In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for the non-preemptive and the preemptive problems have a ratio of $O(\log n)$, where $n$ is the number of jobs. This means that there exist instances for which the lower bound of Mingozzi has a bad relative error of $O(\log n)$, and the calculation of this bound is an NP-hard problem. In addition, we give a proof that there exists a type of instances for which known approximation algorithms with polynomial time complexity have an approximation ratio of at least equal to $O(\sqrt{n})$, and known lower bounds have a relative error of at least equal to $O(\log n)$. This type of instances corresponds to the single machine parallel-batch scheduling problem $1|p-batch, b=\infty|C_{max}$
E.R. Gafarov, A.A. Lazarev and F. Werner (2012), Approximability Results for the Resource-Constrained Project Scheduling Problem with a Single Type of Resources. Annals of Operations Research, doi:10.1007/s10479-012-1106-5 (accepted, in print) (journal impact factor 2018: 2.284). Q1