A Solution Approach for the Joint Order Batching and Picker Routing Problem in a Two-Block Layout

Order Batching and Picker Routing Problems arise in warehouses when articles have to be retrieved from their storage location in order to satisfy a given demand specified by customer orders. The Order Batching Problem includes the grouping of a given set of customer orders into feasible picking orders such that the total length of all picker tours is minimized. The problem of determining the sequence according to which articles have to be picked is known as the Picker Routing Problem. Although these problems occur at the same planning level, it is common to solve these problems not simultaneously, but separately and in sequence. As for the batching problem it is usually assumed that the order pickers, when making their ways through the warehouse, follow a certain, simple routing strategy. Based on this routing strategy, the customer orders are grouped into picking orders. The advantage of this approach can be seen in the fact that – in particular for single-block warehouse layouts – the corresponding order picker tours are very straightforward and can be memorized easily by the order pickers. This advantage diminishes, however, when more complex, multi-block layouts have to be dealt with. Furthermore, in such case, the approach may result in picker tours that can be far from optimal. Therefore, for multi-block layouts, we develop a new approach, namely an iterated local search algorithm into which different routing algorithms have been integrated and which allows for solving the Order Batching Problem and the Picker Routing Problem simultaneously. By means of numerical experiments it is shown that this approach results in a substantial improvement of the solution quality without increasing computing times

Order Picking in Narrow-Aisle Warehouses: A Fast Approach to Minimize Waiting Times

Mail order companies like Zalando or Amazon reported a significant increase regarding the number of incoming customer orders in recent years. Customers are served from a central distribution center (warehouse) where requested items of the orders have to be retrieved (picked) from their storage locations. The picking process is performed by human operators (order pickers) who are employed on a large scale in order to enable a fast processing of the orders. However, due to limited space, aisles are often very narrow in warehouses, and order pickers cannot pass or overtake each other. Thus, an order picker may have to wait until another picker has performed his/her operations. The arising waiting times may significantly increase the processing times of the orders, implying that a large number of pickers does not guarantee for small processing times. Therefore, in this paper, the impact of several problem parameters on the amount of waiting time is investigated first and situations are identified where the consideration of waiting times is inevitable for an efficient organization of the picking process. In the second part of the paper, a solution approach, namely a truncated branch-and-bound algorithm, is proposed which aims for the minimization of the waiting times. By means of extensive numerical experiments, it is demonstrated that this approach provides high-quality solutions within a very small amount of computing time

A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout

The Single-Picker Routing Problem (SPRP) arises in warehouses when items have to be retrieved from their storage locations in order to satisfy a given demand. It deals with the determination of the sequence according to which the requested items have to be picked in the picking area of the warehouse and the identification of the corresponding paths to be travelled by human operators (order pickers). The picking area typically possesses a block layout, i.e. the items are located in parallel picking aisles, and the order pickers can only change over to another picking aisle at certain positions by means of so-called cross aisles. Using this special structure, Scholz et al. (2016) developed a model formulation whose size is independent of the number of locations to be visited. They presented the model for a single-block layout and briefly described how it can be extended to the case of multiple blocks. However, by extending this formulation, the number of variables and constraints is multiplied by the number of blocks and, therefore, the model is not suitable for solving the SPRP in warehouses composed of several blocks. In this paper, the extension to multiple blocks is considered and it is pointed out how to drastically reduce the size of the formulation. Depending on the storage locations of the requested items, the number of variables can be decreased by up to 96%

Order picking with multiple pickers and due dates: Simultaneous solution of order batching, batch assignment and sequencing, and picker routing problems

In manual picker-to-parts order picking systems of the kind considered in this article, human operators (order pickers) walk or ride through the warehouse, retrieving items from their storage location in order to satisfy a given demand specified by customer orders. Each customer order is characterized by a certain due date until which all requested items included in the order are to be retrieved and brought to the depot. For the actual picking process, customer orders may be grouped (batched) into more substantial picking orders (batches). The items of a picking order are then collected on a picker tour through the warehouse. Thus, the picking process of each customer order in the batch is only completed when the picker returns to the depot after the last item of the batch has been picked. Whether and to which extend due dates are violated (tardiness) depends on how the customer orders are batched, how the batches are assigned to order pickers, how the assigned batches are sequenced and how the pickers are routed through the warehouse. Existing literature has only treated special aspects of this problem (i.e. the batching problem or the routing problem) so far. In this paper, for the first time, an approach is proposed which considers all aspects simultaneously. A mathematical model of the problem is introduced that allows for solving small problem instances in reasonable computing times. For larger instances, a variable neighborhood descent (VND) algorithm is presented which includes various neighborhood structures regarding the batching and sequencing problem. Furthermore, two sophisticated routing algorithms are integrated into the VND algorithm. By means of numerical experiments, it is shown that this algorithm provides solutions of excellent quality

SLOPPGEN: A Problem Generator for the Two-Dimensional Rectangular Single Large Object Placement Problem With Defects

In this paper, a problem generator for the Two-Dimensional Rectangular Single Large Object Placement Problem is presented in which the large object includes one or several defective areas. The parameters defining this problem are identified and described. The features of the problem generator are pointed out, and it is shown how the program can be used for the generation of reproducible random problem instances

Integrated Order Picking and Vehicle Routing with Due Dates

Supermarkets typically order their goods from a centrally located distribution center (warehouse). Each order that the warehouse receives is characterized by the requested items, the location of the respective supermarket and a due date by which the items have to be delivered. For processing an order, a human operator (order picker) retrieves the requested items from their storage locations in the warehouse first. The items are then available for shipment and loaded on the vehicle which performs the tour including the respective location of the supermarket. Whether and to which extent a due date is violated (tardiness) depends on the composition of the tours, the corresponding routes and the start dates of the tours (vehicle routing subproblem). The start date of a tour, however, is also affected by the assignment of orders to pickers and the sequence according to which the orders are processed by the pickers (order picking subproblem). Although both subproblems are closely interconnected, they have not been considered simultaneously in the literature so far. In this paper, an iterated local search algorithm is designed for the simultaneous solution of the subproblems. By means of extensive numerical experiments, it is shown that the proposed approach is able to generate high-quality solutions even for large instances. Furthermore, the economic benefits of an integrated solution are investigated. Problem classes are identified, where the sequential solution of the subproblems leads to acceptable results, and it is pointed out in which cases an integrated solution is inevitable

A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout

The Single-Picker Routing Problem deals with the determination of sequences according to which items have to be picked in a distribution warehouse and the identification of the corresponding paths which have to be travelled by human operators (order pickers). The Single-Picker Routing Problem represents a special case of the classic Traveling Salesman Problem (TSP) and, therefore, can also be modeled as a TSP. However, the picking area of a warehouse typically possesses a block layout, i.e. the items are located in parallel picking aisles, and the order pickers can only change over to another picking aisle at certain positions by means of so-called cross aisles. In this paper, for the first time a mathematical programming formulation is proposed which takes into account this specific property. Based on extensive numerical experiments, it is shown that the proposed formulation is superior to standard TSP formulations

A search for pre-substellar cores and proto-brown dwarf candidates in Taurus: multiwavelength analysis in the B213-L1495 clouds

In an attempt to study whether the formation of brown dwarfs (BDs) takes place as a scaled-down version of low-mass stars, we conducted IRAM30m/MAMBO-II observations at 1.2 mm in a sample of 12 proto-BD candidates selected from Spitzer/IRAC data in the B213-L1495 clouds in Taurus. Subsequent observations with the CSO at 350 micron, VLA at 3.6 and 6 cm, and IRAM30m/EMIR in the 12CO(1-0), 13CO(1-0), and N2H+(1-0) transitions were carried out toward the two most promising Spitzer/IRAC source(s), J042118 and J041757. J042118 is associated with a compact (<10 arcsec or <1400 AU) and faint source at 350 micron, while J041757 is associated with a partially resolved (~16 arcsec or ~2000 AU) and stronger source emitting at centimetre wavelengths with a flat spectral index. The corresponding masses of the dust condensations are ~1 and ~5 Mjup for J042118 and J041757, respectively. In addition, about 40 arcsec to the northeast of J041757 we detect a strong and extended submillimetre source, J041757-NE, which is not associated with NIR/FIR emission down to our detection limits, but is clearly detected in 13CO and N2H+ at ~7 km/s, and for which we estimated a total mass of ~100 Mjup, close to the mass required to be gravitationally bound. In summary, our observational strategy has allowed us to find in B213-L1495 two proto-BD candidates and one pre-substellar core candidate, whose properties seem to be consistent with a scaled-down version of low-mass stars.Comment: MNRAS, 424, 2778; corrected typos, mass estimate refined in Section 3.2.1 and Section 5.3; conclusions unchange

The role of risk communication in public health interventions. An analysis of risk communication for a community quarantine in Germany to curb the SARS-CoV-2 pandemic

Background: Separating ill or possibly infectious people from their healthy community is one of the core principles of non-pharmaceutical interventions. However, there is scarce evidence on how to successfully implement quarantine orders. We investigated a community quarantine for an entire village in Germany (Neustadt am Rennsteig, March 2020) with the aim of better understanding the successful implementation of quarantine measures. Methods: This cross-sectional survey was conducted in Neustadt am Rennsteig six weeks after the end of a 14-day mandatory community quarantine. The sample size consisted of 562 adults (64% of the community), and the response rate was 295 adults, or 52% (33% of the community). Findings: National television was reported as the most important channel of information. Contact with local authorities was very limited, and partners or spouses played a more important role in sharing information. Generally, the self-reported information level was judged to be good (211/289 [73.0%]). The majority of participants (212/289 [73.4%]) approved of the quarantine, and the reported compliance was 217/289 (75.1%). A self-reported higher level of concern as well as a higher level of information correlated positively with both a greater acceptance of quarantine and self-reported compliant behaviour. Interpretation: The community quarantine presented a rare opportunity to investigate a public health intervention for an entire community. In order to improve the implementation of public health interventions, public health risk communication activities should be intensified to increase both the information level (potentially leading to better compliance with community quarantine) and the communication level (to facilitate rapport and trust between public health authorities and their communities). © 2021 Scholz et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited