{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T17:08:04Z","timestamp":1776877684396,"version":"3.51.2"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T00:00:00Z","timestamp":1759276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Center for Scientific and Technical Research"},{"name":"Agency for Digital Development"},{"name":"Moroccan Ministry of Higher Education"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Tactical production\u2013distribution planning in paper manufacturing involves hierarchical decision-making under hybrid uncertainty, where aleatory randomness (demand fluctuations, machine variations) and epistemic uncertainty (expert judgments, market trends) simultaneously affect operations. Existing approaches fail to address the bi-level nature under hybrid uncertainty, treating production and distribution decisions independently or using single-paradigm uncertainty models. This research develops a bi-level dependent-chance goal programming framework based on uncertain random theory, where the upper level optimizes distribution decisions while the lower level handles production decisions. The framework exploits structural symmetries through machine interchangeability, symmetric transportation routes, and temporal symmetry, incorporating symmetry-breaking constraints to eliminate redundant solutions. A hybrid intelligent algorithm (HIA) integrates uncertain random simulation with a Reinforcement-Learning-enhanced Arithmetic Optimization Algorithm (RL-AOA) for bi-level coordination, where Q-learning enables adaptive parameter tuning. The RL component utilizes symmetric state representations to maintain solution quality across symmetric transformations. Computational experiments demonstrate HIA\u2019s superiority over standard metaheuristics, achieving 3.2\u20137.8% solution quality improvement and 18.5% computational time reduction. Symmetry exploitation reduces search space by approximately 35%. The framework provides probability-based performance metrics with optimal confidence levels (0.82\u20130.87), offering 2.8\u20134.5% annual cost savings potential.<\/jats:p>","DOI":"10.3390\/sym17101624","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T07:58:13Z","timestamp":1759305493000},"page":"1624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bi-Level Dependent-Chance Goal Programming for Paper Manufacturing Tactical Planning: A Reinforcement-Learning-Enhanced Approach"],"prefix":"10.3390","volume":"17","author":[{"given":"Yassine","family":"Boutmir","sequence":"first","affiliation":[{"name":"Laboratory of Engineering Sciences, Department of Informatics, Logistics and Mathematics, National School of Applied Sciences, Ibn Tofa\u00efl University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2628-1608","authenticated-orcid":false,"given":"Rachid","family":"Bannari","sequence":"additional","affiliation":[{"name":"Laboratory of Engineering Sciences, Department of Informatics, Logistics and Mathematics, National School of Applied Sciences, Ibn Tofa\u00efl University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3286-8747","authenticated-orcid":false,"given":"Abdelfettah","family":"Bannari","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Sultan Moulay Slimane University, Beni Mellal 23000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naoufal","family":"Rouky","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Techniques, Hassan 1st University, Settat 26000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7864-6886","authenticated-orcid":false,"given":"Othmane","family":"Benmoussa","sequence":"additional","affiliation":[{"name":"Euromed University of Fes, UEMF, Fes 30000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0882-4402","authenticated-orcid":false,"given":"Fay\u00e7al","family":"Fedouaki","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, National Higher School of Arts and Professions, University Hassan 2nd of Casablanca, 150 Avenue Nil, Casablanca 20670, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/S0377-2217(99)00332-X","article-title":"Decentralized inventory control in a two-level distribution system","volume":"127","author":"Andersson","year":"2000","journal-title":"Eur. 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