Complexity of some project scheduling problem with nonrenewable resources
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 105-112 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the project scheduling problem with nonreneawble resources and criterion of Net Present Value is considered. We prove that this problem is strongly $NP$-hard. Special case of independent jobs was investigated. We propose the exact algorithm for this case of the problem which is based on dynamic programming scheme. We obtain the cases of the problem when the algorithm became pseudopolynomial.
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V. V. Servakh; T. A. Shcherbinina. Complexity of some project scheduling problem with nonrenewable resources. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 105-112. http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a6/

[1] Gimadi E. Kh., Zalyubovskii V. V., Sevastyanov S. V., “Polinomialnaya razreshimost zadach kalendarnogo planirovaniya so skladiruemymi resursami i direktivnymi srokami”, Diskretnyi analiz i issledovanie operatsii. Ser. 2, 7:1 (2000), 9–34 | MR | Zbl

[2] Servakh V. V., Scherbinina T. A., “O zadache kalendarnogo planirovaniya proekta s razlichnymi kriteriyami i skladiruemymi resursami”, Problemy optimizatsii i ekonomicheskie prilozheniya, III Vseros. konf. (Omsk, 2006), 125

[3] Brucker P., Drexl A., Mohring R. et al., “Resource-constrained Project Scheduling: Notation, Classification, Models, and Methods”, European Journal of Operational Research, 112 (1999), 3–41 | DOI | Zbl

[4] Brucker P., Lenstra J. K., Rinnooy Kan A. H. G., Complexity of Machine Scheduling Problems, BW 43, Math. Cent. Afd. Math. Beslisk., Amsterdam, 1975

[5] Doersch R. H., Patterson J. H., “Scheduling a Project to Maximaze its Present Value: A Zero-one Programming Approach”, Management Science, 23:8 (1977), 882–889 | DOI | Zbl

[6] Garey M. R., Johnson D. S., “Complexity Result for Multiprocessor Scheduling Under Resource Constraints”, SIAM J. Comput., 4:4 (1975), 397–411 | DOI | MR | Zbl

[7] Gimadi E., Sevastianov S., “On Solvability of the Project Scheduling Problem with Accumulative Resources of an Arbitrary Sign”, Operations Research Proceedings, Springer, 2002, 241–246

[8] Icmeli O., Erenguc S. S., “A Branch and Bound Procedure for the Resource Constrained Project Scheduling Problem with Discounted Cash Flows”, Management Science, 42:10 (1996), 1395–1408 | DOI | Zbl

[9] Herroelen W. S., Van Dommelen P., Demeulemeester E. L., “Project Network Models with Discounted Cash Flows a Quided Tour through Recent Revelopments”, European Journal of Operational Research, 100 (1997), 97–121 | DOI | Zbl

[10] Karp R. M., “Reducibility among Combinatorial Problems”, Complexity of Computer Computations, eds. R. E. Miller, J. W. Thatcher (eds.), Plenum Press, N.Y., 1972, 85–103 | DOI | MR

[11] Kolish R., Padman R., “An Integrated Survey of Deterministic Project Scheduling”, OMEGA — The International Journal of Management Science, 29 (2001), 249–272 | DOI