Tropical (idempotent) mathematics, which investigates the theory and applications of algebraic systems with idempotent operations, finds increasing use in solving challenging problems in operations research, including time-constrained scheduling problems. We consider a project that consists of a set of activities performed in parallel under temporal constraints on their start and finish times. The problem of interest is to schedule the activities to minimize both the project makespan and the maximum flow-time over all activities. We formulate and solve the problem in the framework of tropical mathematics as a tropical bi-criteria optimization problem. As a result, we derive a complete Pareto-optimal solution in a direct explicit form, ready for further analysis and straightforward computation. We examine the computational complexity of the solution and give an illustrative example.