# A Simulation-Based Optimization Method for Warehouse Worker Assignment
## 7 Numerical Results  
Using the simulation-based optimization method, the software tool was developed. The graphical user interface (GUI) design of the software is shown in Figure 4. The warehouse planner can select the workload data as an input and run the tool. The output includes the service level, along with other metrics.  
In a set of experiments, we tested different values of \(\lambda\) for inbound and outbound service levels, with the input data sampled from different months of years 2018 and 2019. The simulation-based optimization was run with different values of the coefficient \(\lambda\).  
We used the historical data provided by the warehouse. Specifically, inbound shipment arrival and outbound shipment order information for the following months were chosen: July 2018, January 2019 and March 2019. For each month, we conducted the assignment optimization week by week, and calculated the summation over all weeks of the month. The value of coefficient \(\lambda\) ranges from 1.0 to 2.0, with a step of 0.1. Data analyses of historical workload demand suggest that the outbound order volume generally prevails the inbound one. To diversify our sample pools, the sampling was done in the following way:  
1. In July 2018, the outbound pallet number was nearly 5% less than inbound pallet number;
2. In January 2019, the outbound pallet number was nearly 13% larger than the inbound one;
3. In May 2019, the outbound pallet number was nearly 29% larger than the inbound one.  
For the warehouse, outbound service level is considered to be more critical than the inbound service level. As shown in Figures 5-7, the results suggest that the optimized worker assignment can always achieve a better performance for the outbound service level, compared to the current assignment shown in Table 3. Regarding the inbound service level, the performance may be better when the value of \(\lambda\) is relatively small, that is, when the priority of outbound service level performance is not considered to be so high. Generally, with a decrease of less than 10% for the inbound service level, an increase of more than 30% can be obtained in the outbound service level performance. This indicates that our assignment can achieve a higher utilization of workers and a higher level of customer satisfaction.  
As seen from the reported results, when the value of \(\lambda\) increases, the outbound service level increases, while the inbound service level decreases. This indicates that the parameter \(\lambda\) can be used to control the trade-off between inbound and outbound service level performance metrics.  
Figure 4: The GUI of the manpower allocation tool.  
Figure 5: Numerical results for January 2019 data, given the total numbers of inbound/outbound pallets of 1508/1702, and the numbers of completed pallets with the current worker allocation are 906/606.  
Figure 6: Numerical results for May 2019 data, given the numbers total inbound/outbound pallets of 1541/1981, and the numbers of completed pallets with the current worker allocation are 1085/613.  
To demonstrate the improvements via the simulation-based optimization method, we generated additional service level outputs for a benchmark worker allocation case under the same workload scenarios. This benchmark worker allocation refers to the worker allocation matrix previously used by the warehouse manager prior to the implementation of our simulation-based optimization tool. In generating the service level statistics for the benchmark worker allocation, we preset the worker allocation and conducted simulations without any optimization. The comparisons of performance outputs from the optimized and non-optimized (benchmark) manpower allocations are shown in Figures 5-7, indicating that with less than 10% decrease for the inbound service level, on average, the outbound service level can be increased by 30% across all three scenarios considered.