The robustness of scheduling for trade-off balancing in one-stage production

Production and operations management (POM) faces three challenges in production scheduling, specifically trade-offs at two levels and variation in processing times. Trade-offs at level one are between key performance indicators (KPIs), to balance which we apply a modern portfolio theory (MPT) model. Trade-offs at level two are between the expected value and the variance in the MPT model, to balance which we apply a Lagrange multiplier (LM) model. Because variation in processing times blurs the boundary of solution space for balancing trade-offs at the two levels, we propose an innovative scheme to model the state space of production by linking the concepts of displacement and velocity in physics with the completion time and material flow in production, respectively. Through our modeling scheme, we explain why a scheduling method can be robust to variation in processing times to some extent.