{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T05:57:57Z","timestamp":1787637477621,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,5]]},"abstract":"\n A bicriterion problem of scheduling jobs on a single machine is studied. The processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job. A solution is specified by a sequence of the jobs and a resource allocation. The quality of a solution is measured by two criteria, F\n 1<\/jats:sub>\n and F\n 2<\/jats:sub>\n . The first criterion is the maximal or total (weighted) resource consumption, and the second criterion is a regular scheduling criterion depending on the job completion times. Both criteria have to be minimized. General schemes for the construction of the Pareto set and the Pareto set $\\epsilon$-approximation are presented. Computational complexities of problems to minimize F\n 1<\/jats:sub>\n subject to F_2\\le K$ and to minimize F\n 2<\/jats:sub>\n subject to $F_1\\le K$, where K is any number, are studied for various functions F\n 1<\/jats:sub>\n and F\n 2<\/jats:sub>\n . Algorithms for solving these problems and for the construction of the Pareto set and the Pareto set $\\epsilon$-approximation for the corresponding bicriterion problems are presented.\n <\/jats:p>","DOI":"10.1137\/s1052623495288192","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"617-630","source":"Crossref","is-referenced-by-count":74,"title":["Bicriterion Single Machine Scheduling with Resource Dependent Processing Times"],"prefix":"10.1137","volume":"8","author":[{"given":"T. C. Edwin","family":"Cheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adam","family":"Janiak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail Y.","family":"Kovalyov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"T. C. E. Cheng and Z.\u2010L. Chen,\n Single\u2010Machine Scheduling to Minimize the Sum of Compression and Late Costs\n , Working paper, Department of Management, Hong Kong Polytechnic, Hong Kong, 1994."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(96)00035-1"},{"key":"R3","unstructured":"M. R. Garey and D. S. Johnson,\n Computers and Intractability: A Guide of the Theory of NP\u2010Completeness\n , W. H. 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Kovalyov,\n Single Machine Scheduling with Deadlines and Resource Dependent Processing Times\n , Working paper, Institute of Engineering Cybernetics, Technical University of Wroclaw, Wroclaw, Poland, 1993."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.19.5.544"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(82)90022-0"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.16.1.77"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"C.\u2010Y. Lee and G. Vairaktarakis,\n Single machine dual criteria scheduling: A survey\n , in Complexity in Numerical Optimization, P. M. 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Williams,\n Analysis and Design of Hierarhical Control Systems with Special Reference to Steel Plant Operations\n , North\u2013Holland, Amsterdam, 1985."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623495288192","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:18:29Z","timestamp":1787332709000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623495288192"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,5]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,5]]}},"alternative-id":["10.1137\/S1052623495288192"],"URL":"https:\/\/doi.org\/10.1137\/s1052623495288192","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,5]]}}}