# Applying Simheuristics to Minimize Overall Costs of an MRP Planned Production System
## 5 Simulation Study  
To evaluate the performance of the proposed approach, a computational study was performed. During the simulation experiments, the simheuristic versions are applied to find and update the base and best solutions and set them for the remaining iterations. The simulation results are stored in an in-memory database, and are afterwards used to analyze the simulation results. To reduce the variance in the simulation results, outliers (runs with very high or very low costs of an iteration), were excluded from the average overall cost per iteration. The simulation time was set to 1800 days and 20 replications per iteration are applied when SBM is not activated. Different amounts of simulation runs were evaluated to compare the performance of the different simheuristics. Based on the existing simheuristic versions, the developed SBM and SA extensions were evaluated during the simulation study with 100, 200 and 300 iterations, i.e., a _simulationBudget_ of 2000, 4000 and 6000 runs. To get promising settings for the the remaining parameters, a set of preliminary test simulations was performed. For the STR, no additional simulation parameter is required. For the ERR, the \(\alpha\) value for the range reduction was set to 0.0025, thus avoiding a too quick convergence of the LB and UB. For the BSBR, the best 7 solutions are used to compute lower and upper parameter bounds.  
To illustrate the simhueristic application, one optimization run is described here in detail. The starting values for the MRP parameters are: item 10 [FOQ 600, SS 3, PL 2], item 11 [FOQ 700, SS 3, PL 2], item 20 [FOQ 450, SS 3, PL 2] and item 21 [FOQ 450, SS 3, PL 2]. These MRP parameter values are applied for the first iteration within the optimization run and lead to the initial overall costs. Note that all MRP parameter values generated by the simheuristic are firstly calculated as double values and then rounded to be applicable for the simulation model. In the presented example, the STR simheuristic is applied with 100 iterations. The MRP parameters lead to initial overall costs of 7151 CU with inventory costs of 1697 CU and backorder costs of 5454 CU. This is also our base and best solution used for the subsequent iteration. Applying the STR heuristic for the second iteration leads to the following MRP parameter values: item 10 [FOQ 778, SS 4, PL 2], item 11 [FOQ 678, SS2, PL 3], item 20 [FOQ 452, SS 5, PL 1] and item 21 [FOQ 470, SS 3, PL 2]. These values result in deceasing overall costs of 6343 CU (1888 CU inventory costs, 4455 CU backorder costs).  
This process of finding new base and best solutions with the associated MRP parameter values is done until the maximum number of iterations, i.e., 100 in this example, is reached. When SBM is applied, the number of iterations is limited by the overall number of simulation runs. Finally, the minimum overall costs can be computed and used for comparison with other simulation results. In this example, the minimum overall costs are 3490 (1899 CU inventory costs, 1591 CU tardiness costs) at iteration 55 with parameter values of item 10 [FOQ 539, SS 5, PL 2], item 11 [FOQ 615, SS 5, PL 3], item 20 [FOQ 478, SS 3, PL 3], item 21 [FOQ 427, SS 4, PL 2]. Compared to the initial solution, this is a decrease of the overall costs by 3661 CU, the inventory costs increased by 202 CU and the backorder costs decreased by 3863 CU. Comparison of MRP parameters of the initial solution and the best solution shows a decrease in the lot sizes, an increase in the safety stock for items 10, 11 and 21 and an increase in the planned lead time for item 11 and 20. Please note that the safety stock parameter is passed as factor to the MRP run and multiplied by associated stock units.