Abstract
The scheduling model we consider now is more complicated than the previous ones, because any task, besides processors, may require for its processing some additional scarce resources. Resources, depending on their nature, may be classified into types and categories. The classification into types takes into account only the functions resources fulfill: resources of the same type are assumed to fulfill the same functions. The classification into categories will concern two points of view. First, we differentiate three categories of resources from the viewpoint of resource constraints. We will call a resource renewable, if only its total usage, i.e. temporary availability at every moment, is constrained. A resource is called non-renewable, if only its total consumption, i.e. integral availability up to any given moment, is constrained (in other words this resource once used by some task cannot be assigned to any other task). A resource is called doubly constrained, if both total usage and total consumption are constrained. Secondly, we distinguish two resource categories from the viewpoint of resource divisibility: discrete (i.e. discretely-divisible) and continuous (i.e. continuously-divisible) resources. In other words, by a discrete resource we will understand a resource which can be allocated to tasks in discrete amounts from a given finite set of possible allocations, which in particular may consist of one element only. Continuous resources, on the other hand, can be allocated in arbitrary, a priori unknown, amounts from given intervals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Błażewicz, J. Barcelo, W. Kubiak, H. Rock, Scheduling tasks on two processors with deadlines and additional resources, European J. Oper. Res. 26, 1986, 364–370.
J. Błażewicz, W. Cellary, R. Słowiński, J. Weglarz, Scheduling under Resource Constraints: Deterministic Models, J. C. Baltzer, Basel, 1986.
P. Brucker, A. Drexl, R. Möhring, K. Neumann, E. Pesch, Resource-constrained project scheduling: notation, classification, models, and methods, European J. Oper. Res. 112, 1999, 3–41.
J. Błażewicz, K. Ecker, A linear time algorithm for restricted bin packing and scheduling problems, Oper. Res. Lett. 2, 1983, 80–83.
J. Błażewicz, K. Ecker, Multiprocessor task scheduling with resource requirements, Real-Time Systems 6, 1994, 37–54.
J. Błażewicz, W. Kubiak, J. Szwarcfiter, Scheduling independent fixed-type tasks, in: R. Słowiński, J. Weglarz (eds.), Advances in Project Scheduling, Elsevier, Amsterdam, 1989, 225–236.
J. Błażewicz, Complexity of computer scheduling algorithms under resource constraints, Proc. I Meeting AFCET-SMF on Applied Mathematics, Palaiseau, 1978, 169–178.
J. Błażewicz, J. K. Lenstra, A. H. G. Rinnooy Kan, Scheduling subject to resource constraints: classification and complexity, Discrete Appl. Math. 5, 1983, 11–24.
E. G. Coffman Jr., P. J. Denning, Operating Systems Theory, Prentice-Hall, Englewood Cliffs, N. J., 1973.
E. G. Coffman Jr., M. R. Garey, D. S. Johnson, Approximation algorithms for bin-packing-an updated survey, in: G. Ausiello, M. Lucertini, P. Serafini (eds.), Algorithms Design for Computer System Design, Springer, Vienna, 1984, 49–106.
E. G. Coffman Jr., M. R. Garey, D. S. Johnson, A. S. La Paugh, Scheduling file transfers in a distributed network, Proc. 2nd ACM SIGACT-SIGOPS Symp. on Principles of Distributed Computing, Montreal, 1983.
T.C.E. Cheng, A. Janiak, A permutation flow-shop scheduling problem with convex models of operation processing times, Annals of Oper. Res. 96, 2000, 39–60.
T.C.E. Cheng, A. Janiak, M.Y. Kovalyov, Bicriterion single machine scheduling with resource dependent processing times, SIAM J. Optim. 8, 1998, 617–630.
T.C.E. Cheng, A. Janiak, M.Y. Kovalyov, Single machine batch scheduling with resource dependent setup and processing times, European J. Oper. Res. 135, 2001, 177–183.
M. R. Garey, R. L. Graham, Bounds for multiprocessor scheduling with resource constraints, SIAM J. Comput. 4, 1975, 187–200.
M. R. Garey, D. S. Johnson, Complexity results for multiprocessor scheduling under resource constraints, SIAM J. Comput. 4, 1975, 397–411.
J. Grabowski, A. Janiak, Job-shop scheduling with resource-time models of operations, European J. Oper. Res. 28, 1987, 58–73.
D. Iwanowski, A. Janiak, A. Rogala, Scheduling jobs with start time and resource dependent processing times, in: K. Inderfurth, G. Schwodianer, W. Domschke, F. Juhnke, P. Kleinschmidt, G. Wascher (eds), Oper. Res. Proc. 1999, Springer, 2000, 389–396.
A. Janiak, One-machine scheduling problems with resource constraints, in: A. Prékopa, J. Szelezán, B. Strazicky (eds.), System Modelling and Optimization, Lecture Notes in Control and Information Sciences, Vol. 84, Springer, Berlin, 1986, 358–364.
A. Janiak, Flow-shop scheduling with controllable operation processing times, in: H. P. Geering, M. Mansour (eds.), Large Scale Systems: Theory and Applications, Pergamon Press, 1986, 602–605.
A. Janiak, Time-optimal control in a single machine problem with resource constraints, Automatica 22, 1986, 745–747.
A. Janiak, Single machine sequencing with linear models of jobs subject to precedence constraints, Archiwum Aut. i Telem. 33, 1988, 203–210.
A. Janiak, Permutacyjny problem przepływowy z liniowymi modelami operacji, Zeszyty Naukowe Politechniki Ślqskiej. ser. Automatyka 94, 1988, 125–138.
A. Janiak, Minimization of the total resource consumption in permutation flow-shop sequencing subject to a given makespan, J. Model. Simul. Control 13, 1988, 1–11.
A. Janiak, General flow-shop scheduling with resource constraints, Internal J. Production Res. 26, 1988, 1089–1103.
A. Janiak, Minimization of resource consumption under a given deadline in two-processor flow-shop scheduling problem, Inform. Process. Lett. 32, 1989, 101–112.
A. Janiak, Minimization of the blooming mill standstills-mathematical model. Suboptimal algorithms, Zesz. Nauk. AGH s. Mechanika 8, 1989, 37–49.
A. Janiak, Dokladne i przyblizone algorytmy szeregowania zadan i rozdzialu zasobow w dyskretnych procesach przemyslowych, Prace Naukowe Instytutu Cybernetyki Technicznej Politechniki Wroclawskiej 87, Monografie 20, Wroclaw, 1991.
A. Janiak, Single machine scheduling problem with a common deadline and resource dependent release dates, European J. Oper. Res. 53, 1991, 317–325.
A. Janiak, Computational complexity analysis of single machine scheduling problems with job release dates dependent on resources, in: U. Zimmermann, U. Derigs, W. Gaul, R.H. Möhring, K.P. Schuster (eds.), Oper. Res. Proc. 1996, Springer, Berlin, 1997, 203–207.
A. Janiak, Single machine sequencing with linear models of release dates, Naval Res. Logistics, 45, 1998, 99–113.
A. Janiak, Minimization of the makespan in a two-machine problem under given resource constraints, European J. Oper. Res. 107, 1988, 325–337.
A. Janiak, Chosen Problems and Algorithms of Scheduling and Resource Allocation, Akademicka Oficyna Wydawnicza PLJ, Warszawa 1999.
A. Janiak, T. C. E. Cheng, Resource optimal control in some simple-machine scheduling problems, IEEE Trans. Aut. Control 39, 1994, 1243–1246.
A. Janiak, M.Y. Kovalyov, Single machine scheduling subject to deadlines and resource dependent processing times, European J. Oper. Res. 94, 1996, 284–291.
A. Janiak, M.Y. Kovalyov, M.-C. Portmann, Single machine group scheduling with resource dependent setups and processing times, European J. Oper. Res. 162, 2005, 112–121.
A. Janiak, C.-L. Li, Scheduling to minimize the total weighted completion time with a constraint on the release time resource consumption, Math. Comput. Modelling 20, 1994, 53–58.
A. Janiak, M.-C. Portmann, Genetic algorithm for the permutation flow-shop scheduling problem with linear models of operations, Annals of Oper. Res. 83, 1998, 95–114.
A. Janiak, A. Stankiewicz, On time-optimal control of a sequence of projects of activities under time-variable resource, IEEE Trans. Aut. Control 33, 1988, 313–316.
A. Janiak, T. Szkodny, Job-shop scheduling with convex models of operations, Math. Comput. Modelling 20, 1994, 59–68.
J. Józefowska, J. Weglarz, On a methodology for discrete-continuous scheduling, Research Report RA-004/95, Institute of Computing Science, Poznań University of Technology, Poznań, 1995.
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4, 1984, 373–395.
O. Kariv, S. Even, An O(n2) algorithm for maximum matching in general graphs, Proc. 16th Annual IEEE Symp. on Foundations of Computer Science, 1975, 100–112.
K. L. Krause, V. Y. Shen, H. D. Schwetman, Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems, J. Assoc. Comput. Mach. 22, 1975, 522–550. Erratum: J. Assoc. Comput. Mach. 24, 1977, 527.
E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York 1976.
H. W. Lenstra, Jr., Integer programming with a fixed number of variables, Math. Oper. Res. 8, 1983, 538–548.
R. McNaughton, Scheduling with deadlines and loss functions, Management Sci. 12, 1959, 1–12.
C.T. Ng, T.C.E. Cheng, A. Janiak, M. Y. Kovalyov, Group scheduling with controllable setup and processing times: Minimizing total weighted completion time, Annals of Oper. Res. 133, 2005, 163–174.
E. Nowicki, S. Zdrzalka, Optimal control of a complex of independent operations, Internal J. Systems Sci. 12, 1981, 77–93.
E. Nowicki, S. Zdrzalka, Optimal control policies for resource allocation in an activity network, European J. Oper. Res. 16, 1984, 198–214.
E. Nowicki, S. Zdrzalka, Scheduling jobs with controllable processing times as an optimal control problem, Internat. J. Control 39, 1984, 839–848.
R. Słowiński, J. Weglarz (eds.), Advances in Project Scheduling, Elsevier, Amsterdam, 1989.
J. Weglarz, J. Błażewicz, W. Cellary, R. Słowiński, An automatic revised simplex method for constrained resource network scheduling, ACM Trans. Math. Software 3, 295–300, 1977.
J. Weglarz, Multiprocessor scheduling with memory allocation-a deterministic approach, IEEE Trans. Comput. C-29, 1980, 703–709.
J. Weglarz, Project scheduling with continuously-divisible, doubly constrained resources, Management Sci. 27, 1981, 1040–1052.
J. Weglarz, Modelling and control of dynamic resource allocation project scheduling systems, in: S. G. Tzafestas (ed.), Optimization and Control of Dynamic Operational Research Models, North-Holland, Amsterdam, 1982.
J. Weglarz, Project scheduling under continuous processing speed vs. resource amount functions, 1989. in: R. Słowiński, J. Weglarz (eds.), Advances in Project Scheduling, Elsevier, 1989.
J. Weglarz, Synthesis problems in allocating continuous, doubly constrained resources, in: H. E. Bradley (ed.), Operational Research’ 90-Selected Papers from the 12 th IFORS International Conference, Pergamon Press, Oxford, 1991, 715–725.
J. Weglarz (ed.), Project Scheduling-Recent Models, Algorithms and Applications, Kluwer Academic Publ., 1999.
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Scheduling under Resource Constraints. In: Handbook on Scheduling. International Handbook on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32220-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-32220-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28046-0
Online ISBN: 978-3-540-32220-7
eBook Packages: Business and EconomicsBusiness and Management (R0)
Publish with us
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.