{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:40:22Z","timestamp":1760240422298,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T00:00:00Z","timestamp":1560124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013099","name":"Scientific Research Fund of Liaoning Provincial Education Department","doi-asserted-by":"publisher","award":["No. L2017LQN030","No. L2017LQN032"],"award-info":[{"award-number":["No. L2017LQN030","No. L2017LQN032"]}],"id":[{"id":"10.13039\/501100013099","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Talent Scientific Research Fund of LSHU","award":["No. 2016XJJ-101","No. 2016XJJ-102"],"award-info":[{"award-number":["No. 2016XJJ-101","No. 2016XJJ-102"]}]},{"name":"Youth Innovation Talent Program by Department of Education of Guangdong Province, China","award":["601821K42050"],"award-info":[{"award-number":["601821K42050"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Production planning and scheduling are important bases for production decisions. Concerning the traditional modeling of production planning and scheduling based on Resource-Task Network (RTN) representation, uncertain factors such as utilities are rarely considered as constraints. For the production planning and scheduling problem based on RTN representation in an uncertain environment, this paper formulates the multi-period bi-level integrated model of planning and scheduling, and introduces the uncertainties of demand and utility in planning and scheduling layers respectively. Rolling horizon optimization strategy is utilized to solve the bi-level integrated model iteratively. The simulation results show that the proposed model and algorithm are feasible and effective, can calculate the consumption of utility in every period, decrease the effects of uncertain factors on optimization results, more accurately describe the uncertain factors, and reflect the actual production process.<\/jats:p>","DOI":"10.3390\/a12060120","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T11:39:47Z","timestamp":1560166787000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Integration of Production Planning and Scheduling Based on RTN Representation under Uncertainties"],"prefix":"10.3390","volume":"12","author":[{"given":"Tao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7726-5267","authenticated-orcid":false,"given":"Yue","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China"},{"name":"National Experimental Teaching Demonstration Center of Petrochemical Process Control, Liaoning Shihua University, Fushun 113001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1904-9424","authenticated-orcid":false,"given":"Xin","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China"},{"name":"National Experimental Teaching Demonstration Center of Petrochemical Process Control, Liaoning Shihua University, Fushun 113001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Intelligence Science and Engineering, Shenzhen Polytechnic, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.compchemeng.2014.02.023","article-title":"Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method","volume":"72","author":"Chu","year":"2015","journal-title":"Comput. Chem. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.3724\/SP.J.1004.2013.01476","article-title":"Solution Strategy of Integrated Optimization of Production Planning and Scheduling in a Flexible Job-shop","volume":"39","author":"An","year":"2013","journal-title":"Acta Autom. Sin."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, W., Ong, S.K., and Nee, A.Y.C. (2007). A Unified Model-based Integration of Process Planning and Scheduling. Process Planning & Scheduling for Distributed Manufacturing, Springer.","DOI":"10.1007\/978-1-84628-752-7_12"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1016\/j.cor.2008.07.006","article-title":"Integration of process planning and scheduling\u2014A modified genetic algorithm-based approach","volume":"36","author":"Shao","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1287\/mnsc.38.8.1201","article-title":"An Integrated Model for Job-Shop Planning and Scheduling","volume":"38","author":"Lasserre","year":"1992","journal-title":"Manag. Sci."},{"key":"ref_6","first-page":"183","article-title":"Integrated production planning and scheduling of multi-stage workshop based on alternant iterative genetic algorithm","volume":"42","author":"Xiong","year":"2012","journal-title":"J. Southeast Univ. (Nat. Sci. Ed.)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1016\/j.compchemeng.2009.11.016","article-title":"Production planning and scheduling integration through augmented Lagrangian optimization","volume":"34","author":"Li","year":"2010","journal-title":"Comput. Chem. Eng."},{"key":"ref_8","first-page":"57","article-title":"Integration of Production Planning and Scheduling under Demand and Utility Uncertainties","volume":"51","author":"Wang","year":"2017","journal-title":"J. Zhejiang Univ. (Eng. Sci.)"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00291-016-0450-2","article-title":"Integrated versus hierarchical approach to aggregate production planning and master production scheduling","volume":"39","author":"Vogel","year":"2017","journal-title":"OR Spectr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"156","DOI":"10.4028\/www.scientific.net\/JERA.39.156","article-title":"New Approach to Integrate Planning and Scheduling of Production System: Heuristic Resolution","volume":"39","author":"Hassani","year":"2018","journal-title":"Int. J. Eng. Res. Afr."},{"key":"ref_11","unstructured":"Pantelides, C.C. (1993, January 18\u201323). Unified Frameworks for the Optimal Process Planning and Scheduling. Proceedings of the Second Conference on the Foundations of Computer Aided Process Operations, Crested Butte, CO, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1016\/0098-1354(95)00186-7","article-title":"The optimal operation of mixed production facilities\u2014A general formulation and some approaches for the solution","volume":"20","author":"Zhang","year":"1996","journal-title":"Comput. Chem. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2059","DOI":"10.1021\/ie000683r","article-title":"An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants","volume":"40","author":"Castro","year":"2001","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1016\/S1004-9541(14)60085-9","article-title":"Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants","volume":"22","author":"Chen","year":"2014","journal-title":"Chin. J. Chem. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"S1221","DOI":"10.1016\/0098-1354(96)00211-6","article-title":"A simple continuous-time process scheduling formulation and a novel solution algorithm","volume":"20","author":"Schilling","year":"1996","journal-title":"Comput. Chem. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"S1061","DOI":"10.1016\/S0098-1354(97)00190-7","article-title":"RTN-based rolling horizon algorithms for medium term scheduling of multipurpose plants","volume":"21","author":"Dimitriadis","year":"1997","journal-title":"Comput. Chem. Eng."},{"key":"ref_17","first-page":"53","article-title":"Distributionally robust optimization for planning and scheduling under uncertainty","volume":"110","author":"Chao","year":"2017","journal-title":"Comput. Chem. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.ijpe.2018.04.012","article-title":"Adaptation and approximate strategies for solving the lot-sizing and scheduling problem under multistage demand uncertainty","volume":"202","author":"Curcio","year":"2018","journal-title":"Int. J. Prod. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/S1570-7946(03)80596-5","article-title":"Optimal production planning under uncertain market conditions","volume":"15","author":"Li","year":"2003","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, Y., Jin, X., Xie, L., Zhang, Y., and Lu, S. (2017). Uncertain Production Scheduling Based on Fuzzy Theory Considering Utility and Production Rate. Information, 8.","DOI":"10.3390\/info8040158"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"777","DOI":"10.4028\/www.scientific.net\/AMR.204-210.777","article-title":"Flow Shop Production Scheduling under Uncertainty within Infinite Intermediate Storage","volume":"204\u2013210","author":"Chen","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1021\/ie010010o","article-title":"Scheduling Parallel Production Lines with Resource Constraints. 1. Model Formulation","volume":"41","author":"Lamba","year":"2002","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/S1570-7946(02)80148-1","article-title":"An MILP framework for short-term scheduling of single-stage batch plants with limited discrete resources","volume":"10","year":"2002","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_24","first-page":"3552","article-title":"Chemical Production Planning and Scheduling Integration under Uncertainty","volume":"65","author":"Tian","year":"2014","journal-title":"J. Chem. Ind."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1023\/A:1018961818782","article-title":"Rolling horizon procedures for the single machine deterministic total completion time scheduling problem with release dates","volume":"70","author":"Chand","year":"1997","journal-title":"Ann. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1021\/ie030529f","article-title":"Risk management in the scheduling of batch plants under uncertain market demand","volume":"43","author":"Bonfill","year":"2004","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/S0952-1976(01)00011-2","article-title":"Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates","volume":"14","author":"Chanas","year":"2001","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4343","DOI":"10.1002\/aic.15792","article-title":"A data-driven multistage adaptive robust optimization framework for planning and scheduling under uncertainty","volume":"63","author":"Ning","year":"2017","journal-title":"AIChE J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.ejor.2006.06.011","article-title":"A robust optimization model for multi-site production planning problem in an uncertain environment","volume":"181","author":"Leung","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.trb.2019.02.013","article-title":"Recoverable robustness in weekly berth and quay crane planning","volume":"122","author":"Iris","year":"2019","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_31","first-page":"97","article-title":"Supply chain planning model under uncertainty","volume":"21","author":"Cheng","year":"2004","journal-title":"Comput. Appl. Chem."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Safaei, A.S., Farsad, S., and Paydar, M.M. (2018). Emergency logistics planning under supply risk and demand uncertainty. Oper. Res., Available online: https:\/\/doi.org\/10.1007\/s12351-018-0376-3.","DOI":"10.1007\/s12351-018-0376-3"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"6192","DOI":"10.1080\/00207543.2016.1162917","article-title":"Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment","volume":"54","author":"Englberger","year":"2016","journal-title":"Int. J. Prod. Res."},{"key":"ref_34","unstructured":"Fajie Wei, R.Z. (2007). Activity-Oriented Production Theory and Cost Theory of Enterprises, Beijing University of Aeronautics and Astronautics Press."},{"key":"ref_35","unstructured":"Wang, Y. (2016). Research on Production Planning and Scheduling under Uncertainty. [Ph.D. Thesis, Zhejiang University]."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Iris, C., and Cevikcan, E. (2014). A fuzzy linear programming approach for aggregate production planning. Supply Chain Management under Fuzziness, Springer.","DOI":"10.1007\/978-3-642-53939-8_15"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1016\/j.fss.2009.11.006","article-title":"Fuzzy hierarchical production planning (with a case study)","volume":"161","author":"Torabi","year":"2010","journal-title":"Fuzzy Sets Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0165-0114(92)90318-X","article-title":"A new approach to some possibilistic linear programming problems","volume":"49","author":"Lai","year":"1992","journal-title":"Fuzzy Sets Syst."},{"key":"ref_39","unstructured":"Basyigit, A., Ulu, C., and Guzelkaya, M. (2014, January 25\u201327). A New Fuzzy Time Series Model Using Triangular and Trapezoidal Membership Functions. Proceedings of the International Work-Conference on Time Series, Granada, Spain."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5887","DOI":"10.1016\/j.ces.2010.08.010","article-title":"Rolling horizon based planning and scheduling integration with production capacity consideration","volume":"65","author":"Li","year":"2010","journal-title":"Chem. Eng. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.1021\/ie970927g","article-title":"Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes","volume":"37","author":"And","year":"1998","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"12630","DOI":"10.1016\/j.eswa.2011.04.051","article-title":"Production capacity planning and scheduling in a no-wait environment with controllable processing times: An integrated modeling approach","volume":"38","author":"Mokhtari","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5589","DOI":"10.1080\/00207540701413912","article-title":"Capacity and material requirement planning modelling by comparing deterministic and fuzzy models","volume":"46","author":"Garciasabater","year":"2008","journal-title":"Int. J. Prod. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1080\/09537280701340631","article-title":"Hierarchical production planning for multi-product lines in the beverage industry","volume":"18","author":"Christou","year":"2007","journal-title":"Prod. Plan. 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