Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals
RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 1, pp. 71-83.

This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an $O\left(nlogn\right)$ algorithm (where $n$ is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.

Classification : 90B36
Mots clés : single machine scheduling, release and due dates, deadlines, number of late jobs
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title = {Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals},
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Gordon, Valery S.; Werner, F.; Yanushkevich, O. A. Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals. RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 1, pp. 71-83. http://www.numdam.org/item/RO_2001__35_1_71_0/

[1] V. Gordon, E. Potapneva and F. Werner, Single machine scheduling with deadlines, release and due dates. Optimization 42 (1997) 219-244. | MR 1612048 | Zbl 0891.90083

[2] V.S. Gordon and V.S. Tanaev, Single machine deterministic scheduling with step functions of penalties, in: Computers in Engineering. Minsk (1971) 3-8 (in Russian).

[3] R.L. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5 (1979) 287-326. | MR 558574 | Zbl 0411.90044

[4] R.M. Karp, Reducibility among combinatorial problems, edited by R.E. Miller and J.W. Thatcher, Complexity of Computer Computations. Plenum Press, New York (1972) 85-103. | MR 378476

[5] H. Kise, T. Ibaraki and H. Mine, A solvable case of the one-machine scheduling problem with ready and due times. Oper. Res. 26 (1978) 121-126. | MR 462552 | Zbl 0377.90054

[6] E.L. Lawler, Sequencing to minimize the weighted number of tardy jobs. RAIRO Oper. Res. 10 (1976) 27-33. | MR 503698 | Zbl 0333.68044

[7] E.L. Lawler, Scheduling a single machine to minimize the number of late jobs. Preprint. Computer Science Division, University of California, Berkeley (1982).

[8] E.L. Lawler, A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs. Ann. Oper. Res. 26 (1990) 125-133. | MR 1087819 | Zbl 0709.90064

[9] E.L. Lawler, Knapsack-like scheduling problems, the Moore-Hodgson algorithm and the “tower of sets” property. Math. Comput. Modelling 20 (1994) 91-106. | Zbl 0810.90070

[10] E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling: Algorithms and complexity, edited by S.C. Graves, A.H.G. Rinnooy Kan and P.H. Zipkin, Logistics of Production and Inventory. North-Holland, Handbooks Oper. Res. Management Sci. 4 (1993) 445-522.

[11] E.L. Lawler and J.M. Moore, A functional equation and its application to resource allocation and sequencing problems. Management Sci. 16 (1969) 77-84. | Zbl 0184.23303

[12] J.K. Lenstra and A.H.G. Rinnooy Kan, Complexity results for scheduling chains on a single machine. European J. Oper. Res. 4 (1982) 270-275. | MR 568928 | Zbl 0439.90041

[13] J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems. Ann. Discrete Math. 1 (1977) 343-362. | MR 456421 | Zbl 0353.68067

[14] C.L. Monma, Linear-time algorithms for scheduling on parallel processors. Oper. Res. 30 (1980) 116-124. | Zbl 0481.90048

[15] J.M. Moore, An $n$ job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15 (1968) 102-109. | Zbl 0164.20002

[16] J.B. Sidney, An extension of Moore's due date algorithm, edited by S.E. Elmaghraby, Symposium on the Theory of Scheduling and its Applications. Springer, Berlin, Lecture Notes in Econom. and Math. Systems 86 (1973) 393-398. | Zbl 0273.90032

[17] V.S. Tanaev and V.S. Gordon, On scheduling to minimize the weighted number of late jobs. Vestsi Akad. Navuk Belarus Ser. Fizi.-Mat. Navuk 6 (1983) 3-9 (in Russian). | MR 714131 | Zbl 0534.90045

[18] V.S. Tanaev, V.S. Gordon and Y.M. Shafransky, Scheduling Theory. Single-Stage Systems. Kluwer Academic, Dordrecht (1994). | MR 1331600 | Zbl 0827.90079