We show the polynomial solvability of the PERT-COST project scheduling problem in the case of: (i) the objective being a piecewise-linear, convex (possibly, non- monotone) function of the job durations as well as of job start/finish times, and (ii) the precedence relations between jobs being presented in the form of a general (not necessary, acyclic) directed graph with arc lengths of any sign. For the latter problem, we present a network flow algorithm (of pseudo-linear complexity) which is easy to implement and which behaves well when the objective values grow slowly with the growth of the problem size while the number of breakpoints in the objective grows fast
