Konrad Stephan’s research while affiliated with Friedrich Schiller University Jena and other places

Due to high real estate costs in urban areas, shop floor space is scarce in most brick‐and‐mortar stores. Maneuvering newly arrived merchandise through narrow aisles during shelf replenishment is time‐consuming for the sales staff and impedes customers. Therefore, many retail chains nowadays aim for store‐friendly shipments (SFS). By mirroring the layout of a store in the buildup of its dedicated shipments, the need for a zigzag movement through the store when replenishing shelves can be avoided. On the negative side, however, additional effort arises in the distribution centers. A suitable warehousing system to assemble SFS without excessive effort is a pocket (or pouch or bag) sorter, where each item is put into its separate bag. These bags, filled with items, are automatically transported while hanging from an overhead conveyor and can be sorted into any sequence before being delivered to the workstations that build SFS. This article investigates the assembly of SFS with a pocket sorter and presents scheduling procedures to enhance the efficiency of this process for a given set of store orders. We demonstrate that, despite its notorious complexity, the problem can be solved by simple decision rules with good performance. In a case study, we show that this approach can dramatically reduce the completion times of store orders, resulting in savings of more than 60% of the total working hours compared to a simple real‐world policy. Another 30% of reduction can be obtained by standardized store layouts.

Triggered by the great success of e-commerce, today’s warehouses more and more evolve to fully-automated fulfillment factories. Many of them follow the parts-to-picker paradigm and employ shelf-lifting mobile robots or conveyors to deliver stock keeping units (SKUs) to stationary pickers operating in picking workstations. This paper aims to structure and review the family of synchronization problems that arise in this environment: If multiple orders demanding the same SKU can be serviced jointly, then a more efficient picking process and a relief of the bin supply system can be achieved. This paper classifies the family of slightly varying synchronization problems arising with different workstation setups in alternative warehouses. This classification scheme is applied to analyze computational complexity, to systematically quantify the gains of alternative workstation setups, and to benchmark the performance gains of synchronization with those of other well-established decision tasks. Our results show that the right workstation setup can greatly improve throughput performance, so that the gains of synchronization can outreach those promised by other well-researched decision tasks.

To relieve human order pickers from unproductive walking through a warehouse, parts-to-picker systems deliver demanded stock keeping units (SKUs) toward picking workstations. In a wide-spread parts-to-picker setup, a crane-operated automated storage and retrieval system (ASRS) delivers bins with demanded SKUs toward an end-of-aisle picking workstation and returns them back into the rack once the picks are completed. We consider the scheduling of the crane that operates subsequent dual commands. Each dual command combines a retrieval request for another SKU bin demanded at the picking workstation with a storage request, where a bin that has already been processed and passed through the bin buffer is returned to its dedicated storage position in the ASRS. This system setup in general and the resulting crane scheduling problem in particular have been an active field of research for more than 30 years. We add the following contributions to this stream of research: We finally prove that the crane scheduling problem is strongly NP-hard. Furthermore, we show that, although only a single vehicle (namely, the crane) is applied, the problem is equivalent to the traditional vehicle routing problem (VRP). This opens the rich arsenal of very efficient VRP solvers, which substantially outperform existing tailor-made algorithms from the literature.

Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries. Solving this problem under the min-makespan objective is well known to be strongly NP-hard. We consider a special case of the problem arising from products having a modular design. This means that product characteristics, (mass-)customizable by customers, are realized by separate components that can freely be combined. If consecutive products differ by a component, then a setup is necessary. This results in a specially structured setup matrix that depends on the similarities of product characteristics. We differentiate alternative problem cases where, for instance, the setup operations for multiple components either have to be executed sequentially or are allowed to be conducted in parallel. We analyze the computational complexity of various problem settings. Our findings reveal some special cases that are solvable in polynomial time, whereas most problem settings are shown to remain strongly NP-hard.

To improve picking performance, many warehouses apply order batching and/or zoning in their picking areas. The former policy collects multiple customer orders jointly on a picker tour to increase picking density, and the latter partitions the picking area into smaller zones to enable a parallel order processing. Both picking policies require an additional consolidation stage, where bins filled with partial orders arriving from multiple zones are sorted according to customer orders. To connect both stages, a conveyor system is applied on which the picked products, each being a piece of a specific stock keeping unit (SKU), move from the picking area toward the consolidation stage. If multiple pieces of the product sequence, approaching the consolidation area on the conveyor, refer to the same SKU, these products are interchangeable among customer orders, and our product-to-order assignment problem arises: Given a product sequence where each product refers to some SKU, we assign products to customer orders, such that demands are fulfilled and order-related objectives, e.g., the sum of completion times, are optimized. We investigate different objectives for this very basic optimization task and show that some problem versions are solvable in polynomial time, whereas others turn out to be NP-hard. Furthermore, we provide exact and heuristic solution approaches. By applying these algorithms in a comprehensive simulation study, we show that our product-to-order assignment problem can be an impactful lever to improve consolidation performance.

High-occupancy vehicle (HOV) lanes are restricted traffic lanes that are reserved for vehicles with multiple car occupants. Depending on the current number of passengers, a driver must either travel slower on the often-congested general-purpose lane or can access the faster HOV lane. In this paper, we provide optimization approaches for matching supply and demand when building carpools along HOV lanes. In current applications, carpools form spontaneously in slugging areas where potential passengers queue. However, internet-enabled mobile phones that are connected to a central ride sharing platform enable dynamic carpool formation based on sophisticated scheduling procedures. We investigate various versions of the carpool formation problem. The computational complexity is analyzed in depth, and suitable solution procedures are developed. These procedures are applied to quantify the benefit of an optimized carpool formation process. In a comprehensive computational study, we compare our optimization approaches with spontaneous ride sharing and show that substantially better solutions for all stakeholders can be obtained.

There is a vivid debate in cities all over the world on how to distribute the restricted space in urban areas among stakeholders. Urban design movements such as new pedestrianism or Copenhagenization advocate that too much space is attributed to cars. In this context, our research investigates the optimization of parking lots with the help of mathematical programming. For the given ground plot of a parking lot, we maximize the number of parking spaces each reachable via a driving lane, so that the urban space attributed to the parking of cars is efficiently used. Based on a grid of squares in which we rasterize the ground plot, this paper presents mixed-integer programs based on three different resolutions for orthogonal parking. Our computational study explores the tradeoff between the additional parking spaces promised by a higher resolution and the increased computational effort because of the larger solution space (and vice versa). We compare our optimization approaches with a sample of 177 real-world parking lots and show that optimization can be a serviceable car park design tool with the help of a case study.

Put‐to‐light order picking systems invert the basic logic of conventional picker‐to‐parts systems. Instead of successively visiting the storage positions of the stock keeping units (SKUs) when collecting picking orders, an order picker accompanies successive bins each containing multiple items of a specific SKU along a lane of subsequent orders. Whenever the picker passes an order requiring the current SKU, which is indicated by a light signal, she puts the requested number of items into the bin associated with the order. Such an order picking system is well‐suited if the assortment is not overly large and all orders demand similar SKUs, so that it is mainly applied in distribution centers of brick‐and‐mortar retail chains. This paper evaluates four different setups of put‐to‐light systems, which, during operations, require the solution of different storage assignment and SKU sequencing problems. We formulate these problems, prove computational complexity, and suggest suited solution algorithms. By applying these algorithms in a comprehensive computational study, we benchmark the impact of the four different setups on picking performance. In this way, warehouse managers receive decision support on how to set up their put‐to‐light systems.