Jackson’s pseudo-preemptive schedule and cumulative scheduling problems. (English) Zbl 1058.90023

Summary: The aim of this paper is to show the usefulness of the Jackson’s pseudo-preemptive schedule (JPPS) for solving cumulative scheduling problems. JPPS was introduced for the \(m\)-processor scheduling problem \(Pm/r_i, q_i/C_{\max}\). In the latter problem, a set \(I\) of \(n\) operations has to be scheduled without preemption on \(m\) identical processors in order to minimize the makespan. Each operation \(i\) has a release date (or head) \(r_i\), a processing time \(p_i\), and a tail \(q_i\). In the cumulative scheduling problem (CuSP), an operation \(i\) requires a constant amount \(e_i\) of processors throughout its processing. A CuSP is obtained, for instance, from the resource constrained project scheduling problem (RCPSP) by choosing a resource and relaxing the constraints induced by the other resources. We state new properties on JPPS and we show that it can be used for studying the CuSP and for performing adjustments of heads and tails using a strategy very close to the one designed by Carlier and Pinson for the \(1/r_i\), \(q_i/C_{\max}\) sequencing problem. It confirms the interest of JPPS for solving RCPSP.


90B35 Deterministic scheduling theory in operations research
Full Text: DOI


[1] Balas, E., Machine sequencing via disjunctive graphsan implicit enumeration algorithm, Oper. Res, 17, 941-957 (1969) · Zbl 0183.49404
[2] Baptiste, P.; Le Pape, C.; Nuijten, W., Satifiability tests and time-bound adjustments for cumulative scheduling problems, Ann. Oper. Res, 92, 305-333 (1999) · Zbl 0958.90037
[3] Brucker, P.; Jurisch, B.; Krämer, A., The job-shop and immediate selections, Ann. Oper. Res, 50, 93-114 (1992)
[4] Brucker, P.; Jurisch, B.; Sievers, B., A branch & bound algorithm for the job-shop scheduling problem, Discrete Appl. Math, 49, 109-127 (1994) · Zbl 0802.90057
[5] Carlier, J., The one-machine sequencing problem, European J. Oper. Res, 11, 42-47 (1982) · Zbl 0482.90045
[7] Carlier, J., Scheduling jobs with release dates and tails on identical machines to minimize makespan, European J. Oper. Res, 29, 298-306 (1987) · Zbl 0622.90049
[8] Carlier, J.; Latapie, B., Une méthode arborescente pour résoudre les problèmes cumulatifs, RAIRO, 25, 3, 311-340 (1991) · Zbl 0733.90036
[9] Carlier, J.; Pinson, E., An algorithm for solving the job shop problem, Management Sci, 35, 164-176 (1989) · Zbl 0677.90036
[10] Carlier, J.; Pinson, E., A practical use of Jackson’s preemptive schedule for solving the job-shop problem, Ann. Oper. Res, 26, 269-287 (1991) · Zbl 0709.90061
[11] Carlier, J.; Pinson, E., Adjusting heads and tails for the job-shop problem, European J. Oper. Res, 78, 146-161 (1994) · Zbl 0812.90063
[12] Carlier, J.; Pinson, E., Jackson’s pseudo preemptive schedule for the \(Pm/r_i, q_{i\) · Zbl 0911.90203
[13] Coffman, E. G.; Muntz, R. R., Preemptive scheduling on two-processor systems, IEEE Trans. Comput, C-18, 1014-1020 (1970) · Zbl 0184.20504
[14] Demeulemeester, E.; Herroelen, W., A branch and bound procedure for the multiple resource-constrained project scheduling problem, Management Sci, 38, 1803-1818 (1992) · Zbl 0761.90059
[15] Demeulemeester, E.; Herroelen, W., Recent advances in branch and bound procedures for resource-constrained project scheduling problems, (Chretienne, P.; etal., Scheduling Theory and Its Applications (1995), Wiley: Wiley New York)
[17] Horn, W., Some simple scheduling algorithms, Naval. Res. Logist. Quart, 21, 177-185 (1974) · Zbl 0276.90024
[20] Lageweg, B. J.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Minimizing maximum lateness on one machinecomputational experience and some applications, Statist. Neerlandica, 30, 25-41 (1976) · Zbl 0336.90029
[21] Lawler, E. L., Preemptive scheduling of precedence constrainted jobs on parallel machines, (Dempster; etal., Deterministic and Stochastic Scheduling (1982), Reidel: Reidel Dordrecht), 101-123 · Zbl 0495.68031
[22] Liu, Z.; Sanlaville, E., Profile scheduling by list algorithms, (Chretienne, P.; etal., Scheduling Theory and Its Applications (1995), Wiley: Wiley New York)
[24] Pinson, E., The job shop scheduling problem : a concise survey and recent developments, (Chretienne, P.; etal., Scheduling Theory and Its Applications (1995), Wiley: Wiley New York)
[25] Sanlaville, E., Nearly on line scheduling of preemptive independent tasks, Discrete Appl. Math, 57, 229-241 (1995) · Zbl 0830.68011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.