A Production Inventory Model With Imperfect Item and Low Quality Manufacturing Under α-Cut Type-2 Fuzzy Environment Using Fuzzy H2 Differentiation
Abstract
This study delves into a fuzzy economic manufacturing model focused on inventory models encountering imperfect and low-quality production processes, inclusive of rework scenarios. The concern arises primarily during epidemics when unsold items accumulate, escalating maintenance costs due to constant deterioration. Uniquely, this research incorporates a special mathematical formulation contrasting discounted lowquality items with non-discounted ones under fuzzy conditions. Enhanced computer techniques founded on fuzzy logic are employed to refine identification, decision-making, and optimization. These situations are depicted through a bi-objective framework aiming for a simultaneous minimization of overall cost and emissions, subject to a meticulously devised constraint set. The significance of optimal manufacturing is accentuated by attributing a triangular fuzzy number to economic production quantity. The EPQ model’s optimal total cost is discerned in its crisp form, meriting emphasis. Production inventory, varying from raw materials to unfinished products, sometimes includes imperfect items, posing significant challenges like increased production costs and delayed processes. Addressing this involves implementing rigorous quality control measures and possibly adopting lean manufacturing principles aimed at minimizing waste and enhancing production efficiency. These strategies aid in maintaining quality, ensuring customer satisfaction, and sustaining profits by mitigating the challenges posed by inferior quality items within the production inventory.
References
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P. Korkidis and A. Dounis, “On training non-uniform fuzzy partitions for function approximation using differential evolution: A study on fuzzy transform and fuzzy projection,” Information Sciences, vol. 619, pp. 867–888, 2023. doi: 10.1016/j.ins.2022.11.050.
M. Najariyan and N. Pariz, “Stability and controllability of fuzzy singular dynamical systems,” Journal of the Franklin Institute, vol. 359, no. 15, pp. 8171–8187, October 2022. doi: 10.1016/j.jfranklin.2022.07.035.
Y. Chalco-Cano, T. Costa, H. Roman-Flores, and A. Rufi ´ an-Lizana, “New properties of the ´ switching points for the generalized hukuhara differentiability and some results on calculus,” Fuzzy Sets and Systems, vol. 404, pp. 62–74, 2021, Fuzzy Numbers in Analysis. doi: 10.1016/j.fss.2020.06.016.
D. Qiu and Y. Yu, “Some notes on the switching points for the generalized hukuhara differentiability of interval-valued functions,” Fuzzy Sets and Systems, vol. 453, pp. 115–129, 2023, fuzzy numbers and analysis. doi: 10.1016/j.fss.2022.04.004.
M. Mazandarani and M. Najariyan, “Differentiability of type-2 fuzzy number-valued functions,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 3, pp. 710–725, 2014. doi: 10.1016/j.cnsns.2013.07.002.
D. Qiu and C. Ouyang, “Optimality conditions for fuzzy optimization in several variables under generalized differentiability,” Fuzzy Sets and Systems, vol. 434, pp. 1–19, 2022, Optimisation and Decision Analysis. doi: 10.1016/j.fss.2021.05.006.
P. Guchhait, M. Kumar Maiti, and M. Maiti, “A production inventory model with fuzzy production and demand using fuzzy differential equation: An interval compared genetic algorithm approach,” Engineering Applications of Artificial Intelligence, vol. 26, no. 2, pp. 766–778, 2013. doi: 10.1016/j.engappai.2012.10.017.
R. Alikhani and F. Bahrami, “Fuzzy partial differential equations under the cross product of fuzzy numbers,” Information Sciences, vol. 494, pp. 80–99, 2019. doi: 10.1016/j.ins.2019.04.030.
Y. Shen, “Comparison between the linearly correlated difference and the generalized hukuhara difference of fuzzy numbers,” Fuzzy Sets and Systems, vol. 435, pp. 27–43, 2022, Fuzzy Numbers. doi: 10.1016/j.fss.2021.05.007.
D. Mohapatra and S. Chakraverty, “Initial value problems in type-2 fuzzy environment,” Mathematics and Computers in Simulation, vol. 204, pp. 230–242, February 2023. doi: 10.1016/j.matcom.2022.08.002.
F. Santo Pedro, M. M. Lopes, V. F. Wasques, E. Esmi, and L. C. de Barros, “Fuzzy fractional differential equations with interactive derivative,” Fuzzy Sets and Systems, 2023. doi: 10.1016/j.fss.2023.02.009.
J. Zhang, Z. Xu, F. Feng, and R. R. Yager, “Two classes of granular solutions and related optimality conditions for interval type-2 fuzzy optimization,” Information Sciences, vol. 612, pp. 974–993, 2022. doi: 10.1016/j.ins.2022.09.029.
D. Peng, J. Wang, D. Liu, and Y. Cheng, “The interactive fuzzy linguistic term set and its application in multi-attribute decision making,” Artificial Intelligence in Medicine, vol. 131, p. 102 345, 2022. doi: 10.1016/j.artmed.2022.102345.
H. M. Athar Farid, M. Riaz, and Z. A. Khan, “T-spherical fuzzy aggregation operators for dynamic decision-making with its application,” Alexandria Engineering Journal, vol. 72, pp. 97–115, 2023. doi: 10.1016/j.aej.2023.03.053.
L. Stefanini, “A generalization of hukuhara difference and division for interval and fuzzy arithmetic,” Fuzzy Sets and Systems, vol. 161, no. 11, pp. 1564–1584, 2010, Theme: Decision Systems. doi: 10.1016/j.fss.2009.06.009.
J.-S. Yao, L.-Y. Ouyang, and H.-C. Chang, “Models for a fuzzy inventory of two replaceable merchandises without backorder based on the signed distance of fuzzy sets,” European Journal of Operational Research, vol. 150, no. 3, pp. 601–616, 2003, Financial Modelling. doi: 10.1016/S0377-2217(02)00542-8.
D. K. Jana, B. Bej, M. H. A. Wahab, and A. Mukherjee, “Novel type-2 fuzzy logic approach for inference of corrosion failure likelihood of oil and gas pipeline industry,” Engineering Failure Analysis, vol. 80, pp. 299–311, 2017. doi: 10.1016/j.engfailanal.2017.06.046.
J. Qin, T. Xu, and P. Zheng, “Axiomatic framework of entropy measure for type-2 fuzzy sets with new representation method and its application to product ranking through online reviews,” Applied Soft Computing, vol. 130, p. 109 689, 2022. doi: 10.1016/j.asoc.2022.109689.
A. Hasani, S. M. H. Hosseini, and S. S. Sana, “Scheduling in a flexible flow shop with unrelated parallel machines and machine-dependent process stages: Trade-off between makespan and production costs,” Sustainability Analytics and Modeling, vol. 2, p. 100 010, 2022. doi: 10.1016/j.samod.2022.100010.
S. Bera, P. K. Giri, D. K. Jana, K. Basu, and M. Maiti, “Fixed charge 4d-tp for a breakable item under hybrid random type-2 uncertain environments,” Information Sciences, vol. 527, pp. 128–158, 2020. doi: 10.1016/j.ins.2020.03.050.
A. M. El-Nagar, M. El-Bardini, and A. A. Khater, “A class of general type-2 fuzzy controller based on adaptive alpha-plane for nonlinear systems,” Applied Soft Computing, vol. 133, p. 109 938, 2023. doi: 10.1016/j.asoc.2022.109938.
A. Mohammadzadeh and E. Kayacan, “A non-singleton type-2 fuzzy neural network with adaptive secondary membership for high dimensional applications,” Neurocomputing, vol. 338, pp. 63–71, 2019. doi: 10.1016/j.neucom.2019.01.095.
J. Schneider, D. Kuchta, and R. Michalski, “A vector visualization of uncertainty complementing the traditional fuzzy approach with applications in project management,” Applied Soft Computing, vol. 137, p. 110 155, 2023. doi: 10.1016/j.asoc.2023.110155.
X. Qu, J. Han, L. Shi, et al., “An extended itl-vikor model using triangular fuzzy numbers for applications to water-richness evaluation,” Expert Systems with Applications, vol. 222, p. 119 793, 2023. doi: 10.1016/j.eswa.2023.119793.
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Published
2025-05-12
How to Cite
SAHA, Chinmay; JANA, Dipak Kumar; DUARY, Avijit.
A Production Inventory Model With Imperfect Item and Low Quality Manufacturing Under α-Cut Type-2 Fuzzy Environment Using Fuzzy H2 Differentiation.
Yugoslav Journal of Operations Research, [S.l.], may 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1338>. Date accessed: 13 may 2025.
doi: https://doi.org/10.2298/YJOR230515002S.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
