Parallel machine scheduling to minimize the sum of quadratic completion times

References

• Alidaee , B. 1991 . Single machine scheduling with nonlinear cost functions . Computers & Operations Research , 18 : 317 – 322 .
   Web of Science ®Google Scholar
• Alidaee , B. 1993 . Numerical methods for single machine scheduling with non-linear cost functions to minimize total cost . Journal of the Operational Research Society , 44 : 125 – 132 .
   Web of Science ®Google Scholar
• Alon , N. , Azar , Y. , Woeginger , G. J. and Yadid , T. 1998 . Approximation schemes for scheduling on parallel machines . Journal of Scheduling , 1 : 55 – 66 .
   Google Scholar
• Bagga , P. C. and Kalra , K. R. 1980 . A node elimination procedure for Townsend's algorithm for solving the single machine quadratic penalty function scheduling problem . Management Science , 26 : 633 – 636 .
   Web of Science ®Google Scholar
• Chandra , A. K. and Wong , C. K. 1975 . Worst-case analysis of a placement algorithm related to storage allocation . SIAM Journal on Computing , 4 : 249 – 263 .
   Google Scholar
• Cheng , T. C. E. and Sin , C. C. S. 1990 . A state-of-the-art review of parallel-machine scheduling research . European Journal of Operational Research , 47 : 271 – 292 .
   Web of Science ®Google Scholar
• David , H. A. 1981 . Order Statistics , 2nd edn. , pp. 35 – 36 . New York : Wiley .
   Google Scholar
• la Croce , F. , Szwarc , W. , Tadei , R. , Baracco , P. and Di Tullio , R. 1995 . Minimizing the weighted sum of quadratic completion times on a single machine . Naval Research Logistics , 42 : 1263 – 1270 .
   Web of Science ®Google Scholar
• Fisher , M. L. and Krieger , A. M. 1984 . Analysis of a linearization heuristic for single-machine scheduling to maximize profit . Mathematical Programming , 28 : 218 – 225 .
   Web of Science ®Google Scholar
• Garey , M. R. and Johnson , D. S. 1979 . Computers and Intractability: A Guide to the Theory of NP-completeness , San Francisco, CA : Freeman .
   Google Scholar
• Gupta , S. K. and Sen , T. 1984 . On the single machine scheduling problem with quadratic penalty function of completion times: an improved branching procedure . Management Science , 30 : 644 – 647 .
   Web of Science ®Google Scholar
• Lawler , E. L. , Lenstra , J. K. , Rinnooy , KanA. H. G. and Shmoys , D. B. 1993 . “ Sequencing and scheduling: algorithms and complexity ” . In Handbooks in Operations Research and Management Science, Volume 4, Logistics of Production and Inventory Edited by: Graves , S. C. , Rinnooy , KanA. H. G. and Zipkin , P. H. 445 – 522 . North Holland, Amsterdam
   Google Scholar
• Leung , J. Y.-T. and Wei , W.-D. 1995 . Tighter bounds on a heuristic for a partition problem . Information Processing Letters , 56 : 51 – 57 .
   Web of Science ®Google Scholar
• Ng , C. T. , Cai , X. and Cheng , T. C. E. 1999 . Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem . Naval Research Logistics , 46 : 373 – 398 .
   Web of Science ®Google Scholar
• Sen , T. , Dileepan , P. and Ruparel , B. 1990 . Minimizing a generalized quadratic penalty function of job completion times: an improved branch-and-bound approach . Engineering Costs and Production Economics , 18 : 197 – 202 .
   Web of Science ®Google Scholar
• Spiegel , M. R. and Liu , J. 1999 . Mathematical Handbook of Formulas and Tables , 2nd edn. , pp. 131 – 132 . New York : McGraw-Hill .
   Google Scholar
• Szwarc , W. and Mukhopadhyay , S. K. 1996 . Solution of the generalized Townsend single machine scheduling model . European Journal of Operational Research , 91 : 203 – 210 .
   Web of Science ®Google Scholar
• Szwarc , W. , Posner , M. E. and Liu , J. J. 1988 . The single machine problem with a quadratic cost function of completion times . Management Science , 34 : 1480 – 1488 .
   Web of Science ®Google Scholar
• Townsend , W. 1978 . The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution . Management Science , 24 : 530 – 534 .
   Web of Science ®Google Scholar