## 4 Methodology: Problem-Solving Methodology
### Two-Stage Adaptive Large Neighbourhood Search (Two-Stage ALNS)
#### 4.1.4 Repair Operator  
Seven repair operators were customised for the proposed two-stage ALNS method. The main characteristic of the repair operator is cell-transfer prevention. Before removing each cell from the current solution, the repair operator prevents cell-transfer situations by omitting the already assigned workers in each removed cell. 1. Random cell insertion \(R_{1-1}\): The operator randomly selects the removed cells one at a time. After selecting the cell, it randomly selects the available workers for the removed cell until the number of workers in the cell reaches the total number of tasks. The procedure is repeated until all removed cells are reinserted into the current solution. 2. Greedy-\(B\) cell insertion \(R_{1-2}\): The operator sequentially selects the removed cell to repair and reinsert into the current solution, one at a time, based on the ascending order of the number of total tasks. In each removed cell, the operator selects the available workers as follows: The operator generates \(B\) worker combinations, where the total number of workers in each combination is equal to \(T_{c}\). The operator chooses the combination of workers that contributes most to the Model B1 objective value. 3. Regret-\(B\) cell insertion \(R_{1-3}\): The operator works similarly to repair operator \(R_{1-2}\) by generating \(B\) combinations of workers in each removed cell. In addition to the mechanism of \(R_{1-2}\), the operator applies look-ahead information by calculating the regret value \(reg_{c}\) of all \(B\) worker combinations as follows: \[reg_{c}=\sum_{\textit{compl}=1}^{B}\left( \begin{array}{c}f_{1-\textit{compl }}-f_{1-\textit{compl}}^{*}\end{array} \right)\] (45) where \(f_{1-\textit{compl}}^{*}\) = Model B1 objective value when placing the removed cell back to the current solution with the best worker combination. \(f_{1-\textit{compl}}\) = Model B1 objective value when placing the removed cell back to the current solution with the worker combination, starting from the second-best combination to the last combination. 4. Workers idle time variation based on part insertion \(R_{2-1}\): The operator aims to minimise the cell workers' idle time variation in each cell by assigning workers to parts in a distributional manner. Initially, the heuristic generates a list of sorted removed parts with respect to their demands, in descending order. For each removed part, the skilled worker with the highest remaining working time is prioritised for the assignment. The heuristic stops assigning workers to the removed part after the demand is satisfied. The overall framework of \(R_{2-1}\) heuristic can be found in the Supplementary Materials. 5. Pseudorandom part insertion \(R_{2-2}\): At the beginning of the repair operation, the operator creates a list of skilled workers, whose remaining working time is still available for part assignment, denoted as Wlist. The operator randomly assigns workers from the Wlist to the part until part production demand is satisfied. 6. Pseudorandom greedy-\(B\) part insertion \(R_{2-3}\): The operator reinserts the removed part into the current solution one at a time. In each repair procedure, the operator creates the list Wlist for worker assignments for each part. The operator then generates B worker assignment combinations for each removed part. Workers in each combination are chosen from Wlist. Finally, the operator chooses the combination of workers that contributes most to the Model B2 objective value. 7. Pseudorandom regret-\(B\) part insertion \(R_{2-4}\): This operator works similarly to operator \(R_{2-3}\). In addition to the procedure of \(R_{2-3}\), the operator selects the worker assignment combination based on regret value (\(reg_{p}\)), which is calculated as follows: \[reg_{p}=\sum_{combi=1}^{B}\big{(}\ f_{2-combi}-f_{2-combi}^{*}\big{)}\] (46) where \(f_{2-combi}^{*}\) = Model B2 objective value when placing the removed part back to the current solution with the best worker assignment combination.