This process is called order picking, which may constitute about 50-65% of operating costs. Therefore order picking is considered the highest-priority area for productivity improvements (see De Koster et al. (2007)). In a traditional manual order picking system (also called a picker-to-parts system), the pickers spend 50% of their working time on the task of walking (see Tompkins (2010); for an overview of manual order picking systems see De Koster et al. (2007)). The unproductive working times require the picker-to-parts system to have a large workforce, especially for companies which have millions of small-sized items in large warehouses, such as the retailers Amazon, Alibaba, Zara, Zalando and Walmart. Many of them provide both brick-and-mortar stores and online shops to create a seamless shopping experience for customers (omnichannel flexibility). Due to the diversity of online shops, we concentrate on both single-line and multi-line small-sized orders. Especially during the COVID-19 pandemic, online grocery sales are growing threefold faster (see Fabric (2020)). There are increasing demands for alternative warehousing systems to increase the efficiency of order picking, for example, robot-based compact storage and retrieval systems and robotic mobile fulfillment systems (see more details in Azadeh et al. (2019)). Here we consider a relatively new warehousing concept that does not use expensive fixed hardware and can be easily and quickly implemented, called AGV-assisted picking (see Boysen et al. (2019), Azadeh et al. (2019)).

In picker-to-parts warehouses, order picking is a cost- and labor-intensive operation that must be designed efficiently. It comprises the construction of order batches and the associated order picker routes, and the assignment and sequencing of those batches to multiple order pickers. The ever-increasing competitiveness among e-commerce companies has made the joint optimization of this order picking process inevitable. Inspired by the large number of product returns and the many but small-sized customer orders, we address a new integrated order picking process problem. We integrate the restocking of returned products into regular order picking routes and we allow for the decomposition of customer orders so that multiple batches may contain products from the same customer order. We thereby generalize the existing models on order picking processing. We provide Mixed Integer Programming (MIP) formulations and a tailored adaptive large neighborhood search heuristic that, amongst others, exploits these MIPs. We propose a new set of practically-sized benchmark instances, consisting of up to 5547 to be picked products and 2491 to be restocked products. On those large-scale instances, we show that integrating the restocking of returned products into regular order picker routes results in cost-savings of 10 to 15%. Allowing for the decomposition of the customer orders' products results in cost savings of up to 44% compared to not allowing this. Finally, we show that on average cost-savings of 17.4% can be obtained by using our ALNS instead of heuristics typically used in practice.

Robotic mobile fulfillment systems (RMFSs) are a new type of warehousing system, which has received more attention recently, due to increasing growth in the e-commerce sector. Instead of sending pickers to the inventory area to search for and pick the ordered items, robots carry shelves (called "pods") including ordered items from the inventory area to picking stations. In the picking stations, human pickers put ordered items into totes; then these items are transported by a conveyor to the packing stations. This type of warehousing system relieves the human pickers and improves the picking process. In this paper, we concentrate on decisions about the assignment of pods to stations and orders to stations to fulfill picking for each incoming customer's order. In previous research for an RMFS with multiple picking stations, these decisions are made sequentially. Instead, we present a new integrated model. To improve the system performance even more, we extend our model by splitting orders. This means parts of an order are allowed to be picked at different stations. To the best of the authors' knowledge, this is the first publication on split orders in an RMFS. We analyze different performance metrics, such as pile-on, pod-station visits, robot moving distance and order turn-over time. We compare the results of our models in different instances with the sequential method in our open-source simulation framework RAWSim-O.

We introduce the asprilo [1] framework to facilitate experimental studies of approaches addressing complex dynamic applications. For this purpose, we have chosen the domain of robotic intra-logistics. This domain is not only highly relevant in the context of today's fourth industrial revolution but it moreover combines a multitude of challenging issues within a single uniform framework. This includes multi-agent planning, reasoning about action, change, resources, strategies, etc. In return, asprilo allows users to study alternative solutions as regards effectiveness and scalability. Although asprilo relies on Answer Set Programming and Python, it is readily usable by any system complying with its fact-oriented interface format. This makes it attractive for benchmarking and teaching well beyond logic programming. More precisely, asprilo consists of a versatile benchmark generator, solution checker and visualizer as well as a bunch of reference encodings featuring various ASP techniques. Importantly, the visualizer's animation capabilities are indispensable for complex scenarios like intra-logistics in order to inspect valid as well as invalid solution candidates. Also, it allows for graphically editing benchmark layouts that can be used as a basis for generating benchmark suites. [1] asprilo stands for Answer Set Programming for robotic intra-logistics