Journal of Scheduling

, Volume 7, Issue 4, pp 261–276 | Cite as

A Weighted Modified Due Date Rule for Sequencing to Minimize Weighted Tardiness



Priority dispatching for minimizing job tardiness has been the subject of research investigation for several decades. Minimizing weighted tardiness however has considerably more practical relevance, but for this objective only a few dispatching rules have been advanced and scientifically compared. We introduce here a new rule, which we call “Weighted Modified Due Date” (WMDD) and test its effectiveness against other competing rules that have been developed for weighted tardiness. The test is accomplished via a simulation study of a simple queueing system and by static problem analysis. The WMDD rule is found to compare favorably to all the rules tested.

weighted tardiness priority rules single machine scheduling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdul-Razaq, T. S., C. N. Potts, and L. N. van Wassenhove, “A Survey of algorithms for the single machine total weighted tardiness scheduling problem,” Discrete Appl. Math., 26, 235–253 (1990).Google Scholar
  2. Adler, L., N. M. Fraiman, E. Kobacker, M. Pinedo, J. C. Plotnitcoff, and T. P. Wu, “BPSS: A scheduling system for the packaging industry,” Oper. Res., 41, 641–648 (1993).Google Scholar
  3. Akturk, M. S. and M. B. Yildirim, “A new lower bounding scheme for the total weighted tardiness problem,” Comput. Oper. Res., 25(4), 265–278 (1998).Google Scholar
  4. Arkin, E. M. and R. O. Roundy, “Weighted-tardiness scheduling on parallel machines with proportional weights,” Oper. Res., 39(1), 64–81 (1991).Google Scholar
  5. Baker, K.R., “Sequencing rules and due date assignments in a job shop,” Manage. Sci., 30, 1093–1104 (1984).Google Scholar
  6. Baker, K. R. and J. W. M. Bertrand, “A dynamic priority rule for scheduling against due-dates,” J. Oper. Manage. 3(1), 37–42 (1983).Google Scholar
  7. Baker, K. R. and J. J. Kanet, “Job shop scheduling with modified due dates,” J. Oper. Manage. 4(1), 11–22 (1983).Google Scholar
  8. Baker, K. R. and J. J. Kanet, “Improved decision rules in a combined system for minimizing job tardiness,” Int. J. Prod. Res., 22(6), 917–922 (1984).Google Scholar
  9. Bhaskaran, K. and M. Pinedo, “Dispatching,” in G. Salvendy (ed.), Handbook of Industrial Engineering, John Wiley & Sons, New York, 1992, pp. 2184–2198.Google Scholar
  10. Carroll, D. C., “Heuristic sequencing of single and multiple component jobs,” Ph.D. Thesis, Sloan School of Management, MIT, Cambridge, MA, 1965.Google Scholar
  11. Chu, C. and M.-C. Portmann, “Some new efficient methods to solve the n/1/r i/∑Tischeduling problem,” Eur. J. Oper. Res., 58, 404–413 (1992).Google Scholar
  12. Du, J. and J. Y. T. Leung, “Minimizing total tardiness on one machine is NP-hard,” Math. Oper. Res., 15(3), 483–495 (1990).Google Scholar
  13. Duncan, D. B., “Multiple range and multiple F-tests,” Biometrics, 11, 1–42 (1955).Google Scholar
  14. Huegler, P. A. and F. J. Vasko, “A performance comparison of heuristics for the total weighted tardiness problem,” Comput. Ind. Eng., 32(4), 753–767 (1997).Google Scholar
  15. Kanet, J. J. and J. C. Hayya, “Priority dispatching with operation due dates in a job shop” J. Oper. Manage., 2(4), 167–176 (1982).Google Scholar
  16. Kanet, J. J. and X. Li, “On Adjacent Job Precedence for 1‖∑wjTj” working paper, University of Dayton, 2002.Google Scholar
  17. Kanet, J. J. and Z. Zhou, “A decision theory approach to priority dispatching for job shop scheduling,” Prod. Oper. Manage., 2(1), 2–14 (1993).Google Scholar
  18. Koulamas, C. P., “The total tardiness scheduling problem: Review and extensions,” Oper. Res., 42, 1025–1041 (1994).Google Scholar
  19. Lawler, E., “A ‘Pseudopolynomial’ algorithm for sequencing jobs to minimize total tardiness,” Ann. Discrete Math., 1, 331–342 (1977).Google Scholar
  20. Lee, Y. H., K. Bhaskaran, and M. Pinedo, “A heuristic to minimize the total weighted tardiness with sequence-dependent setups,” IIE Trans., 29, 45–52 (1997).Google Scholar
  21. Mason, S. J., J.W Fowler, and W. M. Carlyle, “A modified shifting bottleneck heuristic for minimizing total weighted tardiness in complex job shops,” J. Scheduling, 5(3), 247–262 (2002).Google Scholar
  22. Morton, T E. and D. W. Pentico, Heuristic Scheduling Systems with Applications to Production and Project Management, John Wiley & Sons, New York, 1993.Google Scholar
  23. Pinedo, M., “Scheduling,” in G. Salvendy (ed.), Handbook of Industrial Engineering, John Wiley & Sons, New York, 1992, pp. 2131–2153.Google Scholar
  24. Potts, C.N. and L. N. Van Wassenhove, “A branch and bound algorithm for the total weighted tardiness problem,” Oper. Res., 33, 363–377 (1985).Google Scholar
  25. Rachamadugu, R. V., “A note on the weighted tardiness problem,” Oper. Res. 35(3), 450–452 (1987).Google Scholar
  26. Raman, N., R. V. Rachamadugu, and F. B. Talbot, “Real time scheduling of an automated manufacturing center,” Eur. J. Oper. Res., 40, 222–242 (1989).Google Scholar
  27. Smith, W. E., “Various optimizers for single-stage production,” Naval Res. Logistics Quar., 3, 59–66 (1956).Google Scholar
  28. Szwarc, W. and J. J. Liu, “Weighted tardiness single machine scheduling with proportional weights” Manage. Sci., 39(5), 626–632 (1993).Google Scholar
  29. Vepsalainen, A. P. and T. E. Morton, “Priority rules for job shops with weighted tardiness costs,” Manage. Sci., 33(3), 1035–1047 (1987).Google Scholar
  30. Volgenant, A. and E. Teerhuis, “Improved heuristics for the n-job single-machine weighted tardiness problem,” Comput. Oper. Res., 26(1) 35–44 (1999).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of MIS, Operations Management, and Decision SciencesUniversity of DaytonDaytonUSA
  2. 2.Department of Business AdministrationTennessee State UniversityNashvilleUSA

Personalised recommendations