We consider the discrete version of the well-known time-cost tradeoff problem for project networks, which has been extensively studied in the project management literature. We prove a strong in-approximability result with respect to polynomial time bicriteria approximation algorithms for this problem.
Deineko, V. G., & Woeginger, G. J. (2001). Hardness of approximation of the discrete time-cost tradeoff problem. Operations Research Letters, 29(5), 207-210. https://doi.org/10.1016/S0167-6377(01)00102-X