  We consider the Generalized Makespan Problem (GMP) on unrelated machines,
where we are given $n$ jobs and $m$ machines and each job $j$ has arbitrary
processing time $p_{ij}$ on machine $i$. Additionally, there is a general
symmetric monotone norm $\psi_i$ for each machine $i$, that determines the load
on machine $i$ as a function of the sizes of jobs assigned to it. The goal is
to assign the jobs to minimize the maximum machine load.
  Recently, Deng, Li, and Rabani (SODA'22) gave a $3$ approximation for GMP
when the $\psi_i$ are top-$k$ norms, and they ask the question whether an
$O(1)$ approximation exists for general norms $\psi$? We answer this negatively
and show that, under natural complexity assumptions, there is some fixed
constant $\delta>0$, such that GMP is $\Omega(\log^{\delta} n)$ hard to
approximate. We also give an $\Omega(\log^{1/2} n)$ integrality gap for the
natural configuration LP.
