Abstract
In this paper some discrete-continuous project scheduling problems to minimize the makespan are considered. These problems are characterized by the fact that activities of a project simultaneously require for their execution discrete and continuous resources. A class of these problems is considered where the number of discrete resources is arbitrary, and one continuous, renewable, limited resource occurs. A methodology for solving the defined problems is presented. The continuous resource allocation problem is analyzed. An exact, as well as a heuristic approach to the problem is discussed. The idea of the continuous resource discretization is described, and a special case of the problem with identical processing rate functions is analyzed. Some computational experiments for evaluating the efficiency of the proposed heuristic approaches are presented. Conclusions and directions for future research are given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Błażewicz, J., Kovalyov, M.Y., Machowiak, M., Trystram, D., Węglarz, J.: Malleable task scheduling to minimize the makespan. Ann. Oper. Res. 129(1–4), 65–80 (2004)
Burkov, V.N.: Raspriedielenije riesursow kak zadacza optimalnogo bystrodiejstwia. Avtom. Telem. 27(7) (1966)
Demeulemeester, E.L., Herroelen, W.S.: Project Scheduling—A Research Handbook. Kluwer, Boston (2002)
Floudas, C.A.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, Oxford (1995)
Herroelen, W.S., Demeulemeester, E.L., De Reyck, B.: A classification scheme for project scheduling. In: Węglarz, J. (ed.) Project Scheduling—Recent Models, Algorithms and Applications, pp. 1–26. Kluwer, Dordrecht (1999)
Janiak, A.: Scheduling and resource allocation problems in some flow type manufacturing processes. In: Fandel, G., Zapfel, G. (eds.) Modern Production Concepts, pp. 404–415. Springer, Berlin (1991)
Janiak, A.: Single machine scheduling problem with a common deadline and resource dependent release dates. Eur. J. Oper. Res. 53(3), 317–325 (1991)
Józefowska, J., Waligóra, G.: Heuristic procedures for allocating the continuous resource in discrete-continuous scheduling problems. Found. Comput. Decis. Sci. 29(4), 315–328 (2004)
Józefowska, J., Węglarz, J.: On a methodology for discrete-continuous scheduling. Eur. J. Oper. Res. 107(2), 338–353 (1998)
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., Węglarz, J.: Project scheduling under discrete and continuous resources. In: Węglarz, J. (ed.) Project Scheduling—Recent Models, Algorithms and Applications, pp. 289–308. Kluwer, Dordrecht (1999)
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., Węglarz, J.: Solving the discrete-continuous project scheduling problem via its discretization. Math. Methods Oper. Res. 52(3), 489–499 (2000)
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., Węglarz, J.: Simulated annealing for multi-mode resource-constrained project scheduling problem. Ann. Oper. Res. 102(1–4), 137–155 (2001)
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., Węglarz, J.: A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan. J. Sched. 5(6), 487–499 (2002)
Kelley, J.E.: The critical path method: resource planning and scheduling. In: Muth, J.F., Thompson, G.L. (eds.) Industrial Scheduling, pp. 347–365. Prentice-Hall, Englewood Cliffs (1963)
Kolisch, R.: Project Scheduling under Resource Constraints—Efficient Heuristics for Several Problem Classes. Physica, Heidelberg (1995)
Lawrence, C., Zhou, J.L., Tits, A.L.: Users guide for CFSQP Version 2.5. Available by email: andre@eng.umd.edu (1997)
Waligóra, G.: Discrete-continuous project scheduling with discounted cash flows—a tabu search approach. Comput. Oper. Res. 35(7), 2141–2153 (2008)
Waligóra, G.: Tabu search for discrete-continuous scheduling problems with heuristic continuous resource allocation. Eur. J. Oper. Res. 193(3), 849–856 (2009)
Węglarz, J.: Time-optimal control of resource allocation in a complex of operations framework. IEEE Trans. Syst. Man Cybern. 6(11), 783–788 (1976)
Węglarz, J.: Multiprocessor scheduling with memory allocation—a deterministic approach. IEEE Trans. Comput. C-29, 703–709 (1980)
Węglarz, J.: Project scheduling with continuously-divisible, doubly constrained resources. Manag. Sci. 27(9), 1040–1052 (1981)
Węglarz, J.: Modelling and control of dynamic resource allocation project scheduling systems. In: Tzafestas, S.G. (ed.) Optimization and Control of Dynamic Operational Research Models, pp. 105–140. North-Holland, Amsterdam (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Waligóra, G. Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan. Comput Optim Appl 48, 399–421 (2011). https://doi.org/10.1007/s10589-010-9343-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10589-010-9343-5