Fulfillment scheduling for buy‐online‐pickup‐in‐store orders

One of the most popular ways of shopping in an omnichannel retailing environment is buy‐online‐pickup‐in‐store (BOPS). Retailers often promise BOPS shoppers short in‐store pickup ready times. We study fulfillment scheduling decisions of BOPS orders destined for a single store of a retailer. There are two fulfillment options for BOPS orders: they can be either processed at a fulfillment center (FC) and delivered to the store or processed at the store without needing delivery. There are two types of trucks available to deliver the BOPS orders fulfilled at the FC: prescheduled trucks that are already committed to replenishing store inventory and have some spare capacity that can be utilized, and additional trucks that can be hired from third‐party logistics providers. There is a fixed cost for using each truck; the cost for using a prescheduled truck is lower than that for using an additional truck. If an order is fulfilled at the store, it incurs a processing cost and a processing time, whereas the processing cost and time are negligible if an order is fulfilled at the FC. The problem is to determine where to fulfill each order (FC vs. the store), how to assign the orders fulfilled at the FC to trucks for delivery, and how to schedule the orders fulfilled at the store for store processing, so as to minimize the total fulfillment cost, including the delivery cost from the FC to the store incurred by the orders processed at the FC, and the processing cost for fulfilling the rest of the orders at the store, subject to the constraint that each order is ready for pickup at the store by its promised pickup ready time. We consider various cases of the problem by clarifying their computational complexity, developing optimal algorithms and heuristics, and analyzing theoretical performance of the heuristics. We also conduct computational experiments to validate the effectiveness of the proposed heuristics in both static and dynamic settings and derive important insights about how the presence of prescheduled trucks and the presence of store fulfillment option impact the fulfillment cost and decisions.