Proposing a conceptual model for influential factors in determining the aggregation coefficient in production planning using fuzzy interpretive structural modeling

Document Type : Original Article

Authors

1 Department of Industrial Engineering, Na.C., Branch, Islamic Azad University, Najafabad, Iran.

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Abstract
Purpose: Given that determining the aggregate coefficient is a key constraint in Aggregate Production Planning (APP), this study seeks to identify the factors influencing this coefficient and to analyze them using Fuzzy Interpretive Structural Modeling (FISM) to explore their interrelationships.
Methodology: After identifying the key factors influencing the aggregate coefficient, an Interpretive Structural Modeling (ISM) questionnaire was distributed among experts, and the responses were aggregated. Subsequently, the FISM steps were carried out. Finally, an interaction network was constructed, and an analysis was performed to evaluate the degree of dependence and driving power among the identified factors.
Findings: The developed interpretive structural model comprised 11 hierarchical levels. The fuzzy analysis of dependence and driving power indicated that none of the factors were categorized as autonomous, reflecting a strong degree of interconnection among the variables within the model.
Originality/Value: Production planning for multiple products utilizing shared resources is a complex challenge. Thus, analyzing the variables that influence the determination of the aggregate coefficient in production planning provides valuable insights, facilitating informed decision-making, particularly in optimizing resource allocation to achieve an optimal production level.

Keywords

Subjects

[1]     Kalir, A., Zorea, Y., Pridor, A., & Bregman, L. (2013). On the complexity of short-term production planning and the near-optimality of a sequential assignment problem heuristic approach. Computers & industrial engineering, 65(4), 537-543. https://doi.org/10.1016/j.cie.2013.05.005
[2]     Nishi, T., Konishi, M., & Hasebe, S. (2005). An autonomous decentralized supply chain planning system for multi-stage production processes. Journal of intelligent manufacturing, 16, 259-275. https://doi.org/10.1007/s10845-005-7022-7
[3]     Nishi, T., Sekiya, E., & Yin, S. (2012). Distributed optimization of energy portfolio and production planning for multiple companies under resource constraints. Procedia CIRP, 3, 275-280. https://doi.org/10.1016/j.procir.2012.07.048.
[4]     S. Auer, W. Mayrhofer, and W. Sihn, (2012). "Implementation of a comprehensive production planning approach in special purpose vehicle production". Procedia CIRP, 3, 43-48, https://doi.org/10.1016/j.procir.2012.07.009.
[5]     Lai, Y. J., Hwang, C. L., Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming (pp. 74-186). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-48753-8_3
[6]     Kiran, D. R. (2019). Production planning and control: A comprehensive approach. Butterworth-Heinemann. https://www.amazon.com/Production-Planning-Control-Comprehensive-Approach/dp/0128183640
[7]     Nam, S. J., & Logendran, R. (1992). Aggregate production planning—a survey of models and methodologies. European journal of operational research, 61(3), 255-272. https://doi.org/10.1016/0377-2217(92)90356-E
[8]     Wang, R. C., & Fang, H. H. (2001). Aggregate production planning with multiple objectives in a fuzzy environment. European journal of operational research, 133(3), 521-536. https://doi.org/10.1016/S0377-2217(00)00196-X
[9]     Baykasoglu, A., & Gocken, T. (2010). Multi-objective aggregate production planning with fuzzy parameters. Advances in engineering software, 41(9), 1124-1131. https://doi.org/10.1016/j.advengsoft.2010.07.002
[10]   Mirzapour Al-E-Hashem, S. M. J., Malekly, H., & 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(1), 28-42. https://doi.org/10.1016/j.ijpe.2011.01.027
[11]   Lefta, F., Gozali, L., & Marie, I. A. (2020, July). Aggregate and disaggregate production planning, material requirement, and capacity requirement in PT. XYZ. IOP Conference series: Materials science and engineering (Vol. 852, No. 1, p. 012123). IOP Publishing. https://doi.org/10.1088/1757-899X/852/1/012123.
[12]   Barman, S., & Tersine, R. J. (1991). Sensitivity of cost coefficient errors in aggregate production planning. Omega, 19(1), 31-36. https://doi.org/10.1016/0305-0483(91)90031-N
[13]   A. Goli, E. B. Tirkolaee, B. Malmir, G. B. Bian, and A. K. Sangaiah. (2019). "A multi-objective invasive weed optimization algorithm for robust aggregate production planning under uncertain seasonal demand," Computing, 101, 499-529, https://doi.org/10.1007/s00607-018-00692-2.
[14]   Kourentzes, N., Rostami-Tabar, B., & Barrow, D. K. (2017). Demand forecasting by temporal aggregation: Using optimal or multiple aggregation levels?. Journal of business research, 78, 1-9. https://www.sciencedirect.com/science/article/pii/S0148296317301376
[15]   Cheraghalikhani, A., Khoshalhan, F., & Mokhtari, H. (2019). Aggregate production planning: A literature review and future research directions. International journal of industrial engineering computations, 10(2), 309-330. https://doi.org/10.5267/j.ijiec.2018.6.002.
[16]   Cheng, C., & Shafir, E. (2019). Aggregate production planning for engineer-to-order products. Department of supply chain management,1-56. https://B2n.ir/mx5579
[17]   Girkes, F., Reimche, M., Bergmann, J. P., Töpfer-Kerst, C. B., & Berghof, S. (2022, October). Aggregated production planning for engineer-to-order products using reference curves. Congress of the German academic association for production technology (pp. 642-651). Springer International Publishing. https://doi.org/10.1007/978-3-031-18318-8_64
[18]   Holt, C. C., Modigliani, F., & Simon, H. A. (1955). A linear decision rule for production and employment scheduling. Management science, 2(1), 1-30. https://doi.org/10.1287/mnsc.2.1.1
[19]   Saad, G. H. (1982). An overview of production planning models: Structural classification and empirical assessment. The international journal of production research, 20(1), 105-114. https://doi.org/10.1080/00207548208947752
[20]   Kendall, K. E., & Schniederjans, M. J. (1985). Multi-product production planning: A goal programming approach. European journal of operational research, 20(1), 83-91. https://www.sciencedirect.com/science/article/pii/0377221785902863
[21]   Mortezaei, N., Zulkifli, N., & Nilashi, M. (2015). Trade-off analysis for multi-objective aggregate production planning. Journal of soft computing and decision support systems, 2(2), 1-4. http://www.jscdss.com/index.php/files/article/view/29
[22]   Da Silva, C. G., Figueira, J., Lisboa, J., & Barman, S. (2006). An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming. Omega, 34(2), 167-177. https://www.sciencedirect.com/science/article/pii/S0305048304001409
[23]   Leung, S. C., & Chan, S. S. (2009). A goal programming model for aggregate production planning with resource utilization constraint. Computers & industrial engineering, 56(3), 1053-1064. https://www.sciencedirect.com/science/article/pii/S0360835208002301
[24]   Safari, M., Mahdavi, I., Rezaeian, J., & Shirazi, B. (2025). Crowdsourcing-based material requirement optimization in the automotive parts production network with online demand coverage. Journal of decisions and operations research, 10(1), 169-193. https://doi.org/10.22105/dmor.2025.482155.1875.
[25]   Wang, S. C., & Yeh, M. F. (2014). A modified particle swarm optimization for aggregate production planning. Expert systems with applications, 41(6), 3069-3077. https://doi.org/10.1016/j.eswa.2013.10.038
[26] Warfield, J. N. (1974). Structuring complex systems. Battelle Memorial Institute, Columbus, OH. https://www.amazon.com/Structuring-Complex-Systems-John-Warfield/dp/B002DIJNV4
[27]   Charan, P., Shankar, R., & Baisya, R. K. (2008). Analysis of interactions among the variables of supply chain performance measurement system implementation. Business process management journal, 14(4), 512-529. https://doi.org/10.1108/14637150810888055/full/html
[28]   Govindan, K., Kannan, D., Mathiyazhagan, K., Jabbour, A. B. L. D. S., & Jabbour, C. J. C. (2013). Analysing green supply chain management practices in Brazil’s electrical/electronics industry using interpretive structural modelling. International journal of environmental studies, 70(4), 477-493. https://doi.org/10.1080/00207233.2013.798494
[29]   Eslamian Koupaei, M. R., & Shirouyehzad, H. (2023). Identification and evaluate the critical success factors of sustainable supply chain using interpretive structural modeling (Case study: Golnoor Co.). Modern research in performance evaluation, 1(4), 226-243. https://doi.org/10.22105/mrpe.2023.140567.
[30]   Shokr, H., & Afrazeh, A. (2024). Interpretive structural modeling (ISM) of risk management in Iran's construction industry. Innovation management and operational strategies, 5(1), 54-78. https://doi.org/10.22105/imos.2024.453441.1348.
[31]   Abbas, H., Asim, Z., Ahmed, Z., & Moosa, S. (2022). Exploring and establishing the barriers to sustainable humanitarian supply chains using fuzzy interpretive structural modeling and fuzzy MICMAC analysis. Social responsibility journal, 18(8), 1463-1484. https://doi.org/10.1108/SRJ-12-2020-0485
[32]   Faghidian, S. F., & Mahmodi, S. (2024). Evaluation of total quality management enablers using the DEMATEL-ISM integration method in the steel industry. Systemic analytics, 2(1), 14-26. https://doi.org/10.31181/sa2120246
[33]   Khalifa, H. A. E. W., Edalatpanah, S. A., & Bozanic, D. (2023). Enhanced a novel approach for smoothing data in modelling and decision-making problems under fuzziness. Computational algorithms and numerical dimensions, 2(3), 163-172. https://doi.org/10.22105/cand.2023.192505.
[34]   Ragade, R. K. (1976). Fuzzy interpretive structural modeling. Cybernetics and system, 6(3-4), 189-211. https://doi.org/10.1080/01969727608927531
[35]   Wang, L., Ma, L., Wu, K. J., Chiu, A. S., & Nathaphan, S. (2018). Applying fuzzy interpretive structural modeling to evaluate responsible consumption and production under uncertainty. Industrial management & data systems, 118(2), 432-462. https://doi.org/10.1108/IMDS-03-2017-0109
[36]   Ajalli, M., Asgharizadeh, E., Jannatifar, H., & Abbasi, A. (2016). A fuzzy ISM approach for analyzing the implementation obstacles of electronic government in Iran. Science, technology, humanities and business management (ICSTHBM-16), 15. https://B2n.ir/up3519
[37]   Sarma, P. R. S., & Pramod, V. R. (2014). Structural flexibility in supply chains: TISM and FISM approach. In Systemic flexibility and business agility (pp. 305-321). New Delhi: Springer India. https://doi.org/10.1007/978-81-322-2151-7_19
[38]   Tseng, M. L. (2013). Modeling sustainable production indicators with linguistic preferences. Journal of cleaner production, 40, 46-56. https://doi.org/10.1016/j.jclepro.2010.11.019
[39]   Khodadadi-Karimvand, M., & Shirouyehzad, H. (2021). Well drilling fuzzy risk assessment using fuzzy FMEA and fuzzy TOPSIS. Journal of fuzzy extension and applications, 2(2), 144-155. https://doi.org/10.22105/jfea.2021.275955.1086.
[40]   Lee, E. S., & Li, R. J. (1988). Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computers & mathematics with applications, 15(10), 887-896. https://doi.org/10.1016/0898-1221(88)90124-1
[41]   Cheng, C. H. (1999). Evaluating weapon systems using ranking fuzzy numbers. Fuzzy sets and systems, 107(1), 25-35. https://doi.org/10.1016/s0165-0114(97)00348-5 
[42]   Ali, A. R., Albouy-Kissi, A., Vacavant, A., Grand-brochier, M., & Boire, J. Y. (2014). A novel fuzzy c-means based defuzzification approach with an adapted Minkowski distance. 19th computer vision winter workshop Zuzana Kúkelová and Jan Heller (Eds.) KÅ™tiny, Czech Republic. https://cmp.felk.cvut.cz/cvww2014/papers/11/11.pdf
[43]   Das, S. K. (2021). Optimization of fuzzy linear fractional programming problem with fuzzy numbers. Big data and computing visions, 1(1), 30-35. https://doi.org/10.22105/bdcv.2021.142084
[44]   Khalifa, H. A. E. W., Bozanic, D., Najafi, H. S., & Kumar, P. (2024). Solving vendor selection problem by interval approximation of piecewise quadratic fuzzy number. Optimality, 1(1), 23-33. https://doi.org/10.22105/opt.v1i1.23
[45]   Liu, J., Wan, L., Wang, W., Yang, G., Ma, Q., Zhou, H., ... & Lu, F. (2023). Integrated fuzzy DEMATEL-ISM-NK for metro operation safety risk factor analysis and multi-factor risk coupling study. Sustainability, 15(7), 5898. https://doi.org/10.3390/su15075898
[46]   Nishat Faisal, M., Banwet, D. K., & Shankar, R. (2006). Supply chain risk mitigation: Modeling the enablers. Business process management journal, 12(4), 535-552. https://doi.org/10.1108/14637150610678113/full/html
[47]   Attri, R., Dev, N., & Sharma, V. (2013). Interpretive structural modelling (ISM) approach: An overview. Research journal of management sciences, 2319(2), 1171. https://B2n.ir/bh3033
[48]   Krynke, M. (2020). Risk management in the process of personnel allocation to jobs. System safety: Human-technical facility-environment, 2(1), 82-99. https://sciendo.com/pdf/10.2478/czoto-2020-0012
[49]   Vaezi, E., Najafi, S. E., Hajimolana, S. M., Hosseinzadeh Lotfi, F., & Ahadzadeh Namin, M. (2020). Production planning and efficiency evaluation of a three-stage network. Journal of industrial and systems engineering, 13(2), 155-178. https://www.jise.ir/article_118487_0.html
[50]   MacDuffie, J. P., Sethuraman, K., & Fisher, M. L. (1996). Product variety and manufacturing performance: Evidence from the international automotive assembly plant study. Management science, 42(3), 350-369. https://pubsonline.informs.org/doi/abs/10.1287/mnsc.42.3.350
[51]   Hobday, M. (1998). Product complexity, innovation and industrial organisation. Research policy, 26(6), 689-710. https://www.sciencedirect.com/science/article/pii/S0048733397000449
[52]   Orfi, N., Terpenny, J., & Sahin-Sariisik, A. (2011). Harnessing product complexity: Step 1—establishing product complexity dimensions and indicators. The engineering economist, 56(1), 59-79. https://doi.org/10.1080/0013791X.2010.549935
[53]   García-Alcaraz, J. L., Sánchez-Ramírez, C., Avelar-Sosa, L., & Alor-Hernández, G. (Eds.). (2020). Techniques, tools and methodologies applied to global supply chain ecosystems. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-26488-8
[54]   Van den Berge, R., Magnier, L., & Mugge, R. (2021). Too good to go? Consumers’ replacement behaviour and potential strategies for stimulating product retention. Current opinion in psychology, 39, 66-71. https://doi.org/10.1016/j.copsyc.2020.07.014