Authors:
Iftikhar Ali Hussein,Hagazy Zahar,Naglaa Ragaa Saied,Rabie Mosaad Rabie,DOI NO:
https://doi.org/10.26782/jmcms.2025.10.00007Keywords:
De Novo programming,Multi-objective linear programming,Resource allocation,Rough Interval,Tong-Shaoching method,Zeleny Approach,Optimal path-ratios.,Abstract
Multi-objective Linear Programming (MOLP) traditionally optimizes multiple conflicting objectives simultaneously. This research extends the De Novo Programming (DNP) concept, which focuses on optimal system design, to situations with uncertainty in resource allocation and budget constraints. A novel mathematical model, Rough Interval Multi-Objective De Novo Programming (RIMODNP), has been introduced. This model incorporates the Rough Interval (RI) concept, where all problem coefficients are represented by lower and upper interval bounds, each having two terms (upper and lower). The study outlines the mathematical formulation of the RIMODNP model, detailing the methodology used to transform its uncertain nature into deterministic sub-problems. It presents two primary approaches, Zeleny's and the Optimum-Path Ratio Method, for finding optimal designs. Applied to the Baghdad Water Department, the model optimizes resource allocation for increased water production, improved water quality, and reduced water loss while considering unknown constraints. The results, obtained by solving the deterministic sub-problems, provide the decision-maker with a range of optimal system designs. The application to the Baghdad Water Department shows significant increases in profit and cost savings across different scenarios, highlighting the model's ability to offer robust and effective solutions under conditions of uncertainty.Refference:
I. A. Hamzehee, A. Yaghoobi, and M. Mashinchi, “Linear programming with rough interval coefficients,” J. Intell. Fuzzy Syst., vol. 26, pp. 1179–1189, 2014. 10.3233/IFS-130804.
II. C. Sen, “Sen’s Multi-Objective Optimization (MOO) technique – A review,” Int. J. Mod. Trends Sci. Technol., vol. 6, no. 9, pp. 208–210, 2020. 10.46501/IJMTST060931.
III. H. M. Saad and M. J. Mhawes, “The relationship and impact of the external auditor’s fees on audit quality of financial statements,” Tech. J. Manag. Sci., vol. 2, no. 1, 2025.
IV. I. A. Hussein, H. Zaher, N. Saeid, and H. Roshdy, “A multi-objective de novo programming models: A review,” Int. J. Prof. Bus. Rev., vol. 9, no. 1, pp. 1–22, 2024. 10.26668/businessreview/2023.v9i1.4180 .
V. I. A. Hussein, H. Zaher, N. Saeid, and H. Roshdy, “Optimum system design using rough interval multi-objective de novo programming,” Baghdad Sci. J., vol. 20, no. 4, p. 8740, 2023. 10.21123/bsj.2023.8740.
VI. J. Chen, T. Du, and G. Xiao, “A multi-objective optimization for resource allocation of emergent demands in cloud computing,” J. Cloud Comput., vol. 10, no. 20, pp. 1–17, 2021. 10.1186/s13677-021-00237-7.
VII. M. Allahdadi and M. Nehi, “The optimal value bounds of the objective function in the interval linear programming problem,” Chiang Mai J. Sci., vol. 42, no. 2, pp. 501–511, 2015.
VIII. M. M. Luhandjula and P. Pandian, “A new method for finding an optimal solution of interval integer transportation problems,” Appl. Math. Sci., vol. 4, no. 37, pp. 1819–1830, 2010.
IX. M. Zeleny, “Multiple criteria decision making (MCDM): From paradigm lost to paradigm regained?,” J. Multiple Criteria Decis. Anal., vol. 18, pp. 77–89, 2011. 10.1002/mcda.473.
X. N. K. Bisuiki, S. Mazumader, and G. A. Panda, “Gradient-free method for multi-objective optimization problem,” in Optimization, Variational Analysis and Applications, vol. 355, 2020, pp. 19–34. 10.1007/978-981-16-1819-2_2.
XI. T. Shaocheng, “Interval number and fuzzy number linear programming,” Fuzzy Sets Syst., vol. 66, no. 3, pp. 301–306, 1994. 10.1016/0165-0114(94)90097-3.
XII. W. C. Lo, C. H. Lu, and Y. C. Chou, “Application of multi-criteria decision making and multi-objective planning methods for evaluating metropolitan parks in terms of budget and benefits,” Mathematics, vol. 8, no. 8, pp. 1–17, 2020. 10.3390/math8081304.
XIII. Y. H. Hasan Al-Karawi and H. Ghodrati, “The effect of the source of commitment and ethical style of auditors on independent auditors’ whistle-blowing,” Tech. J. Manag. Sci., vol. 1, no. 1, 2024.
XIV. Y. Shi, “Studies on optimum-path ratios in multi-criteria de novo programming problems,” Comput. Math. Appl., vol. 29, no. 5, pp. 43–50, 1995. 10.1016/0898-1221(94)00247-I.
XV. Z. Y. Zhuang and A. Hocine, “Meta goal programing approach for solving multi-criteria de novo programing problem,” Eur. J. Oper. Res., vol. 265, no. 1, pp. 228–238, 2018. doi: 10.1016/j.ejor.2017.07.035.