Complexity of the discrete time-cost tradeoff problem for project networks
Dunne, E. J.
Ghosh, J. B.
Wells, C. E.
Institute for Operations Research and the Management Sciences (INFORMS)
302 - 306
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This note addresses the discrete version of the well-known time-cost tradeoff problem for project networks, which has been studied previously in the standard project management literature as well as in the related literature on Decision-CPM. All the algorithms proposed thus far for the solution of the general problem exhibit exponential worst-case complexity, with the notable exception of the pseudo-polynomial dynamic program due to Hindelang and Muth. We first demonstrate that this algorithm is flawed, and that when we correct it, it no longer remains pseudo-polynomial. Continuing on in the main result of the note, we show that this is not at all surprising, since the problem is strongly NP-hard. Finally, we discuss the complexities of various network structures and validate an old conjecture that certain structures are necessarily more difficult to solve.