Document Zbl 1154.90458

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J. Oper. Res.</a> <a href="/?q=in%3A118563" title="Articles in this Issue">167, No. 3, 592-623 (2005)</a>. </div> <div class="abstract">Summary: We give a survey of the most important results on multicriteria scheduling that have appeared in the literature or are to appear. We provide an extensive introduction including two example problems and then discuss the relevant literature. Here we pay special attention to the area of earliness-tardiness scheduling, scheduling with controllable processing times, simultaneous approximation, and new models.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A2210263">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A2210263">Cited in <strong>125</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B35" title="MSC2020">90B35</a> </td> <td class="space"> Deterministic scheduling theory in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90-02" title="MSC2020">90-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C29" title="MSC2020">90C29</a> </td> <td class="space"> Multi-objective and goal programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMachine+scheduling">Machine scheduling</a>; <a href="/?q=ut%3AMulticriteria">Multicriteria</a>; <a href="/?q=ut%3APareto+optimal">Pareto optimal</a>; <a href="/?q=ut%3AEarliness-tardiness">Earliness-tardiness</a>; <a href="/?q=ut%3AControllable+processing+times">Controllable processing times</a>; <a href="/?q=ut%3ASimultaneous+approximation">Simultaneous approximation</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1154.90458" data-ciurl="/ci/02210263" data-biburl="/bibtex/02210263.bib" data-amsurl="/amsrefs/02210263.bib" data-xmlurl="/xml/02210263.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02210263.pdf" title="Zbl 1154.90458 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.ejor.2004.07.011" aria-label="DOI for “Multicriteria scheduling”" title="10.1016/j.ejor.2004.07.011">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Achugbue, J. O.; Chin, F. Y., Scheduling the openshop to minimize mean flow time, SIAM Journal on Computing, 11, 665-679 (1982)</td> </tr><tr> <td>[2]</td> <td class="space">Ahuja, R. K.; Magnanti, T. L.; Orlin, J. B., Network Flows—Theory, Algorithms, and Applications (1993), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · <a href="/1201.90001" class="nowrap">Zbl 1201.90001</a></td> </tr><tr> <td>[3]</td> <td class="space">Alidaee, B.; Ahmadian, A., Two parallel machine sequencing problems involving controllable job processing times, European Journal of Operational Research, 70, 335-341 (1993) · <a href="/0791.90028" class="nowrap">Zbl 0791.90028</a></td> </tr><tr> <td>[4]</td> <td class="space">Alidaee, B.; Dragan, I., A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date, European Journal of Operational Research, 96, 559-563 (1997) · <a href="/0917.90182" class="nowrap">Zbl 0917.90182</a></td> </tr><tr> <td>[5]</td> <td class="space">Aslam, J.A., Rasala, A., Stein, C., Young, N., 1999. Improved bicriteria existence theorems for scheduling. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 846-847; Aslam, J.A., Rasala, A., Stein, C., Young, N., 1999. Improved bicriteria existence theorems for scheduling. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 846-847 · <a href="/1052.90549" class="nowrap">Zbl 1052.90549</a></td> </tr><tr> <td>[6]</td> <td class="space">Bagchi, U., Simultaneous minimization of mean and variation of flow time and waiting time in single machine systems, Operations Research, 17, 381-386 (1989)</td> </tr><tr> <td>[7]</td> <td class="space">Bagchi, U.; Sullivan, R. S.; Chang, Y. L., Minimizing mean absolute deviation of completion times about a common due date, Naval Research Logistics Quarterly, 33, 227-240 (1986) · <a href="/0599.90049" class="nowrap">Zbl 0599.90049</a></td> </tr><tr> <td>[8]</td> <td class="space">Baker, K. R.; Scudder, G. D., Sequencing with earliness and tardiness penalties: A review, Operations Research, 38, 22-36 (1990) · <a href="/0699.90052" class="nowrap">Zbl 0699.90052</a></td> </tr><tr> <td>[9]</td> <td class="space">Baker, K. R.; Smith, J. C., A multiple-criterion model for machine scheduling, Journal of Scheduling, 6, 7-16 (2003) · <a href="/1154.90406" class="nowrap">Zbl 1154.90406</a></td> </tr><tr> <td>[10]</td> <td class="space">Bartal, Y.; Leonardi, S.; Marchetti-Spaccamela, A.; Sgall, J.; Stougie, L., Multiprocessor scheduling with rejection, SIAM Journal on Discrete Mathematics, 13, 64-78 (2000) · <a href="/0936.68012" class="nowrap">Zbl 0936.68012</a></td> </tr><tr> <td>[11]</td> <td class="space">Bazaraa, M. S.; Jarvis, J. J.; Sherali, H. D., Linear Programming and Network Flows (1990), Wiley: Wiley New York · <a href="/0722.90042" class="nowrap">Zbl 0722.90042</a></td> </tr><tr> <td>[12]</td> <td class="space">Bülbül, K., Kaminsky, P., Yano, C., submitted for publication. Preemption in single machine earliness/tardiness scheduling. Naval Research Logistics, Department of IEOR, University of California at Berkeley; Bülbül, K., Kaminsky, P., Yano, C., submitted for publication. Preemption in single machine earliness/tardiness scheduling. Naval Research Logistics, Department of IEOR, University of California at Berkeley · <a href="/1168.90427" class="nowrap">Zbl 1168.90427</a></td> </tr><tr> <td>[13]</td> <td class="space">Bülbül, K., Kaminsky, P., Yano, C., 2003. Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs. Department of IEOR, University of California at Berkeley; Bülbül, K., Kaminsky, P., Yano, C., 2003. Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs. Department of IEOR, University of California at Berkeley · <a href="/1054.90028" class="nowrap">Zbl 1054.90028</a></td> </tr><tr> <td>[14]</td> <td class="space">Chakrabarti, S.; Phillips, C. A.; Schulz, A. S.; Shmoys, D. B.; Stein, C.; Wein, J., Improved scheduling algorithms for minsum criteria, (Meyer auf der Heide, F.; Monien, B., Lecture Notes in Computer Science, vol. 1099 (1996), Springer: Springer Berlin), 646-657 · <a href="/1046.68505" class="nowrap">Zbl 1046.68505</a></td> </tr><tr> <td>[15]</td> <td class="space">Chen, C.-L.; Bulfin, R. L., Scheduling unit processing time jobs on a single machine with multiple criteria, Computers and Operations Research, 17, 1-7 (1990) · <a href="/0681.90049" class="nowrap">Zbl 0681.90049</a></td> </tr><tr> <td>[16]</td> <td class="space">Chen, C.-L.; Bulfin, R. L., Complexity of single machine, multi-criteria scheduling problems, European Journal of Operational Research, 70, 115-125 (1993) · <a href="/0795.90032" class="nowrap">Zbl 0795.90032</a></td> </tr><tr> <td>[17]</td> <td class="space">Chen, Z. L.; Powell, W. P., A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem, European Journal of Operational Research, 116, 220-232 (1999) · <a href="/1009.90040" class="nowrap">Zbl 1009.90040</a></td> </tr><tr> <td>[18]</td> <td class="space">Cheng, T. C.E.; Chen, Z.-L.; Li, C.-L., Single-machine scheduling with trade-off between number of tardy jobs and resource allocation, Operations Research Letters, 19, 237-242 (1996) · <a href="/0874.90105" class="nowrap">Zbl 0874.90105</a></td> </tr><tr> <td>[19]</td> <td class="space">Cheng, T. C.E.; Shakhlevich, N., Proportionate flow shops with controllable processing times, Journal of Scheduling, 2, 253-266 (1999) · <a href="/0949.90039" class="nowrap">Zbl 0949.90039</a></td> </tr><tr> <td>[20]</td> <td class="space">Chrétienne, P.; Sourd, F., PERT scheduling with convex cost functions, Theoretical Computer Science, 292, 145-164 (2003) · <a href="/1059.90066" class="nowrap">Zbl 1059.90066</a></td> </tr><tr> <td>[21]</td> <td class="space">Daniels, R. L.; Chambers, R. J., Multiobjective flow-shop scheduling, Naval Research Logistics, 40, 85-101 (1990)</td> </tr><tr> <td>[22]</td> <td class="space">Dessouky, M. I.; Lageweg, B. J.; Lenstra, J. K.; Van de Velde, S. L., Scheduling identical jobs on uniform parallel machines, Statistica Neerlandica, 44, 115-123 (1990) · <a href="/0716.90053" class="nowrap">Zbl 0716.90053</a></td> </tr><tr> <td>[23]</td> <td class="space">Du, J.; Leung, J. Y.-T., Minimizing total tardiness on one machine is NP-hard, Mathematics of Operations Research, 15, 483-495 (1990) · <a href="/0714.90052" class="nowrap">Zbl 0714.90052</a></td> </tr><tr> <td>[24]</td> <td class="space">Eck, B. T.; Pinedo, M. L., On the minimization of the makespan subject to flowtime optimality, Operations Research, 41, 797-801 (1993) · <a href="/0782.90051" class="nowrap">Zbl 0782.90051</a></td> </tr><tr> <td>[25]</td> <td class="space">Emmons, H., One machine sequencing to minimize mean flow time with minimum number of tardy, Naval Research Logistics Quarterly, 22, 585-592 (1975) · <a href="/0315.90032" class="nowrap">Zbl 0315.90032</a></td> </tr><tr> <td>[26]</td> <td class="space">Emmons, H., A note on a scheduling problem with dual criteria, Naval Research Logistics Quarterly, 22, 615-616 (1975) · <a href="/0314.90045" class="nowrap">Zbl 0314.90045</a></td> </tr><tr> <td>[27]</td> <td class="space">Emmons, H., Scheduling to a common due date on parallel uniform processors, Naval Research Logistics, 34, 803-810 (1987) · <a href="/0648.90043" class="nowrap">Zbl 0648.90043</a></td> </tr><tr> <td>[28]</td> <td class="space">Engels, D. W.; Karger, D. R.; Kolliopoulos, S. G.; Sengupta, S.; Uma, R. N.; Wein, J., Techniques for scheduling with rejection, Journal of Algorithms, 49, 175-191 (2003) · <a href="/1067.68024" class="nowrap">Zbl 1067.68024</a></td> </tr><tr> <td>[29]</td> <td class="space">Evans, G. W., An overview of techniques for solving multiobjective mathematical programs, Management Science, 30, 1268-1282 (1984) · <a href="/0551.90090" class="nowrap">Zbl 0551.90090</a></td> </tr><tr> <td>[30]</td> <td class="space">Fry, T. D.; Armstrong, R. D.; Lewis, H., A framework for single machine multiple objective sequencing research, Omega, 17, 595-607 (1989)</td> </tr><tr> <td>[31]</td> <td class="space">Fry, T. D.; Keong Leong, G., Single machine scheduling: A comparison of two solution procedures, Omega, 15, 277-282 (1987)</td> </tr><tr> <td>[32]</td> <td class="space">Garey, M. R.; Johnson, D. S.; Sethi, R., The complexity of flowshop and jobshop scheduling, Mathematics of Operations Research, 1, 117-129 (1976) · <a href="/0396.90041" class="nowrap">Zbl 0396.90041</a></td> </tr><tr> <td>[33]</td> <td class="space">Garey, M. R.; Tarjan, R. E.; Wilfong, G. T., One-processor scheduling with symmetric earliness and tardiness penalties, Mathematics of Operations Research, 13, 330-348 (1988) · <a href="/0671.90033" class="nowrap">Zbl 0671.90033</a></td> </tr><tr> <td>[34]</td> <td class="space">Gonzalez, T.; Sahni, S., Open shop scheduling to minimize finish time, Journal of the Association for Computing Machinery, 25, 92-101 (1976) · <a href="/0343.68031" class="nowrap">Zbl 0343.68031</a></td> </tr><tr> <td>[35]</td> <td class="space">Gordon, V.; Proth, J.-M.; Chu, C., A survey of the state-of-the-art of common due date assignment and scheduling research, European Journal of Operational Research, 139, 1-25 (2002) · <a href="/1009.90054" class="nowrap">Zbl 1009.90054</a></td> </tr><tr> <td>[36]</td> <td class="space">Graham, R. L., Bounds for certain multiprocessor anomalies, Bell System Technical Journal, 45, 1563-1581 (1966) · <a href="/0168.40703" class="nowrap">Zbl 0168.40703</a></td> </tr><tr> <td>[37]</td> <td class="space">Graham, R. L.; Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics, 5, 287-326 (1979) · <a href="/0411.90044" class="nowrap">Zbl 0411.90044</a></td> </tr><tr> <td>[38]</td> <td class="space">Gupta, J. N.D.; Hariri, A. M.A.; Potts, C. N., Single-machine scheduling to minimize maximum tardiness with minimum number of tardy jobs, Annals of Operations Research, 92, 107-123 (1999) · <a href="/0931.90019" class="nowrap">Zbl 0931.90019</a></td> </tr><tr> <td>[39]</td> <td class="space">Gupta, J. N.D.; Neppalli, V. R.; Werner, F., Minimizing total flow time in a two-machine flowshop problem with minimum makespan, International Journal of Production Economics, 69, 323-338 (2001)</td> </tr><tr> <td>[40]</td> <td class="space">Hall, N. G., Single-and multiple-processor models for minimizing completion time variance, Naval Research Logistics Quarterly, 33, 49-54 (1986) · <a href="/0599.90057" class="nowrap">Zbl 0599.90057</a></td> </tr><tr> <td>[41]</td> <td class="space">Hall, N. G.; Kubiak, W.; Sethi, S. P., Earliness-tardiness scheduling problems, II: Deviation of completion times about a common due date, Operations Research, 39, 847-856 (1991) · <a href="/0762.90037" class="nowrap">Zbl 0762.90037</a></td> </tr><tr> <td>[42]</td> <td class="space">Hall, N. G.; Posner, M. E., Earliness-tardiness scheduling problems, I: weighted deviation of completion times about a common due date, Operations Research, 39, 836-846 (1991) · <a href="/0749.90041" class="nowrap">Zbl 0749.90041</a></td> </tr><tr> <td>[43]</td> <td class="space">Hall, N. G.; Potts, C. N., Rescheduling for new orders, Operations Research, 42, 440-453 (2004) · <a href="/1165.90456" class="nowrap">Zbl 1165.90456</a></td> </tr><tr> <td>[44]</td> <td class="space">Hoogeveen, J.A., 1992. Single-Machine Bicriteria Scheduling. PhD Thesis, CWI, The Netherlands Technology, Amsterdam; Hoogeveen, J.A., 1992. Single-Machine Bicriteria Scheduling. PhD Thesis, CWI, The Netherlands Technology, Amsterdam · <a href="/0749.90042" class="nowrap">Zbl 0749.90042</a></td> </tr><tr> <td>[45]</td> <td class="space">Hoogeveen, J. A., Minimizing maximum promptness and maximum lateness on a single machine, Mathematics of Operations Research, 21, 100-114 (1996) · <a href="/0846.90050" class="nowrap">Zbl 0846.90050</a></td> </tr><tr> <td>[46]</td> <td class="space">Hoogeveen, J. A., Single-machine scheduling to minimize a function of two or three maximum cost criteria, Journal of Algorithms, 21, 415-433 (1996) · <a href="/0857.68012" class="nowrap">Zbl 0857.68012</a></td> </tr><tr> <td>[47]</td> <td class="space">Hoogeveen, J. A.; Oosterhout, H.; van de Velde, S. L., New lower and upper bounds for scheduling around a small common due date, Operations Research, 42, 102-110 (1994) · <a href="/0798.90085" class="nowrap">Zbl 0798.90085</a></td> </tr><tr> <td>[48]</td> <td class="space">Hoogeveen, J. A.; Skutella, M.; Woeginger, G. J., Preemptive scheduling with rejection, Mathematical Programming B, 94, 361-374 (2003) · <a href="/1030.90025" class="nowrap">Zbl 1030.90025</a></td> </tr><tr> <td>[49]</td> <td class="space">Hoogeveen, J. A.; van de Velde, S. L., Scheduling around a small common due date, European Journal of Operational Research, 55, 237-242 (1991) · <a href="/0755.90044" class="nowrap">Zbl 0755.90044</a></td> </tr><tr> <td>[50]</td> <td class="space">Hoogeveen, J. A.; van de Velde, S. L., Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time, Operations Research Letters, 17, 205-208 (1995) · <a href="/0858.90075" class="nowrap">Zbl 0858.90075</a></td> </tr><tr> <td>[51]</td> <td class="space">Hoogeveen, J. A.; van de Velde, S. L., A branch-and-bound algorithm for single-machine earliness-tardiness scheduling with idle time, INFORMS Journal on Computing, 8, 402-412 (1996) · <a href="/0884.90102" class="nowrap">Zbl 0884.90102</a></td> </tr><tr> <td>[52]</td> <td class="space">Hoogeveen, J. A.; van de Velde, S. L., Earliness-tardiness scheduling around almost equal due dates, INFORMS Journal on Computing, 9, 92-99 (1997) · <a href="/0889.90089" class="nowrap">Zbl 0889.90089</a></td> </tr><tr> <td>[53]</td> <td class="space">Hoogeveen, J. A.; van de Velde, S. L., Scheduling with target start times, European Journal of Operational Research, 129, 87-94 (2001) · <a href="/0990.90040" class="nowrap">Zbl 0990.90040</a></td> </tr><tr> <td>[54]</td> <td class="space">Hoogeveen, J. A.; Woeginger, G. J., Some comments on sequencing with controllable processing times, Computing, 68, 181-192 (2002) · <a href="/1002.90027" class="nowrap">Zbl 1002.90027</a></td> </tr><tr> <td>[55]</td> <td class="space">Horn, W. A., Minimizing average flow time with parallel machines, Operations Research, 21, 846-847 (1973) · <a href="/0259.90030" class="nowrap">Zbl 0259.90030</a></td> </tr><tr> <td>[56]</td> <td class="space">Huang, G., Lim, A., 2003. A new approach to solve a 2-machine bicriteria flowshop scheduling problem. In: Proceedings of the 5th International Workshop on Integration of Artificial Intelligence and Operations Research techniques in Constraints Programming for Combinatorial Optimization, CPAIOR’03; Huang, G., Lim, A., 2003. A new approach to solve a 2-machine bicriteria flowshop scheduling problem. In: Proceedings of the 5th International Workshop on Integration of Artificial Intelligence and Operations Research techniques in Constraints Programming for Combinatorial Optimization, CPAIOR’03</td> </tr><tr> <td>[57]</td> <td class="space">Hurkens, C.A.J., Coster, M.J., unpublished manuscript. On the makespan of a schedule minimizing total completion time for unrelated parallel machines; Hurkens, C.A.J., Coster, M.J., unpublished manuscript. On the makespan of a schedule minimizing total completion time for unrelated parallel machines</td> </tr><tr> <td>[58]</td> <td class="space">Jackson, J.R., 1955. Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Sciences Research Project, UCLA; Jackson, J.R., 1955. Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Sciences Research Project, UCLA</td> </tr><tr> <td>[59]</td> <td class="space">Janiak, A.; Kovalyov, M. Y., Single machine scheduling subject to deadlines and resource dependent processing times, European Journal of Operational Research, 94, 284-291 (1996) · <a href="/0947.90584" class="nowrap">Zbl 0947.90584</a></td> </tr><tr> <td>[60]</td> <td class="space">Kanet, J. J., Minimizing the average deviation of job completion times about a common due date, Naval Research Logistics Quarterly, 28, 643-651 (1981) · <a href="/0548.90037" class="nowrap">Zbl 0548.90037</a></td> </tr><tr> <td>[61]</td> <td class="space">Karasakal; Köksalan, A simulated annealing approach to bicriteria scheduling problems on a single machine, Journal of Heuristics, 6, 311-327 (2000) · <a href="/1071.90536" class="nowrap">Zbl 1071.90536</a></td> </tr><tr> <td>[62]</td> <td class="space">Kawaguchi, T.; Kyan, S., Worst case bound of an LRF schedule for the mean weighted flow time problem, SIAM Journal on Computing, 15, 1119-1129 (1986) · <a href="/0621.68024" class="nowrap">Zbl 0621.68024</a></td> </tr><tr> <td>[63]</td> <td class="space">Kim, Y.-D.; Yano, C. A., Minimizing mean tardiness and earliness in single machine scheduling problems with unequal due dates, Naval Research Logistics, 41, 913-933 (1994) · <a href="/0815.90093" class="nowrap">Zbl 0815.90093</a></td> </tr><tr> <td>[64]</td> <td class="space">Köksalan, M.; Azizoglu, M.; Kondakci, S., Minimizing flow time and maximum earliness on a single machine, IIE Transactions, 30, 192-200 (1998)</td> </tr><tr> <td>[65]</td> <td class="space">Kyparisis, G. J.; Koulamas, C., Open shop scheduling with makespan and total completion time criteria, Computers & Operations Research, 27, 15-27 (2000) · <a href="/0959.90022" class="nowrap">Zbl 0959.90022</a></td> </tr><tr> <td>[66]</td> <td class="space">Lawler, E.L., 1982. Scheduling a single machine to minimize the number of late jobs. Preprint, Computer Science Division, University of California, Berkeley; Lawler, E.L., 1982. Scheduling a single machine to minimize the number of late jobs. Preprint, Computer Science Division, University of California, Berkeley</td> </tr><tr> <td>[67]</td> <td class="space">Lawler, E. L.; Labetoulle, J., On preemptive scheduling of unrelated parallel machines with linear programming, Journal of the Association of Computing Machinery, 25, 612-619 (1978) · <a href="/0388.68027" class="nowrap">Zbl 0388.68027</a></td> </tr><tr> <td>[68]</td> <td class="space">Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Minimizing maximum lateness in a two-machine open shop, Mathematics of Operations Research, 6, 153-158 (1981) · <a href="/0496.90047" class="nowrap">Zbl 0496.90047</a></td> </tr><tr> <td>[69]</td> <td class="space">Lenstra, J.K., unpublished manuscript; Lenstra, J.K., unpublished manuscript</td> </tr><tr> <td>[70]</td> <td class="space">Lenstra, J. K.; Tardos, E.; Shmoys, D. B., Approximation algorithms for scheduling unrelated parallel machines, Mathematical Programming, 46, 259-271 (1990) · <a href="/0715.90063" class="nowrap">Zbl 0715.90063</a></td> </tr><tr> <td>[71]</td> <td class="space">Leung, J. Y.-T.; Young, G. H., Minimizing schedule length subject to minimum flow time, SIAM Journal on Computing, 18, 314-326 (1989) · <a href="/0672.90070" class="nowrap">Zbl 0672.90070</a></td> </tr><tr> <td>[72]</td> <td class="space">Liao, C. J.; Yu, C. J.; Joe, C. B., Bicriterion scheduling in the two-machine flowshop, Journal of the Operational Research Society, 48, 929-935 (1997) · <a href="/0892.90106" class="nowrap">Zbl 0892.90106</a></td> </tr><tr> <td>[73]</td> <td class="space">Masuda, T.; Ishii, H., Two machine open shop scheduling problem with bi-criteria, Discrete Applied Mathematics, 52, 253-259 (1994) · <a href="/0830.90072" class="nowrap">Zbl 0830.90072</a></td> </tr><tr> <td>[74]</td> <td class="space">McCormick, S. T.; Pinedo, M. L., Scheduling n independent jobs on m uniform machines with both flowtime and makespan objectives: a parametric analysis, ORSA Journal on Computing, 7, 63-77 (1995) · <a href="/0822.90084" class="nowrap">Zbl 0822.90084</a></td> </tr><tr> <td>[75]</td> <td class="space">Mohri, S.; Masuda, T.; Ishii, H., Bi-criteria scheduling problem on three identical parallel machines, International Journal of Production Economics, 60-61, 529-536 (1999)</td> </tr><tr> <td>[76]</td> <td class="space">Nagar, A.; Heragu, S. S.; Haddock, J., A branch-and-bound approach for a two-machine flowshop scheduling problem, Journal of the Operational Research Society, 46, 721-734 (1995) · <a href="/0832.90058" class="nowrap">Zbl 0832.90058</a></td> </tr><tr> <td>[77]</td> <td class="space">Nelson, R. T.; Sarin, R. K.; Daniels, R. L., Scheduling with multiple performance measures: The one-machine case, Management Science, 32, 464-479 (1986) · <a href="/0603.90070" class="nowrap">Zbl 0603.90070</a></td> </tr><tr> <td>[78]</td> <td class="space">Nowicki, E.; Zdrzałka, S., A two-machine flow shop scheduling problem with controllable job processing times, European Journal of Operational Research, 34, 208-220 (1988) · <a href="/0647.90041" class="nowrap">Zbl 0647.90041</a></td> </tr><tr> <td>[79]</td> <td class="space">Nowicki, E.; Zdrzałka, S., A survey of results for sequencing problems with controllable processing times, Discrete Applied Mathematics, 26, 271-287 (1990) · <a href="/0693.90056" class="nowrap">Zbl 0693.90056</a></td> </tr><tr> <td>[80]</td> <td class="space">Nowicki, E.; Zdrzałka, S., A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times, Discrete Applied Mathematics, 63, 237-256 (1995) · <a href="/0854.68007" class="nowrap">Zbl 0854.68007</a></td> </tr><tr> <td>[81]</td> <td class="space">Pinedo, M. L., Scheduling: Theory, Algorithms, and Systems (2002), Prentice-Hall · <a href="/1145.90394" class="nowrap">Zbl 1145.90394</a></td> </tr><tr> <td>[82]</td> <td class="space">Rajendran, C., Two-stage flow shop scheduling problem with bicriteria, Journal of the Operational Research Society, 43, 871-884 (1992) · <a href="/0757.90037" class="nowrap">Zbl 0757.90037</a></td> </tr><tr> <td>[83]</td> <td class="space">Rasala, A., 1999. Existence theorems for scheduling to meet two objectives. Technical Report PCS-TR99-347, Dartmouth College; Rasala, A., 1999. Existence theorems for scheduling to meet two objectives. Technical Report PCS-TR99-347, Dartmouth College</td> </tr><tr> <td>[84]</td> <td class="space">Sahni, S., Preemptive scheduling with due dates, Operations Research, 27, 925-934 (1979) · <a href="/0424.90031" class="nowrap">Zbl 0424.90031</a></td> </tr><tr> <td>[85]</td> <td class="space">Sayin, S.; Karabati, S., A bicriteria approach to the two-machine flow shop scheduling problem, European Journal of Operational Research, 113, 435-449 (1999) · <a href="/0957.90064" class="nowrap">Zbl 0957.90064</a></td> </tr><tr> <td>[86]</td> <td class="space">Shabtay, D.; Kaspi, M., Minimizing the total weighted flow time in a single machine with controllable processing times, Computers & Operations Research, 31, 2279-2289 (2004) · <a href="/1073.90017" class="nowrap">Zbl 1073.90017</a></td> </tr><tr> <td>[87]</td> <td class="space">Shanthikumar, J. G., Scheduling jobs on one machine to minimize the maximum tardiness with minimum number of tardy, Computers & Operations Research, 10, 253-265 (1983)</td> </tr><tr> <td>[88]</td> <td class="space">Sivrikaya-Serifoglu, F. S.; Ulusoy, G., A bicriteria two machine permutation flowshop problem, European Journal of Operational Research, 107, 414-430 (1998) · <a href="/0943.90041" class="nowrap">Zbl 0943.90041</a></td> </tr><tr> <td>[89]</td> <td class="space">Smith, W. E., Various optimizers for single-stage production, Naval Research Logistics Quarterly, 1, 59-66 (1956)</td> </tr><tr> <td>[90]</td> <td class="space">Sourd, F., Preemptive scheduling with two minimax criteria, Annals of Operations Research, 107, 303-319 (2001) · <a href="/1015.90044" class="nowrap">Zbl 1015.90044</a></td> </tr><tr> <td>[91]</td> <td class="space">Sourd, F., in press. Scheduling a sequence of tasks with general completion costs. European Journal of Operational Research; Sourd, F., in press. Scheduling a sequence of tasks with general completion costs. European Journal of Operational Research · <a href="/1112.90340" class="nowrap">Zbl 1112.90340</a></td> </tr><tr> <td>[92]</td> <td class="space">Sourd, F., The continuous assignment problem and its application to preemptive and non-preemptive scheduling with irregular cost functions, INFORMS Journal on Computing, 16, 198-208 (2004) · <a href="/1239.90054" class="nowrap">Zbl 1239.90054</a></td> </tr><tr> <td>[93]</td> <td class="space">Sourd, F., submitted for publication. Punctuality and idleness in just-in-time scheduling. European Journal of Operational Research; Sourd, F., submitted for publication. Punctuality and idleness in just-in-time scheduling. European Journal of Operational Research · <a href="/1077.90031" class="nowrap">Zbl 1077.90031</a></td> </tr><tr> <td>[94]</td> <td class="space">Sourd, F.; Kedad-Sidhoum, The one machine problem with earliness and tardiness penalties, Journal of Scheduling, 6, 533-549 (2003) · <a href="/1154.90490" class="nowrap">Zbl 1154.90490</a></td> </tr><tr> <td>[95]</td> <td class="space">Stein, C.; Wein, J., On the existence of schedules that are near-optimal for both makespan and total weighted completion time, Operations Research Letters, 21, 115-122 (1997) · <a href="/0888.90095" class="nowrap">Zbl 0888.90095</a></td> </tr><tr> <td>[96]</td> <td class="space">Tadei, R.; Grosso, A.; Della Croce, F., Finding the Pareto-optima for the total and maximum tardiness single machine problem, Discrete Applied Mathematics, 124, 117-126 (2002) · <a href="/1005.90038" class="nowrap">Zbl 1005.90038</a></td> </tr><tr> <td>[97]</td> <td class="space">T’kindt, V.; Billaut, J.-C., Multicriteria Scheduling: Theory, Models and Algorithms (2002), Springer: Springer Berlin · <a href="/1014.90046" class="nowrap">Zbl 1014.90046</a></td> </tr><tr> <td>[98]</td> <td class="space">T’kindt, V.; Billaut, J.-C.; Proust, C., An interactive algorithm to solve bicriteria scheduling problems on unrelated parallel machines, European Journal of Operational Research, 135, 42-49 (2001) · <a href="/1077.90532" class="nowrap">Zbl 1077.90532</a></td> </tr><tr> <td>[99]</td> <td class="space">T’kindt, V.; Gupta, J. N.D.; Billaut, J.-C., Two-machine flowshop with a secondary criterion, Computers & Operations Research, 30, 505-526 (2003) · <a href="/1026.90044" class="nowrap">Zbl 1026.90044</a></td> </tr><tr> <td>[100]</td> <td class="space">T’kindt, V.; Monmarché, N.; Tercinet, F.; Laugt, D., An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem, European Journal of Operational Research, 142, 250-257 (2002) · <a href="/1082.90592" class="nowrap">Zbl 1082.90592</a></td> </tr><tr> <td>[101]</td> <td class="space">Torng, E., Uthaisombut, P., 1999. Lower bounds for sprt-subsequence algorithms for nonpreemptive scheduling. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 973-974; Torng, E., Uthaisombut, P., 1999. Lower bounds for sprt-subsequence algorithms for nonpreemptive scheduling. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 973-974 · <a href="/1052.90564" class="nowrap">Zbl 1052.90564</a></td> </tr><tr> <td>[102]</td> <td class="space">Tuzikov, A.; Makhaniok, M.; Männer, R., Bicriterion scheduling of identical processing time jobs by uniform processors, Computers & Operations Research, 25, 31-35 (1998) · <a href="/0907.90187" class="nowrap">Zbl 0907.90187</a></td> </tr><tr> <td>[103]</td> <td class="space">Vairaktarakis, G. L.; Lee, C.-Y., The single machine problem to minimize total tardiness subject to minimum number of tardy jobs, IIE Transactions, 27, 250-256 (1995)</td> </tr><tr> <td>[104]</td> <td class="space">Verma, S.; Dessouky, M., Single-machine scheduling of unit-time jobs with earliness and tardiness penalties, Mathematics of Operations Research, 23, 930-943 (1998) · <a href="/0977.90017" class="nowrap">Zbl 0977.90017</a></td> </tr><tr> <td>[105]</td> <td class="space">Vickson, R. G., Two single machine sequencing problems involving controllable job processing times, AIIE Transactions, 12, 258-262 (1980)</td> </tr><tr> <td>[106]</td> <td class="space">Vickson, R. G., Choosing the job sequence and processing times to minimize total processing plus flow cost on a single machine, Operations Research, 28, 1155-1167 (1980) · <a href="/0449.90054" class="nowrap">Zbl 0449.90054</a></td> </tr><tr> <td>[107]</td> <td class="space">Wan, G.; Yen, B. P.-C., Tabu search for single machine scheduling with distinct due windows and weighted earliness/tardiness penalties, European Journal of Operational Research, 142, 271-281 (2002) · <a href="/1082.90531" class="nowrap">Zbl 1082.90531</a></td> </tr><tr> <td>[108]</td> <td class="space">Wan, G.; Yen, B. P.-C.; Li, C.-L., Single machine scheduling to minimize total compression plus weighted flow cost is NP-hard, Information Processing Letters, 79, 273-280 (2001) · <a href="/1051.68082" class="nowrap">Zbl 1051.68082</a></td> </tr><tr> <td>[109]</td> <td class="space">Van den Akker, J. M.; Hoogeveen, J. A.; Van de Velde, S. L., Combining column generation and Lagrangean relaxation to solve a single-machine common due date problem, INFORMS Journal on Computing, 14, 37-51 (2002) · <a href="/1238.90096" class="nowrap">Zbl 1238.90096</a></td> </tr><tr> <td>[110]</td> <td class="space">van Wassenhove, L. N.; Baker, K. R., A bicriterion approach to time/cost tradeoffs in sequencing, European Journal of Operational Research, 11, 48-54 (1982) · <a href="/0482.90043" class="nowrap">Zbl 0482.90043</a></td> </tr><tr> <td>[111]</td> <td class="space">Van Wassenhove, L. N.; Gelders, F., Solving a bicriterion scheduling problem, European Journal of Operational Research, 4, 42-48 (1980) · <a href="/0418.90054" class="nowrap">Zbl 0418.90054</a></td> </tr><tr> <td>[112]</td> <td class="space">Wennink, M., 1995. Algorithmic support for automated planning boards. PhD Thesis, Eindhoven University of Technology; Wennink, M., 1995. Algorithmic support for automated planning boards. PhD Thesis, Eindhoven University of Technology · <a href="/0837.90073" class="nowrap">Zbl 0837.90073</a></td> </tr><tr> <td>[113]</td> <td class="space">Zhang, F.; Tang, G.; Chen, Z.-L., A $\frac{3}{2} $-approximation algorithm for parallel machine scheduling with controllable processing times, Operations Research Letters, 29, 41-47 (2001) · <a href="/0981.90027" class="nowrap">Zbl 0981.90027</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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