This paper addresses the pick-and-place robot scheduling problem with rejection and compatibility (PPRC) encountered in a major French mail delivery provider. The problem arises on a shop floor where boxes arrive dynamically (in an unknown order), and a robot or some operators place these boxes in packages according to their destinations. As the company invested in a pick-and-place robot to relieve the operators, the problem aims to maximize the workload of the robots. We provide a mathematical formulation of the PPRC, identify special cases solvable in polynomial time, and propose different online heuristics. Based on real data from our industrial case study, we study the performance of these heuristics, and we provide sensitivity analysis. The results show that the heuristic performs well when compared with the optimal off-line solution.