# A Simulation-Based Optimization Method for Warehouse Worker Assignment
## 3 Problem Description
Worker skill set is an important constraint in the assignment problem, which is also considered here. As shown in Table 1, each worker owns a distinct set of skills that allows the worker to perform the corresponding warehouse activities. If the worker is not trained to perform an activity, that worker cannot be considered as a candidate for assignment to this activity. Nonetheless, we do not impose any constraints on warehouse storage capacity, working areas, and buffer zones between activities. In the following sections, we will show how the simulation-based optimization method can be used to solve this problem. As the situation in reality may vary day by day, and also from one warehouse to another, our tool will provide the solution for the specific settings of the warehouse, including flexibility of both products and workers. First of all, inbound and outbound workload information should be defined. For example, the inbound shipment arrival and/or outbound order start time-stamp, product name, workload in terms of number of pallets, and target completion time-stamp information, are all handled by the warehouse planners. This information is dependent on the forecast or expectation. Hence, this information may vary. Moreover, we allow the model to capture the pending workload from the previous day in pallet quantity, and by each type of inbound and outbound activity. Besides, the more detailed information, such as the product type and processing time for each activity, can also be customized by the user. Here we specify product name, designated storage area, whether the product requires AST for scanning or not, and per-pallet processing time (mean, standard deviation) by all inbound and outbound activities needed by each product type. The tool also allows variability in the worker parameters. The number of workers assigned to a shift and the shift duration can vary. As an example, we consider two shifts in the showcase of Section 7, i.e., morning and night, operating from 8 am to 6 pm and from 9 pm to 7 am (next day), respectively, with a one-hour break in each shift. Besides, the information on national holidays can also be captured by our tool to specify the non-working days. The worker skill set matrix is another important parameter. As defined in Table 1, each worker has a skill set (\"Yes\" if the worker owns the skill for the activity) with respect to each type of activity conducted in the warehouse. To measure the performances of different worker assignment options in the warehouse, the hourly and daily KPIs are generated. The hourly KPIs include worker utilization by each activity in each hour, inbound and outbound throughput in terms of the number of completed pallets by each hour, and overall inbound and outbound team utilization rate by each hour. Overall daily KPIs include inbound and outbound team overall daily utilization, total work-in-progress (WIP) pallet quantity in inbound and outbound activities, total quantity of completed pallets by inbound and outbound seams, and per-worker average productivity rate in terms of number of completed pallets. To express the KPIs formally, we define the following notation:  
* \(w_{occ}\): number of occupied workers;
* \(w_{awa}\): total number of available workers;
* \(p_{com}\): number of completed pallets;
* \(p_{arr}\): number of arrived pallets;
* \(p_{incom}\): number of completed inbound pallets;
* \(p_{outcom}\): number of completed outbound pallets;
* \(w_{in}\): number of inbound workers;
* \(w_{out}\): number of outbound workers. We define \(avg(\cdot)\) as the average function over the simulation days.