Maniezzo and Mingozzi (Oper. Res. Lett. 25 (1999) 175–182) study a project scheduling problem with irregular starting time costs. Starting from the assumption that its computational complexity status is open, they develop a branch-and-bound procedure and they identify special cases that are solvable in polynomial time. In this note, we present a collection of previously established results which show that the general problem is solvable in polynomial time. This collection may serve as a useful guide to the literature, since this polynomial-time solvability has been rediscovered in different contexts or using different methods. In addition, we briefly review some related results for specializations and generalizations of the problem.