With the rapid integration of digital technologies into e-commerce platforms, online sales have increased dramatically in recent years. Additionally, customers' awareness of the global competition among hundreds of e-commerce companies has increased their expectations such as high quality, low price, fast and free delivery like never before. In response, e-commerce companies have started revisiting their logistics systems to survive in such a business environment by meeting rising expectations and minimizing operational costs. Thus, most companies have been focused on order-picking processes, which are characterized by high operating times and labor costs. Accordingly, collaborative robots (cobots) have been used in many warehouses to make order-picking operations more efficient and profitable. Depending on the distance between pick locations, a cobot can either be ridden by the order picker or autonomously move to the next pick location while the order picker is walking. This paper proposes a bi-level programming model to find the optimal designs of order-picking warehouses employing collaborative robots. The top-level model is used to determine the optimal shape factor (width-to-depth ratio) minimizing the order-picking time; whereas, the bottom-level model determines the optimal route and collaboration strategy. Based on Monte Carlo simulation, it is shown that the shape factor significantly affects the length of an order-picking tour when the pick-list size is small. However, it is concluded that the optimal shape factor varies depending on the pick-list size. [ABSTRACT FROM AUTHOR]