Investigating a claim about resource complexity measure

Document Type : Research Article


Department of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-4697, Tehran, Iran.


The utilization factor (UF) measures the ratio of the total resources’ amount required to the availability of resources’ amount during the life cycle of a project. In 1982, in the journal of Management Science, Kurtulus and Davis claimed that “If two resource-constrained problems for each type of resource have the same UF’s value in each period of time, then each problem is subjected to the same amount of delay provided that the same sequencing rule is used (If different tie-breaking rules are used, a different schedule may be obtained)”. In this paper, with a counterexample, we show that the claim of authors cannot be justified.


Main Subjects

 1. Davis, E.W. Project network summary measures constrained resource scheduling, IIE Trans. 7(2), (1975), 132–142.
2. Demeulemeester E., Vanhoucke M. and Herroelen W. RanGen: A random network generator for activity on the node networks, J. Sched. 6(1) (2003), 17–38.
3. Kolisch, R., Sprecher, A. and Drexl, A. Characterization and generation of a general class of resource constrained project scheduling problems, Manage Sci. 41 (10) (1975), 1693–1703.
4. Kurtulus, I. and Davis E.W. Multi Project Scheduling: Categorization of Heuristic Rules Performance, Manage Sci. 28(2) (1982), 161–172.
5. Kurtulus I. and Narula S.C. Multi Project Scheduling: Analysis of Project Management, IIE Trans. 17(1) (1985), 58–65.
6. Yoosefzadeh, H.R., Tareghian, H.R., and Farahi, M.H. Tri-directional Scheduling Scheme: Theory and Computation, J. Math. Model. Algo rithms. 9(4) (2010), 357–373.