## 7 Computational Experiments
For the comparison, we employed the actual layout of an SLC-AS/RS consisting of three racks, each containing 500 storage locations, with two input and two output points. In the computational experiments, 12 different request lists were used, each varying in size (30, 60, 90, and 150 requests). Every algorithm was executed three times on each request list to monitor both its average performance and its variability. The comparison primarily focuses on the total makespan, expressed in minutes (Table 4), and computational time (Table 5). Additionally, we monitored the overall mismatch between the quantities and quality levels required by customers (Table 6). The parameters of the proposed algorithm, namely the betas of the geometric distribution used in the selection of racks (\(\beta_{r}\)) and bundles (\(\beta_{b}\)), were adjusted in each iteration according to trimmed Gaussian distributions. The means of these Gaussian distributions (\(\mu_{r}=0.7\) and \(\mu_{b}=0.9\)) were determined through a series of empirical experiments, exploring combinations of \(\mu_{r}\in(0,1)\) and \(\mu_{b}\in(0,1)\) with a step of 0.1. Both were set with a standard deviation of 0.025. Regarding SA, the same parameter values as proposed in [PERSON] et al. (2018) were employed. All BR-DES and SA results were acquired after exploring 1000 solutions. The makespan results are presented in Table 4. As anticipated, our proposed algorithm consistently outperforms the greedy and random approaches, as well as the SA algorithm, in all instances. Notably, the random and greedy approaches often fail to find feasible solutions, whereas our algorithm consistently obtains feasible solutions in all scenarios. feasibility and making informed decisions at each stage. Consequently, it requires considerably less computational time to achieve comparable or superior solutions compared to those generated by the SA algorithm. Computational times are displayed in Table 5. Notably, our BR-DES consistently outperforms the SA algorithm in terms of solution quality as well as computational efficiency. Throughout the tests, we closely monitored the deviation, encompassing both quantity and quality indicators, between the optimal solution derived by the algorithms and the customer-requested specifications. Table 5 presents the aggregate discrepancy observed after fulfilling all the requests. Each algorithm underwent three executions for each instance. In these terms, BR-DES emerges as the superior approach. The top solutions obtained by BR-DES for each instance are significantly approximate to the customers' specified requirements, both in terms of quality and quantity. Following closely, the SA algorithm constitutes the second-best alternative. At times, the greedy algorithm produces commendable solutions. However, this achievement often prolongs the makespan. Minimizing the divergence between the proposed solution and the customers' stipulations holds immense significance. Even as the primary objective revolves around reducing the makespan, meticulous adherence to the aforementioned quality and quantity requisites significantly augments customer satisfaction. Figures 8 and 9 visually juxtapose the considered approaches with regards to makespan and quantity mismatch. Since the greedy and random approaches fail to produce feasible solutions for Instances 10 to 12, only Instances 1 to 9 are considered in these figures. Notice that the BR-DES algorithm outperforms all other approaches both in terms of the makespan and the quantity mismatch.