Variable Neighborhood Search for the Order Batching and Sequencing Problem with Multiple Pickers

Order picking deals with the retrieval of articles from their storage locations in order to satisfy customer requests. The transformation and consolidation of customer orders into picking orders (batches) is pivotal for the performance of order picking systems. Typically, customer orders have to be completed by certain due dates in order to avoid delays in production or in the shipment to customers. The composition of the batches, their processing times, their assignment to order pickers and the sequence according to which they are scheduled determine whether and the extent to which the due dates are missed. This article shows how Variable Neighborhood Descent and Variable Neighborhood Search can be applied in order to minimize the total tardiness of a given set of customer orders. In a series of extensive numerical experiments, the performance of the two approaches is analyzed for different problem classes. It is shown that the proposed methods provide solutions which may allow order picking systems to operate more efficiently

Solving the Order Batching and Sequencing Problem using Deep Reinforcement Learning

In e-commerce markets, on time delivery is of great importance to customer satisfaction. In this paper, we present a Deep Reinforcement Learning (DRL) approach for deciding how and when orders should be batched and picked in a warehouse to minimize the number of tardy orders. In particular, the technique facilitates making decisions on whether an order should be picked individually (pick-by-order) or picked in a batch with other orders (pick-by-batch), and if so with which other orders. We approach the problem by formulating it as a semi-Markov decision process and develop a vector-based state representation that includes the characteristics of the warehouse system. This allows us to create a deep reinforcement learning solution that learns a strategy by interacting with the environment and solve the problem with a proximal policy optimization algorithm. We evaluate the performance of the proposed DRL approach by comparing it with several batching and sequencing heuristics in different problem settings. The results show that the DRL approach is able to develop a strategy that produces consistent, good solutions and performs better than the proposed heuristics.Comment: Preprin

Designing new models and algorithms to improve order picking operations

Order picking has been identified as a crucial factor for the competitiveness of a supply chain because inadequate order picking performance causes customer dissatisfaction and high costs. This dissertation aims at designing new models and algorithms to improve order picking operations and to support managerial decisions on facing current challenges in order picking. First, we study the standard order batching problem (OBP) to optimize the batching of customer orders with the objective of minimizing the total length of order picking tours. We present a mathematical model formulation of the problem and develop a hybrid solution approach of an adaptive large neighborhood search and a tabu search method. In numerical studies, we conduct an extensive comparison of our method to all previously published OBP methods that used standard benchmark sets to investigate their performance. Our hybrid outperforms all comparison methods with respect to average solution quality and runtime. Compared to the state-of-the-art, the hybrid shows the clearest advantages on the larger instances of the existing benchmark sets, which assume a larger number of customer orders and larger capacities of the picking device. Finally, our method is able to solve newly generated large-scale instances with up to 600 customer orders and six items per customer order with reasonable runtimes and convincing scaling behavior and robustness. Next, we address a problem based on a practical case, which is inspired by a warehouse of a German manufacturer of household products. In this warehouse, heavy items are not allowed to be placed on top of light items during picking to prevent damage to the light items. Currently, the case company determines the sequence for retrieving the items from their storage locations by applying a simple S-shape strategy that neglects this precedence constraint. As a result, order pickers place the collected items next to each other in plastic boxes and sort the items respecting the precedence constraint at the end of the order picking process. To avoid this sorting, we propose a picker routing strategy that incorporates the precedence constraint by picking heavy items before light items, and we develop an exact solution method to evaluate the strategy. We assess the performance of our strategy on a dataset provided to us by the manufacturer. We compare our strategy to the strategy used in the warehouse of the case company, and to an exact picker routing approach that does not consider the given precedence constraint. The results clearly demonstrate the convincing performance of our strategy even if we compare our strategy to the exact solution method that neglects the precedence constraint. Last, we investigate a new order picking problem, in which human order pickers of the traditional picker-to-parts setup are supported by automated guided vehicles (AGVs). We introduce two mathematical model formulations of the problem, and we develop a heuristic to solve the NP-hard problem. In numerical studies, we assess the solution quality of the heuristic in comparison to optimal solutions. The results demonstrate the ability of the heuristic in finding high-quality solutions within a negligible computation time. We conduct several computational experiments to investigate the effect of different numbers of AGVs and different traveling and walking speed ratios between AGVs and order pickers on the average total tardiness. The results of our experiments indicate that by adding (or removing) AGVs or by increasing (or decreasing) the AGV speed to adapt to different workloads, a large number of customer orders can be completed until the respective due date

Metaheuristics for the Order Batching Problem in Manual Order Picking Systems

In manual order picking systems, order pickers walk or drive through a distribution warehouse in order to collect items which are requested by (internal or external) customers. In order to perform these operations effciently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours is minimized which are necessary to collect all items. The authors introduce two metaheuristic approaches for the solution of this problem; the rst one is based on Iterated Local Search, the second one on Ant Colony Optimization. In a series of extensive numerical experiments, the newly developed approaches are benchmarked against classic solution methods. It is demonstrated that the proposed methods are not only superior to existing methods, but provide solutions which may allow for operating distribution warehouses signicantly more effcient.Warehouse Management, Order Picking, Order Batching, Iterated Local Search, Ant Colony Optimization

Data-driven warehouse optimization

Batching orders and routing order pickers is a commonly studied problem in many picker-to-parts warehouses. The impact of individual differences in picking skills on performance has received little attention. In this paper, we show that taking into account differences in the skills of individual pickers when assigning work has a substantial effect on total batch execution time and picker productivity. We demonstrate this for the case of a Finnish retailer. First, using time-stamped picking data, multilevel modeling is used to forecast batch execution times for individual pickers by modeling individual skills of pickers. Next, these forecasts are used to minimize total batch execution time, by assigning the right picker to the right order batch. We formulate the problem as a joint order batching and generalized assignment model, and solve it with an Adaptive Large Neighborhood Search algorithm. For the sample company, we are able to improve state-of-the-art batching and routing methods by almost 10% taking skill differences among pickers into account and minimizing the sum of total order processing time. Compared to assigning order batches to pickers only based on individual picker productivity, savings of 6% in total time are achieved

Tabu Search Heuristics for the Order Batching Problem in Manual Order Picking Systems

In manual order picking systems, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours necessary to collect all items is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first one is a straightforward classic Tabu Search algorithm (TS), the second one is the Attribute-Based Hill Climber (ABHC). In a series of extensive numerical experiments, the newly developed approaches are benchmarked against different solution methods from literature. It is demonstrated that the proposed methods are superior to existing methods and provide solutions which may allow for operating distribution warehouses significantly more efficiently

Integrated zone picking and vehicle routing operations with restricted intermediate storage

The competitiveness of a retailer is highly dependent on an efficient distribution system. This is especially true for the supply of stores from distribution centers. Stores ask for high flexibility when it comes to their supply. This means that fast order processing is essential. Order processing affects different subsystems at the distribution center: Orders are picked in multiple picking zones, transferred to intermediate storage, and delivered via dedicated tours. These processing steps are highly interdependent. The schedule for picking needs to be synchronized with the routing decisions to ensure availability of the delivery orders at the DC’s loading docks when their associated tours are scheduled. Concurrently, intermediate storage represents a bottleneck as capacities for order storage are limited. The simultaneous planning of picking and routing operations with restricted intermediate storage is therefore relevant for retail practice but has not so far been considered within an integrated planning approach. Our work addresses this task and discusses an integrated zone picking and vehicle routing problem with restricted intermediate storage. We present a comprehensive model formulation and introduce a general variable neighborhood search for simultaneous consideration of the given planning stages. We also present two alternative sequential approaches that are motivated by the prevailing planning situation in industry. Numerical experiments that we have conducted show the need for an integrated planning approach to obtain practicable results. Further, we identify the impact of the main problem characteristics on the overall planning problem and provide valuable insights for the application of this approach in industry