{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:54:38Z","timestamp":1769820878778,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T00:00:00Z","timestamp":1664236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems.<\/jats:p>","DOI":"10.3390\/axioms11100510","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T21:23:27Z","timestamp":1664313807000},"page":"510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Development of Integrated Linear Programming Fuzzy-Rough MCDM Model for Production Optimization"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1478-8367","authenticated-orcid":false,"given":"Milan","family":"Dordevic","sequence":"first","affiliation":[{"name":"Higher Colleges of Technology Sharjah, University City, Sharjah P.O. Box 7947, United Arab Emirates"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8272-9804","authenticated-orcid":false,"given":"Rade","family":"Te\u0161i\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Economics, PIM University, Despota Stefana Lazarevi\u0107a bb, 78000 Banja Luka, Bosnia and Herzegovina"}]},{"given":"Srdjan","family":"Todorovi\u0107","sequence":"additional","affiliation":[{"name":"Environmental Protection and Energy Efficiency Fund of Republic of Srpska, King Alfonso XIII Number 21, 78000 Banja Luka, Bosnia and Herzegovina"}]},{"given":"Milo\u0161","family":"Joki\u0107","sequence":"additional","affiliation":[{"name":"Ministry of Spatial Planning, Construction and Ecology of the Republic of Srpska, Trg Republike Srpske, 78000 Banja Luka, Bosnia and Herzegovina"}]},{"given":"Dillip Kumar","family":"Das","sequence":"additional","affiliation":[{"name":"Sustainable Transportation Research Group, Civil Engineering, School of Engineering, University of Kwazulu Natal, Durban 4041, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4452-5768","authenticated-orcid":false,"given":"\u017deljko","family":"Stevi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Transport and Traffic Engineering, University of East Sarajevo, Vojvode Mi\u0161i\u0107a 52, 74000 Doboj, Bosnia and Herzegovina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5013-3878","authenticated-orcid":false,"given":"Sabahudin","family":"Vrtagic","sequence":"additional","affiliation":[{"name":"College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bay\u00e1, G., Canale, E., Nesmachnow, S., Robledo, F., and Sartor, P. (2022). Production Optimization in a Grain Facility through Mixed-Integer Linear Programming. Appl. Sci., 12.","DOI":"10.3390\/app12168212"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chandrawat, R.K., Kumar, R., Garg, B.P., Dhiman, G., and Kumar, S. (2017). An analysis of modeling and optimization production cost through fuzzy linear programming problem with symmetric and right angle triangular fuzzy number. Proceedings of the Sixth International Conference on Soft Computing for Problem Solving, Springer.","DOI":"10.1007\/978-981-10-3322-3_18"},{"key":"ref_3","first-page":"199","article-title":"The Impact of Innovation on the Management of Misapplication of Change in the Production System in the Automotive Industry","volume":"10","author":"Pop","year":"2022","journal-title":"Econ. Innov. Econ. Res. J."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lazzerini, B., and Pistolesi, F. (2015, January 10\u201311). A linear programming-driven MCDM approach for multi-objective economic dispatch in smart grids. Proceedings of the 2015 SAI Intelligent Systems Conference (IntelliSys), London, UK.","DOI":"10.1109\/IntelliSys.2015.7361183"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1108\/JM2-12-2019-0285","article-title":"Hybrid fuzzy MCDM and FMEA integrating with linear programming approach for the health and safety executive risks: A case study","volume":"16","author":"Khalilzadeh","year":"2021","journal-title":"J. Model. Manag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10479-017-2566-4","article-title":"Integrated grey relational analysis and multi objective grey linear programming for sustainable electricity generation planning","volume":"269","author":"Malekpoor","year":"2018","journal-title":"Ann. Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"130297","DOI":"10.1016\/j.jclepro.2021.130297","article-title":"Integrated linear programming and analytical hierarchy process method for diesel\/biodiesel\/butanol in reducing diesel emissions","volume":"337","author":"Razak","year":"2022","journal-title":"J. Clean. Prod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/S0952-1976(03)00069-1","article-title":"An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management","volume":"16","author":"Cheng","year":"2003","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.jclepro.2013.02.010","article-title":"Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain","volume":"47","author":"Kannan","year":"2013","journal-title":"J. Clean. Prod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.jfranklin.2008.03.005","article-title":"An integrated group decision-making process for supplier selection and order allocation using multi-attribute utility theory and linear programming","volume":"345","author":"Sanayei","year":"2008","journal-title":"J. Frankl. Inst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Stoji\u0107, G., Stevi\u0107, \u017d., Antuchevi\u010dien\u0117, J., Pamu\u010dar, D., and Vasiljevi\u0107, M. (2018). A novel rough WASPAS approach for supplier selection in a company manufacturing PVC carpentry products. Information, 9.","DOI":"10.3390\/info9050121"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"34","DOI":"10.31181\/rme200101034c","article-title":"Sustainable supplier selection using combined FUCOM\u2013Rough SAW model","volume":"1","author":"Chatterjee","year":"2020","journal-title":"Rep. Mech. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.24846\/v27i4y201802","article-title":"A novel rough range of value method (R-ROV) for selecting automatically guided vehicles (AGVs)","volume":"27","author":"Zavadskas","year":"2018","journal-title":"Stud. Inform. Control"},{"key":"ref_14","first-page":"1","article-title":"A Novel Integrated Fuzzy-Rough MCDM Model for Evaluation of Companies for Transport of Dangerous Goods","volume":"2021","author":"Sremac","year":"2021","journal-title":"Complexity"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kumar, S., Maity, S.R., and Patnaik, L. (2022). Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques. Oper. Res. Eng. Sci. Theory Appl.","DOI":"10.31181\/110722105k"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., and Urbaniak, K. (2020, January 3\u20135). A new coefficient of rankings similarity in decision-making problems. Proceedings of the International Conference on Computational Science, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-030-50417-5_47"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Vrtagi\u0107, S., Softi\u0107, E., Suboti\u0107, M., Stevi\u0107, \u017d., Dordevic, M., and Ponjavic, M. (2021). Ranking road sections based on MCDM model: New improved fuzzy SWARA (IMF SWARA). Axioms, 10.","DOI":"10.3390\/axioms10020092"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.3846\/tede.2021.16004","article-title":"Evaluating logistics villages in Turkey using hybrid improved fuzzy SWARA (IMF SWARA) and fuzzy MABAC techniques","volume":"27","author":"Zolfani","year":"2021","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Pu\u0161ka, A., Bo\u017eani\u0107, D., Nedeljkovi\u0107, M., and Jano\u0161evi\u0107, M. (2022). Green Supplier Selection in an Uncertain Environment in Agriculture Using a Hybrid MCDM Model: Z-Numbers\u2013Fuzzy LMAW\u2013Fuzzy CRADIS Model. Axioms, 11.","DOI":"10.3390\/axioms11090427"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"11195","DOI":"10.1007\/s10668-021-01902-2","article-title":"Evaluation and selection of healthcare waste incinerators using extended sustainability criteria and multi-criteria analysis methods","volume":"24","year":"2022","journal-title":"Environ. Dev. Sustain."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Pu\u0161ka, A., Nedeljkovi\u0107, M., Prodanovi\u0107, R., Vladisavljevi\u0107, R., and Suzi\u0107, R. (2022). Market assessment of pear varieties in Serbia using fuzzy CRADIS and CRITIC methods. Agriculture, 12.","DOI":"10.3390\/agriculture12020139"},{"key":"ref_22","first-page":"447","article-title":"D numbers\u2013FUCOM\u2013fuzzy RAFSI model for selecting the group of construction machines for enabling mobility","volume":"19","author":"Salabun","year":"2021","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_23","first-page":"13","article-title":"Hybrid MCDM solutions for evaluation of the logistics performance index of the Western Balkan countries","volume":"10","author":"Mastilo","year":"2022","journal-title":"Econ.-Innov. Econ. Res. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102712","DOI":"10.1016\/j.scs.2021.102712","article-title":"Landfill location selection for healthcare waste of urban areas using hybrid BWM-grey MARCOS model based on GIS","volume":"67","author":"Torkayesh","year":"2021","journal-title":"Sustain. Cities Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"169","DOI":"10.31181\/dmame211221075g","article-title":"Supplier selection by integrated IFDEMATEL-IFTOPSIS Method: A case study of automotive supply industry","volume":"5","author":"Gergin","year":"2022","journal-title":"Decis. Mak. Appl. Manag. Eng."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/10\/510\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:40:47Z","timestamp":1760143247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/10\/510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,27]]},"references-count":25,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["axioms11100510"],"URL":"https:\/\/doi.org\/10.3390\/axioms11100510","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,27]]}}}