Abstract
This paper develops a branch and bound algorithm for solving the single‐machine schedulingproblem with the objective of minimizing the maximum tardiness of any job, subjectto the constraint that the total number of tardy jobs is minimum. The algorithm uses a newlower bounding scheme, which is based on due date relaxation. Various dominance rules areused in the algorithm to limit the size of the search tree. Results of extensive computationaltests show that the proposed branch and bound algorithm is effective in solving problemswith up to 1000 jobs.
Similar content being viewed by others
References
C.-L. Chen and R.L. Bulfin, Complexity of single machine, multi-criteria scheduling problems, European Journal of Operational Research 70(1993)115-125.
J.N.D. Gupta and R. Ramnarayanan, Single facility scheduling with dual criteria: Minimizing maximum tardiness subject to minimum number of tardy jobs, Production Planning and Control 7(1996)190-196.
J.R. Jackson, Scheduling a production line to minimize maximum tardiness, Management Science Research Report, University of California at Los Angeles, CA, 1955.
C.-Y. Lee and G.L. Vairaktarakis, Complexity of single machine hierarchical scheduling: A survey, in: Complexity in Numerical Optimization, ed. P.M. Pardalos, World Scientific, 1993, pp. 269-298.
J.M. Moore, An n job, one machine sequencing algorithm for minimizing the number of late jobs, Management Science 15(1968)102-109.
J.G Shanthikumar, Scheduling n jobs on one machine to minimize the maximum tardiness with minimum number tardy, Computers and Operations Research 10(1983)255-266.
J.B. Sidney, An extension of Moore's due date algorithm, in: Symposium on the Theory of Scheduling and its Applications, ed. S.E. Elmaghraby, Lecture Notes in Economics and Mathematical Systems, Vol. 86, Springer, 1973, pp. 393-398.
Rights and permissions
About this article
Cite this article
Gupta, J., Hariri, A. & Potts, C. Single‐machine scheduling to minimize maximumtardiness with minimum number of tardy jobs. Annals of Operations Research 92, 107–123 (1999). https://doi.org/10.1023/A:1018974428912
Issue Date:
DOI: https://doi.org/10.1023/A:1018974428912