",On the Karush–Kuhn–tucker reformulation of the bilevel optimization problem. Nonlinear Analysis: Theory, Methods &Amp; Applications",Vol.75,No.3, pp.1202-1218. https://doi.org/10.1016/j.na.2011.05.097
Douai, A. and Al-Shamrati, H.S.N (2020), "Solving the problem of Bi-level programming (fractal-linear) by applying the genetic algorithm", Journal of Management and Economics, Vol.20, No.126, pp. 257-265.
Dutta, D and Kumar, P. (2012) ,"Fuzzy inventory model without shortage using trapezoidal fuzzy number with sensitivity analysis", IOSR Journal of mathematics, Vol. 4,No.3, pp.32-37.
Feng, C and Wen, C. (2005)",A bi-level programming model for allocating private and emergency vehicle flows in seismic disaster areas", In Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 5,No.55, pp. 1408-1423.
Hassan, D.S, Jaber, A. Sh and Al-Shammari, N. A.A (2013), Operations Research, first edition, Al Jazeera Office, Baghdad ,Iraq.
Hijab, A (2015), "A contribution to identifying decision variables related to the optimal inventory for the use of operations research in the Algerian economic institution", Doctoral thesis, (N.M.) Faculty of Economic, Commercial and Management Sciences, Department of Economic Sciences, Mohamed Khidir University – Biskra, Vol.8, No. 115, pp.112-120.
Hillier F. S. and Lieberman G. J (2021) , Introduction to operations research (Eleventh) , McGraw-Hill Education.
Hosseini, E and Kamal Abadi, I. N. (2013), "A genetic approach for solving bi-level programming problems" ,Advanced Modelling and Optimization, Vol.15,No.3, pp.18-25.
Hosseini, E, and Kamal Abadi, I. N. (2012)." A genetic approach for solving bi-level programming problems ,"Advanced Modelling and Optimization, Vol.15,No.3,pp.12-20.
Hosseini, E., and Kamal Abadi, I. N. (2014) ",Line Search and Genetic Approaches for Solving Linear Tri-level Programming Problem" , International Journal of Management, Accounting, and Economics, Vol.1,No.4,pp.8-12.
https://doi.org/10.33095/jeas.v14i52.1429
Ibrahimis. Kh. (2010),"Research to study the effect of using parametric programming in the linear programming model (an applied study),". Journal of Economic and Administrative Sciences, Vol.16, No.57, pp.184.https://doi.org/10.33095/jeas.v16i57.1444
Jaber, M. Y. (Ed.). (2009), Inventory management: non-classical views, CRC press.
Jackson, I., Tolujevs, J and Kegenbekov, Z.K. (2020), "Review of Inventory Control Models: A Classification Based on Methods of Obtaining Optimal Control Parameters" , Transport and Telecommunication Journal, Vo.21,No.33, pp. 191 - 202. https://doi.org/10.2478/ttj-2020-0015
Jawad, L. B and Jeter, A. Sh (2015) ",Multi-objective probabilistic aggregate production planning with a practical application", Journal of Economic and Administrative Sciences.Vo.21 ,No.82,pp.351. https://doi.org/10.33095/jeas.v21i82.607
Kalashnikov, V. V., Matis, T. I., Camacho-Vallejo, J and Kavun, S. (2015), "Bilevel programming, equilibrium, and combinatorial problems with applications to engineering. Mathematical Problems in Engineering", Vol.8,No.5,PP. 1-3. https://doi.org/10.1155/2015/490758
Khalaf, W.S and Jasem, A.B (2017),"The optimal strategy for managing fuzzy inventory: applied research in the Baghdad Soft Drinks Company" , Journal of Economic and Administrative Sciences, Vol. 23 ,No. 101, pp. 72-98 .https://doi.org/10.33095/jeas.v23i101.170
Lim Yong-taek, and Lim Kang-won (2004)", Bi-level program and Cournot-Nash Game Stackelberg A comparative study of games".
Lotfi, R, Mardani, N and Weber, G. (2021) ,"Robust bi‐level programming for renewable energy location", International Journal of Energy Research,Vol.45,No.55, PP.7521 - 7534.
Lv Y. Hu T. Wang G. and Wan Z. (2008) ," A neural network approach for solving nonlinear bilevel programming problem ",Computers and Mathematics with Applications, Vol.55,No.12 ,pp.2823-2829. https://doi.org/10.1016/j.camwa.2007.09.010
Lv, Y, Hu, T, Wang, G and Wan, Z. (2007) ,A penalty function method based on Kuhn–Tucker condition for solving linear bilevel programming , Applied mathematics and computation,Vol.188,No.1, pp.808-813. https://doi.org/10.1016/j.amc.2006.10.045
Malyshev, A. M. and Strekalovskii, A. S. (2011) ",Connection of some bilevel and nonlinear optimization problems" , Russian Mathematics, Vol.55,No.4,pp.83-86. https://doi.org/10.3103/s1066369x11040104
Marcotte, P, Savard, G and Zhu, D. L. (2001), "A trust region algorithm for nonlinear bilevel programming", Operations research letters, Vol. 29, No.4, pp. 171-179.
Marcotte, P. (1986), "Network design problem with congestion effects: a case of bilevel programming ," Mathematical Programming,Vol.34,No.2, pp.142-162. https://doi.org/10.1007/bf01580580
Metras, B. A.H and Thabit, H.M.M (2009),"Using genetic algorithm to solve some storage models", Iraqi Journal of Statistical Sciences, Vol. 9 ,No. 15, pp. 63-76.
Morgan, S. M (2020), operations Research, Open University, Tripoli, Libya, Vol.2, No. 210, pp.11-20.
Muhammad, L.G (2010) ,"Solving a quadratic programming problem using the Van De Panne method Under foggy environment" , a For the Iraqi Journal of Statistical Sciences ,Vol.10,No.18,pp.13-35.
https://search.emarefa.net/detail/BIM-255534
Murthy. R.(2007) ,Operations Research, second edition ,New Age International (P) Ltd, New Delhi, Vol.33, No.354,pp.112-125.
N. Suresh and Anil Kumar. S (2008), Production and Operations management, Second Edition, New Age International (P) Ltd, New Delhi, 2008,Vol.15 No. 92,pp.55-78.
Naser, O. M (2008) ",Using dynamic programming to solve the static periodic sampling model for the storage problem with a practical application in Al-Aqsa Trading Company for Importin Generators ", Journal of Economic and Administrative Sciences, Vol.14 ,No.52,pp.13-22.
Oduguwa, V, and Roy, R. (2002) ", Bi-level optimization using genetic algorithm, In Proceedings" , IEEE International Conference on Artificial Intelligence Systems (ICAIS 2002),Vol.33,No.55 pp.322-333.
Pal, B. B and Moitra, B. N. (2003)",A fuzzy goal programming procedure for solving quadratic bilevel programming problems", International Journal of Intelligent Systems, Vol.18,No.5,PP. 529-540.
Pradhan, A. and Biswal, M. P. (2015) " ,A bi-level multi-choice programming problem". International Journal of Mathematics in Operational Research,Vol.7,No.1, pp.1-15 .https://doi.org/10.1504/ijmor.2015.065945
Pramanik, S and Roy, T. K (2009)," Fuzzy goal programming approach to multilevel programming problems", European Journal of Operational Research,Vol.176,No.2, pp.1151-1166. https://doi.org/10.1016/j.ejor.2005.08.024
Qing-cheng, Z and Zhong-zhen, Y.( 2006), "A Bi-level Programming Model and Its Algorithm for Scheduling at a Container Terminal", International Conference on Management Science and Engineering. Vol.130,No.55,pp. 402-406.
Rajabi, N., Mozafari, M., & Naimi-Sadigh, A. (2021). "Bi-level pricing and inventory strategies for perishable products in a competitive supply chain," RAIRO - Operations Research, Vol.55,No.4, pp.2395-2412. https://doi.org/10.1051/ro/2021106
Rama, G.C (2009),Accounting for Management, New Age International (P) Ltd, New Delhi,Vol,30 No. 134,PP122-128.
Ravindran, A. R (2008), Operations research and management science , handbook, CRC Press, Taylor and Francis group, Boca Raton London, New York.
Sayal, A, Singh, A. P and Aggarwal, D. (2018), "Inventory model in fuzzy environment without shortage using triangular fuzzy number with sensitivity analysis", Int. J. Agricult, Stat. Sci, Vol. 14,No.1, pp.391-396.
Sharma, A and Arya, V (2016), "Study of Inventory Management in Manufacturing Industry" , International Journal of Advanced Engineering and Global Technology, Vol.4,No.3,pp.1-8.
Shu, Q and Yang, X (2023),"Fixed-index-set based approach for solving a bi-level fuzzy relation programming with addition-min composition", IEEE Transactions on Fuzzy Systems.
Sinha, A, Malo, P, Frantsev, A, and Deb, K . (2013) ,"Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm. Compute ,"Oper. Res ,Vol. 41,No.220,pp. 374-385.
Sinha, A., Malo, P and Deb, K. (2017), "Evolutionary algorithm for bilevel optimization using approximations of the lower-level optimal solution mapping" ,European Journal of Operational Research,Vol.257,No.2, pp.395-411. https://doi.org/10.1016/j.ejor.2016.08.027
Slack, N, Chambers, S and Johnston, R. (2007), Operations management, Fifth edition, Pearson Education, England.
Taha, H. (2007) ,Operations Research an introduction (10th ed) , Pearson Education, Inc, New Jersey, USA, Vol.12, No. 42,pp.12-28.
Talbi, E. (2013), Metaheuristics for bi-level optimization, Studies in Computational Intelligence. https://doi.org/10.1007/978-3-642-37838-6
Wang, Z, Li, H and Chen, A. (2022). "A bi-level optimization approach for portfolio problems with cardinality constraints" , International Conference on Computational Intelligence and Security (CIS) ,pp. 32-37. https://doi.org/10.1109/CIS58238.2022.00015
Waters, D. (2003), "Inventory control and management by Donald waters", (2nd ed.), Wiley.
White , D and Anandalingam, G. (1993",(penalty function approach for solving bi-level linear programs", Journal of Global Optimization, Vol. 3,No.4,pp. 397-419.
Winston W. L. and Goldberg J. B. (2004) ,operations research: applications and algorithms., (4th ed.), Thomson/Brooks/Cole.
Xiang, X, Chang, W and Liu, J (2017) ,"Resource allocation optimization model of collaborative logistics network based on bilevel programming", Scientific Programming, , Vol.5,No.3,pp.1-8. https://doi.org/10.1155/2017/4587098 .
Xiao, Y and Li, H. (2011)," in A genetic algorithm for solving weak nonlinear bilevel programming problems", International Conference on Intelligent Computation Technology and Automation (ICICTA), Vol.1,No.3, pp. 7-9. https://doi.org/10.1109/ICICTA.2011.9
Yu, B, Kong, L., Sun, Y., Yao, B. and Gao, Z . (2015) ,"A bi-level programming for bus lane network design", Transportation Research Part C-emerging Technologies, Vol..55,No.61 pp.310-327.
Zhou, S., Zemkoho, A. B., & Tin, A. (2020), Bolib: bilevel optimization library of test problems. Bilevel Optimization, Vol.45,No.55,pp.563-580. https://doi.org/10.1007/978-3-030-52119-6_19
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