# Planning and Scheduling with Uncertainty in the Steel Sector: A Review
## 4 Scheduling Solutions in Steel Sector Considering Uncertainty: Literature Review
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multicolumn{4}{c}{**Modeling Techniques**} & \multicolumn{4}{c}{**Uncertainty Factor**} \\ \cline{2-10}  & **Stochastic** & **Robust** & **Fuzzy** & **Others** & **Orders** & **Machine** & \
\begin{tabular}{c} **Product** \\ **Specification** \\ \end{tabular} &
\begin{tabular}{c} **Operation** \\ **Time** \\ \end{tabular} \\ \hline Rong and Lahdelmas 2008 [24] & & & X & & & & \(\times\) & \\ [PERSON] et al. 2009 [28] & & X & & & & & \(\times\) \\ [PERSON] and & & & & & & & & \\ [PERSON] 2010 [17] & X & & Montecarlo & X & X & \(\times\) & \(\times\) \\ [PERSON] 2011 [33] & X & & Heuristic & X & & & \(\times\) \\ [PERSON] et al. 2013 [39] & X & & & & & & \(\times\) \\ [PERSON] 2013 [41] & & & & Prediction & & & & \(\times\) \\ [PERSON] et al. 2014 [42] & X & & Forecasting & & X & & \(\times\) \\ [PERSON] et al. 2014 [44] & X & X & & & & & \(\times\) \\ [PERSON] and [PERSON] 2014 [45] & X & & & & & & \(\times\) \\ [PERSON] et al. 2015 [48] & & & & MILP & X & & & \\ [PERSON] and [PERSON] 2015 [49] & & & BN & & & & \(\times\) \\ [PERSON] et al. 2015 [50] & & & Prediction + & & & & \(\times\) \\ [PERSON] et al. 2015 [51] & X & & & MOEA & & & \(\times\) & \\ [PERSON] et al. 2016 [53] & & & GPR & X & & & \(\times\) \\ [PERSON] et al. 2016 [54] & & & IP-MOEA & & & & \(\times\) \\ [PERSON] and [PERSON] 2017 & & & & 2-layer CE & & & & \\ [PERSON] et al. 2017 (b) [58] & & & & EDA & & & & \\ [PERSON] et al. 2017 [60] & & X & & & & & \(\times\) \\ [PERSON] et al. 2017 [64] & & & NSGA-II & X & & & \\ [PERSON] et al. 2018 & & X & & & & & & \(\times\) \\ \(\left[66\right]\) & & & & & & & & \(\times\) \\ [PERSON] et al. 2018 [67] & X & & Forecasting & & & & & \(\times\) \\ [PERSON] et al. 2018 [68] & X & & & & & & & \(\times\) \\ [PERSON] et al. 2018 [70] & X & & & TR-MOEA & & & & \(\times\) \\ [PERSON] et al. 2018 (b) [71] & & & & & & & & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Proactive scheduling models in steel production. layer to calculate the basic processing times and the start casting times, and an inner layer to calculate the machine assignment of the charges. [PERSON] et al. [53] introduce a combined proactive and reactive solution for steelmaking scheduling, combining rescheduling capabilities with Gaussian Process Regression (GPR) procedure to predict the characteristic indexes (slack ratios) aiming to enhance the robustness of the initial schedule of their model against uncertainties. On a similar problem they also propose a continuous Estimation Distribution Algorithm (EDA) [58] applied in two phases: the first EDA calculates the slack ratios as characteristic indexes while a second phase EDA combined with Local Search optimizes the schedule of the jobs at the continuous casting stage. Other authors have relied on multi-objective evolutionary algorithms to deal with the proactive scheduling in steel production. [PERSON] et al. [64] present an Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) to solve the rolling process scheduling under machine breakdown uncertainty, where the breakdown probability is known from historical data analysis. To reduce the duration of the fitness evaluation phase, NSGA-II is combined with a Support Vector Regression (SVR) model. [PERSON] et al. [71] introduce a Target-Ranking Multi-objective Evolutionary Algorithm (TR-MOEA) to solve the charge planning problem tackling the objectives of due date difference within each charge and the minimization of the total weight of open orders. [PERSON] et al. [54] solve the integrated planning of continuous caster and hot rolling processes, considering the throughput uncertainties as interval variables and using a modified Imprecision-propagating Multi-Objective Evolutionary algorithm (MI-MOEA) which is more suitable to work with interval valued objectives. [PERSON] et al.