## 2 Literature Review  
With the growing amount of interest in the topic of Buy-Online-Pick-up-in-Store, the majority of the research up to this point has focused on the effects that launching a BOPS channel would have on the previously existing store. For example, one work [8] investigates how inventory holding costs and lost sales costs are influenced by giving walk-in customers a higher priority than BOPS customers, and how this influence varies depending on whether the BOPS is owned by the shop or by a third party. The work [9] analyzes a Stackelberg game theoretic model involving a manufacturer and a retailer to determine how shop prices should fluctuate in response to the manufacturer's product quality and which scenarios are profitable. There is plenty of research [5; 6; 7; 10; 11; 12], which is helpful in determining if it is beneficial to open the BOPS channel and start planning for a well-functioning business model, but they provide no guidance on how operations should be organized, which is vital for the long term success of the BOPS channel. When the search is expanded to include similar topics, a ship-from-store concept is studied in [13]: in both the concept and the BOPS model, customers place orders via an application or a website and employees go through the store to pick the products. The authors propose a model to determine the optimal time to batch multiple orders before the picking operation is started, the optimal time before starting the delivery process of orders, and the optimal number of pickers and packers. However, this model is not very practical in grocery stores, as the batching/reassembling operations applied to the problem would significantly increase the complexity of the task due to the high number of items on shopping lists, thus implementation of this strategy is not recommended in the scenario of this BOPS research. Similarly in [14], a methodology is proposed to compute the minimal picking rate under single wave or multi wave picking given a demand ordered between two cutoff times and an objective service level. The picking operation is not modeled, but they assume that there exists a certain picking rate \(\mu\) to be defined before the proposed model can be used to validate strategies. A research gap can therefore be identified, given the fact that in the literature no approach optimizing grocery store order picking in a BOPS system was found. Order picking in warehouses is a well examined topic, with an extensive body of work investigating routing, storage, and batch assignment that aims at optimizing and automatizing costly operations [15]. These approaches can not however be utilized in the BOPS contexts, due to the differences in terms of layout, means of transport, and stored units. In fact, while in warehouses one can use robots for moving Unit Load Devices or place the most frequently picked items in easy to reach spots, in brick-and-mortar stores the presence of regular customers and the different packaging shapes makes the implementation of robots almost impossible. Since the design methodology of the stores is selling products, the main factors taken into account are revenue maximization [4] and customer satisfaction [16]. This is accomplished by having a good variety, visibility, and availability of products positioned in strategic ways that increase impulsive purchases, but has no correlation with an employee who picks the articles according to a given shopping list. From the customers' perspective, the in-store picking problem has been discussed in [17]. By analyzing customers' locations detected through devices on the shopping carts, the paper revealed that customers whose path was closer to the shortest path tended to buy items from frequently purchased product categories with higher numbers of products. Larger shopping baskets lead to higher deviations from the optimal path, and most deviations are not caused by not following the optimal zone order but by not taking the shortest route between them.