Will Too Many Cooks (Robots) Spoil the Broth (Order Fulfillment)? Navigating Priority Orders in Warehousing Operations of E-Commerce Supply Chains

E-commerce companies are increasingly facing serious challenges in their supply chains during order fulfillment, as warehouses must simultaneously handle regular and priority (termed as prime) customer orders (COs). Motivated by the concerns of parts-to-picker warehouse operators' need for efficient order picking systems accommodating both prime and regular COs, this study presents a queuing game based analytical model to analyze the COs priority's impact on order fulfillment strategy and order picking system performance. Our model's objective function involves maximizing the benefits gained from completing order picking with incoming mobile robots and the costs associated with waiting in the picking system. Our analyses demonstrate a threshold equilibrium for the incoming robots carrying prime COs beyond which queue joining becomes nonbeneficial. Besides, the likelihood ratio of efficient and inefficient order pickers is decreasing in proportion of prime COs in the system and increasing in the waiting area capacity of the picking station. Therein, unlike the current practices in e-commerce warehouses where static queueing of robots and fixed picking rate of order pickers are prevalent, our findings suggest that warehouse managers should implement dynamic queue joining strategies for robots carrying prime COs. This approach entails modifying robots' strategies based on the proportion of prime COs and the capacity of the waiting area to achieve an optimal queue joining strategy and improve the overall system throughput. Practically, this study equips e-commerce supply chain practitioners with insights for designing flexible picking systems that handle peak-season demand fluctuations.