MULTI-OBJECTIVE INVENTORY MODEL INCORPORATING SHORTAGE COST AND DELAYED REPLENISHMENT WITH DIVERSE FUZZY NUMBER APPLICATIONS USING C++ PROGRAMMING LANGUAGE
Resumen
Today’s supply chains face many problems, especially when it comes to managing inventory. Delays in getting supplies, sudden changes in customer demand, and the high cost of running out of stock make planning difficult. Most traditional models use fixed values, which don’t work well when things are uncertain. Although fuzzy logic has been used to handle uncertainty, many studies only use simple fuzzy numbers, which don’t fully capture the complexity of real-life situations. This study introduces an improved inventory model that considers both shortage costs and delays in restocking. It uses four types of fuzzy numbers—trapezoidal, pentagonal, hexagonal, and decagonal to show different levels of uncertainty more accurately. The model is programmed in C++ and uses a special method called graded mean integration to turn fuzzy numbers into useful values. Results show that while trapezoidal numbers produce basic results, pentagonal and hexagonal numbers are better especially hexagonal, which provides the lowest overall cost. The model also deals with uncertainty in how long restocking takes. A case study and sensitivity validation show the model works well in real-world supply chain problems.
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https://doi.org/10.1016/0377-2217(83)90283-7
[22] Yao, J.S., Wu, K.,(2000), “Ranking Fuzzy Numbers based on Decomposition principle and signed distance”, Fuzzy Sets and Systems. Volume,116, Issue 2, pp - 283-319.
https://doi.org/10.1016/S0165-0114(98)00122-5
[2] Adrian I. Ban.,&Lucian C.Coroianu (2011).“Discontinuity of the trapezoidal fuzzy number- valued operators preserving core”.Computers & Mathematics with applicationsVolume 62, Issue 8, pp - 3103-3110
https://doi.org/10.1016/j.camwa.2011.08.023
[3] Ata Allah Taleizadeh., Vahid Reza Soleymanfar., & Kannan Govindan., (2018). “Sustainable economic production quantity models for inventory systems with shortage”. Journal of Cleaner Production. Volume 174, pp -1011-1020
https://doi.org/10.1016/j.jclepro.2017.10.222
[4] Chen S. H., Wang C.C.,& Arthur Ramer., (1996). “Backorder Fuzzy Inventory Model under function principle”. Information Sciences - Volume 95, Issue 1-2, pp-71-79.
https://doi.org/10.1016/S0020-0255(96)00085-0
[5] Chang H.C., (2004)”. An application of fuzzy sets theory to the EOQ model with imperfect quality items”.Computers&Operations Research.Volume 31, Issue 12,pp-2079-2092 https://doi.org/10.1016/S0305-0548(03)00166-7
[6] Chang S.C., Yao J.S.,& Lee H. M.(1998). “Economic reorder pointfor fuzzy backorder quantity”. European Journal of Operational Research. Volume 109, Issue 1, pp-183-202. https://doi.org/10.1016/S0377-2217(97)00069-6
[7] Cheng T.C.E. (1991) “An economic order quantity model with demand-dependent unit production cost and imperfect production processes”. IIE Transaction (Inst. Ind. Eng.). Volume 23, Issue 1, pp- 23-28
https://doi.org/10.1080/07408179108963838
[8] Chinmay Saha., Dipak Kumar Jana., & Avijit Duary., (2023), “Enhancing production inventory management for imperfect items using fuzzy optimization strategies and Differential Evolution (DE) algorithms”. Franklin Open.Volume 5, Article 100051 https://doi.org/10.1016/j.fraope.2023.100051
[9] Dipankar Chakraborty., Dipak Kumar Jana., & Tapan Kumar Roy., (2018) “Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments”.
Computer & Industrial Engineering”. Volume123, pp- 157-179.
https://doi.org/10.1016/j.cie.2018.06.022
[10] Huey-Ming Lee., Jing-Shing Yao., (2005). “Economic Order Quantity in Fuzzy Sense for Inventory without Backorder model”. Fuzzy Sets and Systems. Volume 105 Issue 1,
pp-13-31https://doi.org/10.1016/S0165-0114(97)00227-3
[11] Jia-Tzer Hsu.,&Lie-Fern Hsu.,(2013). “An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns”. International Journal of Production Economics Volume 143, Issue 1, pp- 162-170
https://doi.org/10.1016/j.ijpe.2012.12.025
[12] Kazemi N., Ehsani, E., & Jaber, M.Y., (2010), “An inventory with backorders with fuzzy parameters and decision variables,” International Journal of Approximate Reasoning. Volume 51, Issue 8, pp - 964-972.
https://doi.org/10.1016/j.ijar.2010.07.001
[13] Muhammad ShamroozAslam., HazratBilal., Shahab S. Band., & Peiman Ghasemi., (2024), “Modeling of nonlinear supply chain management with lead-times based on Takagi-Sugeno fuzzy control model”. Engineering Applications of Artificial Intelligence Volume 133, Part C, 108131 https://doi.org/10.1016/j.engappai.2024.108131
[14] MishraU., WalivR.H., & UmapH.P., (2019). “Optimizing of Multi-objective Inventory Model by Different Fuzzy Techniques”. International Journal Applied and Computational Mathematics. Volume 5,Article number 136 https://doi.org/10.1007/s40819-019-0721-0
[15] Riju Chaudhary., Mandeepa Mittal., & Mahesh Kumar Jayaswal., (2023), “A sustainable inventory model for defective items under fuzzy environment”. Decision Analytics Journal. Volume 7 Article 100207
https://doi.org/10.1016/j.dajour.2023.100207
[16] SalamehM.K.,& Jaber M.Y., (2000). “Economic production quantity model for items with imperfect quality”. International Journal of Production Economics. volume 64, Issue 1-3 pp-59-64. https://doi.org/10.1016/S0925-5273(99)00044-4
[17] Suvetha R., Rangarajan, K., & Rajadurai, P., (2024). “A sustainable three-stage production inventory model with trapezoidal demand and time-dependent holding cost”. Results in Control and Optimization Volume 17, 100493.
https://doi.org/10.1016/j.rico.2024.100493
[18] Sanni S.S.,& Chukwu W.I.E.,(2013). “An economic order quantity model for items with three-parameter Weibull distribution deterioration, ramp-type demand and shortages”.Applied Mathematical Modelling. Volume 37, Issur 23, pp- 9698-9706.
https://doi.org/10.1016/j.apm.2013.05.017
[19] Sankar Prasad Mondal., Manimohan Mandal., (2017), “Pentagonal fuzzy number, its properties and application in fuzzy equation”. Future computing and Informatics Journal.Volume 2, Issue 2, pp - 110-117
https://doi.org/10.1016/j.fcij.2017.09.001
[20] SangeethaK., & ParimalaM., (2021), “On solving a fuzzy game problem using hexagonal fuzzy numbers”, Materials today: proceedings.volume 47, part 9, pp - 2102 -2106 https://doi.org/10.1016/j.matpr.2021.04.591
[21] Urgeletti Tinarelli G., (1983), “Inventory Control Models and Problems”. European Journal of Operational Research. Volume14, Issue 1, pp - 1-12.
https://doi.org/10.1016/0377-2217(83)90283-7
[22] Yao, J.S., Wu, K.,(2000), “Ranking Fuzzy Numbers based on Decomposition principle and signed distance”, Fuzzy Sets and Systems. Volume,116, Issue 2, pp - 283-319.
https://doi.org/10.1016/S0165-0114(98)00122-5
Publicado
2025-09-18
Número
Sección
Research Articles
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