{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T21:15:33Z","timestamp":1778793333010,"version":"3.51.4"},"reference-count":15,"publisher":"Emerald","issue":"5\/6","license":[{"start":{"date-parts":[[2011,6,14]],"date-time":"2011-06-14T00:00:00Z","timestamp":1308009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,6,14]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to set up a two\u2010stage stochastic integer\u2010programming model (TSM) for the multiperiod scheduling of multiproduct batch plants under demand uncertainty involving the constraints of material balances and inventory constraints, as well as the penalty for production shortfalls and excess.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Scheduling model is formulated as a discrete\u2010time State Task Network. Given a scheduling horizon consisting of several time\u2010periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit for a single and multiple product with a given probability level. The stochastic elements of the model are expressed with equivalent deterministic optimization models.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The TSM model not only allows for uncertain product demand correlations, but also gives different processing modes by a range of batch sizes and a task\u2010dependent processing time. The experimental results show that the TSM model is more appropriate than another model for multiperiod scheduling of multiproduct batch plants under correlated uncertain demand.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>The choice of penalty parameter of demand uncertainty is the main limitation.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The paper provides very useful advice for multiperiod scheduling of multiproduct batch plants under demand uncertainty.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>A stochastic model for the multiperiod scheduling of multiproduct batch plants under demand uncertainty was set up. A test problem involving 12 correlated uncertain product demands and two alternative models verified the availability of the TSM.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684921111142421","type":"journal-article","created":{"date-parts":[[2011,7,30]],"date-time":"2011-07-30T07:05:48Z","timestamp":1312009548000},"page":"871-882","source":"Crossref","is-referenced-by-count":7,"title":["Optimal multiperiod scheduling of multiproduct batch plants under demand uncertainty"],"prefix":"10.1108","volume":"40","author":[{"given":"Jin","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingsheng","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2022031520322373600_b12","unstructured":"Balasubramanian, J. (2003), \u201cOptimization models and algorithms for batch process scheduling under uncertainty\u201d, PhD dissertation, Carnegie Mellon University, Pittsburgh, PA, pp. 198\u20109."},{"key":"key2022031520322373600_b15","doi-asserted-by":"crossref","unstructured":"Lin, Y. (1998), \u201cDiscontinuity: a weakness of calculus and beginning of a new era\u201d, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 27 Nos 6\/7, pp. 614\u201018.","DOI":"10.1108\/03684929810223021"},{"key":"key2022031520322373600_b2","doi-asserted-by":"crossref","unstructured":"Liu, M.L. and Sahinidis, N.V. (1996), \u201cOptimization of process planning under uncertainty\u201d, Industrial & Engineering Chemistry Research, Vol. 35, pp. 4154\u201068.","DOI":"10.1021\/ie9504516"},{"key":"key2022031520322373600_b14","doi-asserted-by":"crossref","unstructured":"OuYang, S.C., Lin, Y. and Wu, Y. (2000), \u201cPrediction of natural disasters\u201d, International Journal of General Systems, Vol. 29, pp. 897\u2010912.","DOI":"10.1080\/03081070008960978"},{"key":"key2022031520322373600_b13","doi-asserted-by":"crossref","unstructured":"OuYang, S.C., Lin, Y., Wang, Z. and Peng, T.Y. (2001), \u201cEvolution science and infrastructural analysis of the second stir\u201d, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 30 No. 4, pp. 463\u201079.","DOI":"10.1108\/03684920110386964"},{"key":"key2022031520322373600_b10","unstructured":"Petkov, S.V. and Maranas, C.D. (1998), \u201cMultiperiod planning and scheduling of multiproduct batch plants under demand uncertainty\u201d, American Institute of Chemical Engineers Journal, Vol. 44, pp. 896\u2010931."},{"key":"key2022031520322373600_b3","unstructured":"Reinhart, H.J. and Rippin, D.W.T. (1986), \u201cThe design of flexible batch plants\u201d, AIChE Annual Meeting, New Orleans, LA, pp. 89\u2010101."},{"key":"key2022031520322373600_b7","unstructured":"Ren, Y.H., Yuan, X.H. and Xia, Z.Q. (2004), \u201cOptimization problems with fuzzy relation inequality constraints\u201d, Advances in Systems Science and Applications, Vol. 4 No. 1, pp. 75\u201082."},{"key":"key2022031520322373600_b4","doi-asserted-by":"crossref","unstructured":"Shah, N. and Pantelides, C.C. (1992), \u201cDesign of multipurpose batch plants with uncertain production requirements\u201d, Industrial & Engineering Chemistry Research, Vol. 31, pp. 1325\u201031.","DOI":"10.1021\/ie00005a013"},{"key":"key2022031520322373600_b11","doi-asserted-by":"crossref","unstructured":"Spas, B.P. and Costas, D.M. (1997), \u201cMultiperiod planning and scheduling of multiproduct batch plants under demand uncertainty\u201d, Industrial & Engineering Chemistry Research, Vol. 36, pp. 4864\u201081.","DOI":"10.1021\/ie970259z"},{"key":"key2022031520322373600_b1","doi-asserted-by":"crossref","unstructured":"Subrahmanyam, S., Pekny, J.F. and Reklaitis, G.V. (1994), \u201cDesign of batch chemical plants under market uncertainty\u201d, Industrial & Engineering Chemistry Research, Vol. 33, pp. 2688\u201097.","DOI":"10.1021\/ie00035a019"},{"key":"key2022031520322373600_b5","doi-asserted-by":"crossref","unstructured":"Xia, D.C. and Qin, X.Z. (2002), \u201cPrototyped genetic search: a cybernetical approach to job\u2010shop scheduling problems\u201d, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 31 No. 1, pp. 96\u2010114.","DOI":"10.1108\/03684920210413782"},{"key":"key2022031520322373600_b8","unstructured":"Xia, D.C. and Qin, X.Z. (2005), \u201cA heuristic stochastic method in dynamic system modeling using NN\u201d, Advances in Systems Science and Applications, Vol. 5 No. 3, pp. 502\u20106."},{"key":"key2022031520322373600_b9","doi-asserted-by":"crossref","unstructured":"Yang, W.H. and Liao, C.J. (1999), \u201cSurvey of scheduling research involving setup times\u201d, International Journal of Systems Science, Vol. 30 No. 2, pp. 143\u201055.","DOI":"10.1080\/002077299292498"},{"key":"key2022031520322373600_b6","unstructured":"Zhu, W.F. and Qi, F. (2004), \u201cComplex logistics simulation with uncertain customer demand\u201d, Advances in Systems Science and Applications, Vol. 4 No. 2, pp. 238\u201044."}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684921111142421","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684921111142421\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684921111142421\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:27:17Z","timestamp":1753399637000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/40\/5-6\/871-882\/447020"}},"subtitle":[],"editor":[{"given":"Yi","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,6,14]]},"references-count":15,"journal-issue":{"issue":"5\/6","published-print":{"date-parts":[[2011,6,14]]}},"alternative-id":["10.1108\/03684921111142421"],"URL":"https:\/\/doi.org\/10.1108\/03684921111142421","relation":{},"ISSN":["0368-492X"],"issn-type":[{"value":"0368-492X","type":"print"}],"subject":[],"published":{"date-parts":[[2011,6,14]]}}}