A Review of Robust Machine Scheduling

Robust optimization (RO) has been recognized as an effective means to deal with unanticipated events in highly uncertain and risky environments. This paper systematically reviews two types of emerging RO machine scheduling approaches - robust machine scheduling (R-MS) and distributionally R-MS (DR-MS) methods - which usually offer tractable formulations and analytical results for machine scheduling problems under uncertainty. First, after highlighting the advantages of RO methods over the stochastic approach in terms of tractability and robustness, we use the bibliometric method to analyze the literature related to R-MS/DR-MS problems and classify them from the following aspects: (1) uncertain factors, (2) uncertainty descriptions, (3) robustness criteria, (4) machine environments and (5) solution methods. Second, we discuss the uncertainty descriptions, and the robust feasibility and robust optimality criteria. We further provide a state-of-the-art review of R-MS/DR-MS models in different machine environments and discuss the performance of the R-MS/DR-MS models. Third, we review and discuss the existing exact, approximation, online, and heuristic solution methods for solving R-MS/DR-MS models. Finally, we present future research opportunities in two promising areas: green machine scheduling problems and machine learning-enabled algorithms. Note to Practitioners - Machine scheduling plays an essential role in industrial and service systems, such as manufacturing, power generation, transportation and medical systems. However, in practice, scheduling systems usually operate in highly uncertain environments due to noisy measurements, prediction errors, and implementation deviations. To ensure robust feasibility and robust optimality, robust machine scheduling (R-MS) and distributionally R-MS (DR-MS) approaches have been recently proposed to hedge against the uncertainties related to processing time, release time, due date, machine breakdown, etc. This paper provides a comprehensive review of the R-MS/DR-MS models and algorithms in different machine environments from the aspects of uncertainty descriptions, robustness criteria and solution methods. This paper further highlights the challenges of R-MS problems and provides promising and valuable research opportunities in terms of problem formulations and algorithm designs.