Operations Research ’91 pp 240-243 | Cite as
Minimizing Total Tardiness with Unequal Release Dates
Conference paper
Abstract
We consider the scheduling problem to minimize the total tardiness of a set of n jobs to be processed on a single machine which can perform only one job at a time. No preemption of jobs is allowed. Each job i has a release date ri, a processing time pi and a due date di. The objective is to find a schedule S which minimizes \( T(S) = \sum\nolimits_{{i = 1}}^{n} {{T_{i}}(S)} = \sum\nolimits_{{i = 1}}^{n} {\max ({C_{i}}(S) - {d_{{i,}}}0),} \), where T(S) is the total tardiness of schedule S, Ci(S) and Ti(S) are respectively the completion time and the tardiness of job i in schedule S.
Keywords
Schedule Problem Completion Time Single Machine Single Machine Schedule Total Tardiness
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- Baker K.R., Schräge L.E. (1978), “Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks”, Opns. Res. 26, 111–126CrossRefGoogle Scholar
- Chu C. (1992), “A Branch and Bound Algorithm to Minimize Total Tardiness with Different Release Dates”, Naval Research Logistics 39, to be publishedGoogle Scholar
- Chu C., Portmann M.C. (1991), “Some New Efficient Methods to Solve the n/1/ri/ΣTi Scheduling Problem”, Europ. J. Opnl. Res 56, to be publishedGoogle Scholar
- Du J., Leung J.Y.-T. (1990), “Minimizing Total Tardiness on One Machine is NP-hard”, Math. Oper. Res. 15, 483–495CrossRefGoogle Scholar
- Emmons H. (1969), “One-Machine Sequencing to Minimize Certain Functions of Job Tardiness”, Opns. Res. 17, 701–715CrossRefGoogle Scholar
- Fisher M.L. (1976), “A Dual Algorithm for the One-Machine Scheduling Problem”, Math. Prog. 11, 229–251CrossRefGoogle Scholar
- Gupta S.K., Kyparisis J. (1987), “Single Machine Scheduling Research”, OMEGA Int. J. Mgmt. Sci. 15, 207–227CrossRefGoogle Scholar
- Lawler E.L. (1977), “A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness”, Ann. Disc. Math. 1, 331–342CrossRefGoogle Scholar
- Lawler E.L., Lenstra J.K., Rinnooy Kan A.H.G., Shmoy S.D.B. (1989), “Sequencing and Scheduling: Algorithms and Complexity”, Report BSR8909, Center for Mathematics and Computer Science, AmsterdamGoogle Scholar
- Potts C.N., Van Wassenhove L.N. (1982), “A Decomposition Algorithm for the Single Machine Total Tardiness Problem”, Opns. Res. Lett. 1, 177–181CrossRefGoogle Scholar
- Rinnooy Kan A.H.G. (1976), Machine Sequencing Problems: Classification, Complexity and Computation, Nijhoff, The HagueGoogle Scholar
- Srinivasan V. (1971), “A Hybrid Algorithm for the One-Machine Sequencing Problem to Minimize Total Tardiness”, Nav. Res. Logist. Quart. 18, 317–327CrossRefGoogle Scholar
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© Physica-Verlag Heidelberg 1992