Illustrative Example: Production Line with 20 Workstations
The capability of dealing with dozens of variables simultaneously opens important analysis possibilities ranging from statistical characterization to optimization. This section illustrates, for example, how a 20-variable simulation-optimization problem can be addressed aided by an experimental design with such capability.
Consider a production line with 20 workstations simulated with the software package SIMIO. The simulation is run for 8 hours per day with 10 replicates. The simulation parameters of interest were the mean process time on each of the workstations (WSi). The process time in each workstation was assumed to follow a normal distribution with a mean that varied in three levels (Figure 1) and a constant standard deviation of 0.25 minutes. It is further assumed that the nominal process time can be chosen by a particular user. The response of interest was the system time defined as the period of time elapsed since a raw part to be processed enters the system until it exits as a finished product.
A simulation optimization method based on design of experiments and metamodeling techniques was used (Villarreal-Marroqun et al., 2013). The method starts with an initial experimental design, which for twenty variables has 232 experimental runs. Figure 1 shows the ranges of values to be explored with the objective to minimize the system time per unit. The minimum value for the average cycle time in the experimental design was identified and selected as the first best solution (first incumbent solution) (I-1).
*Villarreal-Marroquín, M. G., Castro, J. M., Chacón-Modragón, O. L., and Cabrera-Ríos, M. 2013. "Optimisation Via Simulation: AMetamodelling-Based Method and a Case Study." European J. Industrial Engineering 7:275-294.