Order picking (OP) is a critical yet time-consuming and labor-intensive warehouse operation within the supply chain. In picker-to-part systems with high demand, pickers are exposed to fatigue due to the excessive repetition of picking activities, which results in high human energy expenditure. The literature indicates that energy expenditure depends on the picking activity and the worker’s attributes, such as pickers’ weight, gender, and age. Studies have shown that as the weights of individuals increase, the energy consumed for the same task increases. This study proposes a two-stage stochastic programming model that minimizes assignment and overtime costs while avoiding excessive fatigue levels for pickers by incorporating rest allowance into the picking tour time. In the first stage, the number of pickers required is decided. In the second stage, orders are assigned to pickers considering uncertain energy expenditure. The two-stage stochastic programming model is solved by the sample average approximation algorithm. Results show that both OP cost and the number of pickers required to fulfill an order increase when the picker’s weight exceeds 80kg. In allocating orders, pickers weighing less than 80kg should be assigned to orders with more items, such as those containing 4- or 5-items. Conversely, pickers weighing more than 80kg should be assigned to orders with fewer items, like those containing 2- or 3-items, to avoid fatigue side effects.