Solving the order batching and sequencing problem with multiple pickers: A grouped genetic algorithm

This paper introduces a grouped genetic algorithm (GGA) to solve the order batching and sequencing problem with multiple pickers (OBSPMP) with the objective of minimizing total completion time. To the best of our knowledge, for the first time, an OBSPMP is solved by means of GGA considering picking devices with heterogeneous load capacity. For this, an encoding scheme is proposed to represent in a chromosome the orders assigned to batches, and batches assigned to picking devices. Likewise, the operators of the proposed algorithm are adapted to the specific requirements of the OBSPMP. Computational experiments show that the GGA performs much better than six order batching and sequencing heuristics, leading to function objective savings of 18.3% on average. As a conclusion, the proposed algorithm provides feasible solutions for the operations planning in warehouses and distribution centers, improving margins by reducing operating time for order pickers, and improving customer service by reducing picking service times

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

Two exponential neighborhoods for single machine scheduling

We study the problem of minimizing total completion time on a single machine with the presence of release dates. We present two different approaches leading to exponential neighborhoods in which the best improving neighbor can be determined in polynomial time. Furthermore, computational results are presented to get insight in the performance of the developed neighborhoods

A new mathematical model for single machine batch scheduling problem for minimizing maximum lateness with deteriorating jobs

This paper presents a mathematical model for the problem of minimizing the maximum lateness on a single machine when the deteriorated jobs are delivered to each customer in various size batches. In reality, this issue may happen within a supply chain in which delivering goods to customers entails cost. Under such situation, keeping completed jobs to deliver in batches may result in reducing delivery costs. In literature review of batch scheduling, minimizing the maximum lateness is known as NP-Hard problem; therefore the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In order to solve the proposed model, a Simulation annealing meta-heuristic is used, where the parameters are calibrated by Taguchi approach and the results are compared to the global optimal values generated by Lingo 10 software. Furthermore, in order to check the efficiency of proposed method to solve larger scales of problem, a lower bound is generated. The results are also analyzed based on the effective factors of the problem. Computational study validates the efficiency and the accuracy of the presented model

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