Balancing trade-offs between first three moments of completion times for one-stage production

For one-stage production, operations management faces the following three challenges to make decisions, which are inconsistencies between key performance indicators (KPIs) for production, trade-offs between the expected return and the risk in modern portfolio theory (MPT), and uncertainties in processing times. Traditionally, total completion time (TCT) and variance of completion times (VCT) are two KPIs for one-stage production scheduling, which relate to the first and second moments of completion times, respectively. We question whether the third moment of completion times is good to address the three challenges. In this paper, we introduce the skewness of completion times (SCT) in scheduling, and propose the ToB($a,b$) heuristics for trade-off balancing. Through case studies with 5 levels of processing time uncertainties and compared to existing ToB($\alpha$) heuristics which balance trade-offs between TCT and VCT, we show that our ToB($a,b$) heuristics dominate ToB($\alpha$) heuristics in terms of smaller expected values (E) of weighted sum of deviations from the best solutions of KPIs and smaller risks ($\sigma$) associated with these KPI deviations. Therefore, our ToB($a,b$) heuristics are more robust to balance trade-offs between the three KPIs under processing time uncertainties.