Multi-objective optimization of production: A case study on simplex, goal programming, and pareto front models

محورهای موضوعی :

Astrid Putri ¹ , Mochamad Hariadi ² , Reza Rachmadi ³

1 - Department of Electrical Engineering, Department of Computer Engineering Institut Teknologi Sepuluh Nopember Surabaya, Indonesia
2 - Department of Electrical Engineering, Department of Computer Engineering Institut Teknologi Sepuluh Nopember Surabaya, Indonesia
3 - Department of Electrical Engineering, Department of Computer Engineering, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia

تاریخ دریافت : 1402/02/20 تاریخ پذیرش : 1402/04/18 تاریخ انتشار : 1403/06/11

کلید واژه: Goal programming, Multi-objective, Simplex, Pareto front, Optimization production,

چکیده مقاله :

Farmers are the essential factor in the productivity chain. However, they can also be the weakest one since the distribution chain of sales transactions took a long way in Indonesia, involving farmers, collectors, wholesalers, retailers in traditional markets, and consumers. It makes consumers buy an agricultural product at a high price from farmers' uncertain stock. A distribution chain needs an optimization model involving good decision-making from organizations or governments in planning, production, warehouse, and transportation. Simulation-based optimization aims to provide adequate stock for consumers' needs and farmers' profits to minimize production costs. The Proposed Framework Integrated Three Methods is Optimization Simplex using POM QM, Optimization Goal Programming Using POM QM, Pareto Front using Phyton based and publicly available via github.This research focuses on optimization using the simplex method to fulfil the objective function with a maximum limit of more than one variable as the parameters: market demand, stock, harvest season, and price. It is also necessary to do re-optimization using goal programming to minimize the achievement deviation of the goal function and Pareto front as a model of optimizing the solution of multiple problems or Multi-Objective Optimization using linear programming. It is the development of the previous research which aims at finding the answer to the product optimization problem by cutting the distribution channel into four; farmers sell products to KUD (Cooperatives Village Unit), and KUD holds buying and selling process between farmers. Consumers and distributors sell products to consumers, and consumers purchase the product from KUD. The research shows the optimization results of the average price are up to 8913060, and the middle market hole is up to 17741000.

چکیده انگلیسی:

Farmers are the essential factor in the productivity chain. However, they can also be the weakest one since the distribution chain of sales transactions took a long way in Indonesia, involving farmers, collectors, wholesalers, retailers in traditional markets, and consumers. It makes consumers buy an agricultural product at a high price from farmers' uncertain stock. A distribution chain needs an optimization model involving good decision-making from organizations or governments in planning, production, warehouse, and transportation. Simulation-based optimization aims to provide adequate stock for consumers' needs and farmers' profits to minimize production costs. The Proposed Framework Integrated Three Methods is Optimization Simplex using POM QM, Optimization Goal Programming Using POM QM, Pareto Front using Phyton based and publicly available via github.This research focuses on optimization using the simplex method to fulfil the objective function with a maximum limit of more than one variable as the parameters: market demand, stock, harvest season, and price. It is also necessary to do re-optimization using goal programming to minimize the achievement deviation of the goal function and Pareto front as a model of optimizing the solution of multiple problems or Multi-Objective Optimization using linear programming. It is the development of the previous research which aims at finding the answer to the product optimization problem by cutting the distribution channel into four; farmers sell products to KUD (Cooperatives Village Unit), and KUD holds buying and selling process between farmers. Consumers and distributors sell products to consumers, and consumers purchase the product from KUD. The research shows the optimization results of the average price are up to 8913060, and the middle market hole is up to 17741000.

منابع و مأخذ:

Adisusilo, A. K. et al. (2020) ‘Optimizing player engagement in an immersive serious game for soil tillage base on Pareto optimal strategies’, Heliyon, 6(3), p. e03613. doi: 10.1016/J.HELIYON.2020.E03613.
Aouam, T., Research, N. B.-E. J. of O. and 2013, undefined (no date) ‘Integrated production planning and order acceptance under uncertainty: A robust optimization approach’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S0377221713001288 (Accessed: 20 March 2023).
Aouni, B., computation, D. L. T.-A. mathematics and and 2010, undefined (no date) ‘A generalized stochastic goal programming model’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S0096300310000032 (Accessed: 3 April 2023).
Chavan, S., Engineering, A. S.-J. of O. in I. and 2019, undefined (no date) ‘Fixture Design and Work Piece Deformation Optimization Using the Iterative Simplex Algorithm’, qjie.ir. Available at: http://www.qjie.ir/article_545833_27fbb82a51b75d689768672143fcd3a0.pdf (Accessed: 12 April 2023).
Daud, A. et al. (no date) ‘Risks in milk supply chain; a preliminary analysis on smallholder dairy production’, researchgate.net. Available at: https://www.researchgate.net/profile/Mursyid-Basri/publication/342715956_Risks_in_milk_supply_chain_a_preliminary_analysis_on_smallholder_dairy_production/links/5f1d457892851cd5fa489447/Risks-in-milk-supply-chain-a-preliminary-analysis-on-smallholder-dairy-production.pdf (Accessed: 30 March 2023).
Davtalab-Olyaie, M., Operational, M. A.-E. J. of and 2021, undefined (no date) ‘On Pareto-optimality in the cross-efficiency evaluation’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S0377221720304860 (Accessed: 20 March 2023).
EDITION, T. (2012) ‘INTRODUCTION TO OPTIMUM DESIGN’. Available at: http://ndl.ethernet.edu.et/bitstream/123456789/61787/1/1148.pdf (Accessed: 3 April 2023).
Gunantara, N.(2018).Teknik Optimasi - Google Scholar (no date). Available at: https://scholar.google.co.id/scholar?hl=id&as_sdt=0%2C5&q=Gunantara%2C+N.%282018%29.Teknik+Optimasi&btnG= (Accessed: 3 April 2023).
Hamta, N., Ehsanifar, M. and Sarikhani, J. (2021) ‘Presenting a goal programming model in the time-cost-quality trade-off’, International Journal of Construction Management, 21(1), pp. 1–11. doi: 10.1080/15623599.2018.1502930.
Inayati, S., Integratif, R. R.-J. M. and 2020, undefined (no date) ‘Penyelesaian Masalah Optimisasi Multiobjektif Nonlinear Menggunakan Pendekatan Pareto Front dalam Metode Pembobotan’, journal.unpad.ac.id. Available at: http://journal.unpad.ac.id/jmi/article/view/29278 (Accessed: 3 April 2023).
Ishigaki, A., Management, Y. H.-J. of J. I. and 2016, undefined (no date) ‘Two-objective Optimization for a Supply Chain Network using the Simplex Method’, jstage.jst.go.jp. Available at: https://www.jstage.jst.go.jp/article/jima/67/2E/67_147/_article/-char/ja/ (Accessed: 3 April 2023).
Jain, S., Ramesh, D. and Bhattacharya, D. (2021) ‘A multi-objective algorithm for crop pattern optimization in agriculture’, Applied Soft Computing, 112, p. 107772. doi: 10.1016/J.ASOC.2021.107772.
Jones, D. and Tamiz, M. (2016) ‘A review of goal programming’, International Series in Operations Research and Management Science, 233, pp. 903–926. doi: 10.1007/978-1-4939-3094-4_21.
Margolis, J. T. et al. (2018) ‘A multi-objective optimization model for designing resilient supply chain networks’, International Journal of Production Economics, 204, pp. 174–185. doi: 10.1016/J.IJPE.2018.06.008.
Multiobjective optimization and advanced topics.... - Google Scholar (no date). Available at: https://scholar.google.co.id/scholar?hl=id&as_sdt=0%2C5&q=Multiobjective+optimization+and+advanced+topics.+Design+Theory+and+Methods+Using+CAD%2FCAE&btnG= (Accessed: 3 April 2023).
Parreño-Marchante, A., … A. A.-M.-J. of food and 2014, undefined (no date) ‘Advanced traceability system in aquaculture supply chain’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S0260877413004597 (Accessed: 3 April 2023).
Perberasan, P. K. et al. (no date) ‘Pengaruh Kebijakan Perberasan, Pertumbuhan Ekonomi dan Kebijakan Fiskal terhadap Kemiskinan di Indonesia’, jurnal.unismabekasi.ac.id. Available at: https://jurnal.unismabekasi.ac.id/index.php/optimal/article/download/1850/1590 (Accessed: 30 March 2023).
Purnomo, H. et al. (no date) ‘Fire economy and actor network of forest and land fires in Indonesia’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S1389934117300023 (Accessed: 30 March 2023).
Rajak, S. et al. (2022) ‘Multi-objective mixed-integer linear optimization model for sustainable closed-loop supply chain network: a case study on remanufacturing steering column’, Environment, Development and Sustainability, 24(5), pp. 6481–6507. doi: 10.1007/S10668-021-01713-5.
Sarker, R. and Ray, T. (2009) ‘An improved evolutionary algorithm for solving multi-objective crop planning models’, Computers and Electronics in Agriculture, 68(2), pp. 191–199. doi: 10.1016/J.COMPAG.2009.06.002.
Selim, H. et al. (no date) ‘Collaborative production–distribution planning in supply chain: a fuzzy goal programming approach’, Elsevier. Available at: https://www.sciencedirect.com/science/article/pii/S1366554506000998 (Accessed: 20 March 2023).
Seren, K., Scientific, M. T.-T. J. of I. and 2019, undefined (no date) ‘Blockchain technology in supply chain’, dergipark.org.tr. Available at: https://dergipark.org.tr/en/pub/isrjournal/article/542536 (Accessed: 3 April 2023).
Soykan, B. and Rabadi, G. (2022) ‘A simulation-based optimization approach for multi-objective runway operations scheduling’, Simulation, 98(11), pp. 991–1012. doi: 10.1177/00375497221099544.
Susanawati et al. (2021) ‘Supply chain efficiency of red chili based on the performance measurement system in Yogyakarta, Indonesia’, Open Agriculture, 6(1), pp. 202–211. doi: 10.1515/OPAG-2021-0224/HTML.
Thakur, M., Wang, L. and Hurburgh, C. R. (2010) ‘A multi-objective optimization approach to balancing cost and traceability in bulk grain handling’, Journal of Food Engineering, 101(2), pp. 193–200. doi: 10.1016/J.JFOODENG.2010.07.001.