## 3 Modeling the Temporary Facility Layout Problem
### Sensitivity Analysis of Multiple Criteria  
The sensitivity analysis of the criteria is capable of determining the most sensitive criteria with weight changes and can assist the decision-makers to find out the optimal alternative. In this research,an OAT-based sensitivity analysis is performed with respect to all weights to assess the stability of the alternative rankings for the temporary facility layout problem.  
The OAT analyzing method is able to identify the most sensitive parameters among all influencing factors in the model [67]. In the sensitivity analysis, the weights of input factors are changed to check the results which the weight changes produce [68]. In this process, the weights of all other factors can be fixed, or at least change to an extent to their baseline value, which makes the comparability of the different results possible. Generally, the OAT-based sensitivity analysis includes three steps as follows [69]:  
1. Range of percent change (RPC) definition. The changing range is defined as a set of discrete percent change from an original criterion weight value. The change range is required to be within the RPC. In this temporary facility layout planning problem, a single weight range of \(\pm 40\%\) is adopted, which is applied to all criteria to see changes of the results.
2. Increment of percent change (IPC) definition. The proposed evaluation engine conducts a series of runs where each criterion weight is changed in percent increments according to the IPC.
3. Weight calculation. When the main changing criterion \(c_{m}\) varies, its weight at the certain percent change (PC) can be calculated as Equation (6): \[W(c_{m},pc)=W(c_{m},0)+W(c_{m},0)\times pc,1\leq m\leq n,\] (6) where \(c_{m}\) represents the main changing criterion; \(W(c_{m},0)\) represents the weight of the main changing criterion \(c_{m}\) at the base run; \(pc\) is the percent change of the main changing criterion; and \(n\) is the total number of criteria.
4. Weight adjustment. In order to satisfy the constraint that the sum of each weight of criterion equals one, the weights of the other criteria need to be adjusted proportionally. The weight of other criterion \(W(c_{i},p)\) is derived in accordance with \(W(c_{m},p)\) as Equation (7): \[W(c_{i},pc)=(1-W(c_{m},pc))\times W(c_{i},0)/(1-W(c_{m},0)),i\
eq m,1\leq i \leq n,\] (7) where \(W(c_{m},pc)\) is the weight of the main changing criterion \(c_{m}\) at the certain percent change; \(W(c_{i},0)\) is the weight of the \(i\)th criterion \(c_{i}\) at the base run; \(W(c_{m},0)\) is the weight of the main changing criterion \(c_{m}\) at the base run.  
Through the described sensitivity analysis, the weight of the main changing criterion is altered by an IPC within the RPC. After the main changing criterion changes from the first criterion (PEO criterion) to the \(n\)th criterion (WPC criterion), the sensitivity evaluation summary is generated for all simulation runs including the input criteria and output results. Combined with the specific performance of each alternative, the overall rankings among all alternatives are generated from the simulation. According to the simulation outputs, the decision-makers can check the result changes due to the weight changes and make the final decisions.