Abstract
In this chapter project scheduling under an additional continuous resource is considered. In particular, we deal with discrete-continuous project scheduling problems to minimize the project duration. These problems are characterized by the fact that activities of a project simultaneously require discrete and continuous resources for their execution. A class of the problems is considered, where the number of discrete resources is arbitrary, and there is one continuous, renewable resource, whose total amount available at a time is limited. Activities are nonpreemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. Theoretical results for the cases of convex and concave processing rate functions of activities are presented, and the methodology developed for solving the problems with concave functions is described in detail. Some conclusions and final remarks are given.
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Brucker P, Drexl A, Möhring R, Neumann K, Pesch E (1999) Resource-constrained project scheduling: notation, classification, models and methods. Eur J Oper Res 112(1):3–41
Floudas CA (1995) Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, Oxford
Józefowska J, Wȩglarz J (1998) On a methodology for discrete-continuous scheduling. Eur J Oper Res 107(2):338–353
Józefowska J, Mika M, Różycki R, Waligóra G, Wȩglarz J (2000) Solving the discrete-continuous project scheduling problem via its discretization. Math Method Oper Res 52(3):489–499
Józefowska J, Mika M, Różycki R, Waligóra G, Wȩglarz J (2002) A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan. J Sched 5(6):487–499
Różycki R, Wȩglarz J (2014) Power-aware scheduling of preemptable jobs on identical parallel processors to minimize makespan. Ann Oper Res 213(1):235–252
Waligóra G (2009) Tabu search for discrete-continuous scheduling problems with heuristic continuous resource allocation. Eur J Oper Res 193(3):849–856
Waligóra G (2011) Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan. Comput Optim Appl 48(2):399–421
Waligóra G (2014) Discrete-continuous project scheduling with discounted cash inflows and various payment models – a review of recent results. Ann Oper Res 213(1):319–340
Wȩglarz J (1976) Time-optimal control of resource allocation in a complex of operations framework. IEEE T Syst Man Cyb 6(11):783–788
Wȩglarz J (1980) Multiprocessor scheduling with memory allocation – a deterministic approach. IEEE T Comput 29(8):703–709
Wȩglarz J (1981) Project scheduling with continuously-divisible, doubly constrained resources. Manag Sci 27(9):1040–1052
Wȩglarz J, Józefowska J, Mika M, Waligóra G (2011) Project scheduling with finite or infinite number of activity processing modes – a survey. Eur J Oper Res 208(3):177–205
Acknowledgements
This chapter is a part of the project no. 2013/11/B/ST6/00970, funded by the Polish National Science Centre.
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Waligóra, G., Wȩglarz, J. (2015). Continuous Resources. In: Schwindt, C., Zimmermann, J. (eds) Handbook on Project Management and Scheduling Vol.1. International Handbooks on Information Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-05443-8_10
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DOI: https://doi.org/10.1007/978-3-319-05443-8_10
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