Joint order batching and picker Manhattan routing problem

https://doi.org/10.1016/j.cie.2016.03.009Get rights and content

Highlights

  • We jointly consider order batching and order routing, measured precisely by Manhattan distance.

  • We develop particle swarm optimization (PSO) with bad experiences for this problem.

  • We propose a solution representation to handle batching and routing simultaneously.

  • We theoretically analyze stability and convergence of the proposed PSO heuristic.

  • We evaluate performance of the proposed PSO heuristic for a real-world PC company.

Abstract

In picking product items in a warehouse to fulfill customer orders, a practical way is to classify similar orders as the same batch and then to plan the optimal picker routing when picking each batch of items. Different from the previous problems, this work investigates the joint order batching and picker Manhattan routing problem, which simultaneously determines the optimal order batching allocation and the shortest picker Manhattan routing that cannot pass through storage shelves in the warehouse, under some practical constraints. This work further addresses this problem by particle swarm optimization with bad experience to avoid bad solutions, in which a novel solution representation is designed for simultaneously handling both order batching and picker routing. The idea of the design is to transform the warehouse floorplan into a grid, in which virtual order center and batch center are defined to represent symbolic positions of orders and batches of the solution, respectively. By calculating the distance between the two centers, similar orders are categorized as the same batch. Additionally, theoretical analysis of convergence and stability of the proposed approach is also derived. Performance of this approach is evaluated via comprehensive experimental analysis and a case study.

Introduction

Order picking is a core operation of warehouse management, based on needs of customer orders to quickly and accurately pick out the ordered product items from product shelves or other locations and move them with a specific procedure. The order picking process consists of information collection of order picking, traveling or moving and picking, as well as sorting and accumulation. A good planning for order picking can help substantially improve efficiency of warehouse management, and hence, it is of interest and importance to appropriately plan the picker routing distance as short as possible to save picker routing time and further to reduce time cost. In practice, customer orders in some industries (e.g., retailing and customized assembly) are often of great diversity and of small quantity of items. To reduce unnecessary repetitive picker routings, the orders for items with similar picking routing are generally categorized as the same batch to be picked before planning the order picking routes. A suitable order batching helps shorten the picker routing distance and reduce the time cost.

In practice, order-picking vehicles are used for picking and moving product items inside a warehouse for higher efficiency, and they are electric in modern warehouses. Design of the routing for order-picking vehicles in warehouses (a.k.a., order picking routing or picker routing) determines the total picker routing distance, which could be viewed as a vehicle routing problem (VRP). Lots of works on designing metaheuristic algorithms for various VRPs existed, e.g., Kumar et al., in press, Luo et al., 2015, Yassen et al., 2015. For designing particle swarm optimization (PSO) approaches for VRPs, the works in Ai and Kachitvichyanukul, 2009a, Ai and Kachitvichyanukul, 2009b, Kachitvichyanukul et al., 2015 proposed the PSO with novel solution representations to solve various VRPs. The work in Goksal, Karaoglan, and Altiparmak (2013) proposed a hybrid discrete PSO for the VRP with simultaneous pickup and delivery. The work in Marinakis, Marinaki, and Dounias (2010) proposed a hybrid PSO for VRP. The work in Marinakis, Iordanidou, and Marinaki (2013) showed that PSO is the best approach to the order picking routing problem as compared with genetic algorithm (GA) and ant colony optimization (ACO). Therefore, PSO is suitable for the order picking routing problem for order-picking vehicles.

Recent works have considered the joint order batching and picker routing problem (Won & Olafsson, 2005), which classifies customer orders into batches and then bases the batching allocation to determine the order picking routing. The work in Kulak, Sahin, and Taner (2011) proposed a two-stage algorithm for the joint problem, which uses a cluster algorithm to allocate order batching according to similarity of orders, and then uses tabu search to plan the shortest picker routing. The work in Tsai, Liou, and Huang (2008) proposed a two-stage GA to solve the joint problem; and the previous work in Cheng, Chen, Chen, and Yoo (2015) proposed a two-stage method based on PSO and ACO to solve the joint problem. However, most of the previous methods tended to provide a solution for either the order batching (Hwang & Lee, 1988) or the order picking routing (Marinakis et al., 2013), or used a two-stage approach (Cheng et al., 2015, Kulak et al., 2011, Tsai et al., 2008) to first determine the order batching allocation and then decide the order picking routing. In calculating the picker routing distance, they adopted the Euclidean distance to measure the shortest distance between two locations in a warehouse, and did not consider that some locations in the warehouse cannot be passed through in practice, so that the picker routing distance under this constraint may be different from the actual warehouse environment. To meet practical situations, this work investigates the joint order batching and picker Manhattan routing problem, and the major difference from previous problems is to adopt the Manhattan distance (i.e., strictly horizontal or vertical path) that cannot pass through any product storage shelves in the warehouse to measure the shortest picker routing distance between two locations in the warehouse. The objective of this problem is to find the optimal batching of orders with diversified items and the shortest picker Manhattan routing in the warehouse under some practical constraints. Inheriting from the original problem in Kulak et al. (2011), this problem is generally NP-hard, i.e., it cannot be solved deterministically in polynomial time.

This work solves the concerned problem by an improved PSO (ImPSO for short) based on Immanuel Selvakumar and Thanushkodi (2007), which additionally introduces each particle’s previous bad experience to accelerate the convergence process of the PSO algorithm. One of the key designs in this work is to propose a novel solution representation for ImPSO, which can simultaneously determine both order batching and picker routing. The idea behind this solution representation is to consider the warehouse floorplan as a grid and to define virtual order center and batch center as the symbolic positions of orders and batches in the warehouse, respectively. By calculating the distance between the two centers, the orders with a high degree of similarity (in terms of the distance between the two centers) are categorized as the same batch.

The main contributions of this work are given as follows:

  • The problem of concern in this work is more general than the previous ones. In calculating the picker routing distance, this work considers the fact that some locations in the warehouse cannot be passed through. Additionally, as compared with the previous work in Kulak et al. (2011) restricted to a fixed warehouse floorplan, this work presents a generalized distance calculation algorithm for different warehouse floorplans, so that the proposed approach can be applied to different warehouse configurations. Another main difference from the previous works is that the picker routing distance in this work is measured precisely by the Manhattan distance that cannot pass through any storage shelves in the warehouse.

  • A novel solution representation is designed for determining both the order batching allocation and the picker Manhattan routing simultaneously.

  • The proposed approach is applicable to customer orders with diversified items and small quantities, which conform to practical situations in some industries (e.g., retailing and customized assembly).

  • This work theoretically analyzes stability and convergence of the proposed ImPSO algorithm. After many experiments under different parameters are conducted, it is discovered that bad experiences of particles in the ImPSO algorithm serve as an indispensable factor in the optimization process in handling the concerned problem.

The remainder of this work is organized as follows. Section 2 introduces the order picking system in warehouses, and gives a detail literature review. Section 3 describes the problem concerned in this work, proposes the algorithm with a novel solution representation for the problem, and derives a theoretical analysis for convergence and stability of the proposed algorithm. Section 4 gives a comprehensive experimental analysis of the proposed algorithm, and then compares the performance of a case study using the proposed approach and the current practice. Section 5 compares the performance of a case study using the proposed approach and the current practice. Lastly, Section 6 gives a conclusion with future work.

Section snippets

Preliminaries

This section first introduces the order picking system in warehouses, and then describes the concerned problem.

The proposed approach

This section first explains main components of the proposed approach, and then derives its algorithm analysis.

Implementation and experimental results

This section conducts a comprehensive experimental analysis on the proposed ImPSO algorithm. Initially, the experimental data and environment are explained, and a suitable parameter setting for the experimental problem is found after a number of experiments. Next, the convergence of ImPSO, the performance using different numbers of particles, and the performance using different scaling factors are analyzed.

Case study

This section adopts the proposed ImPSO algorithm to a real-world case, and compares the experimental results with the current practice of the enterprise in the case. First, the environment and the current practice of the case are described, and then, the experimental results using the proposed ImPSO algorithm are given and compared.

Note that the previous related works (e.g., Kulak et al., 2011, Tsai et al., 2008, Won and Olafsson, 2005) only provided experimental parameter settings, rather than

Conclusion

This work has designed an improved PSO (ImPSO) approach with bad experiences to solve the joint order batching and picker Manhattan routing problem under some practical constraints, in which a novel solution representation is designed for simultaneously determining the order batching allocation and the picker routing distance. In order batching allocation, similar items (in terms of the shortest picker Manhattan distance between order centers and batch centers) are classified into the same

Acknowledgements

The authors thank the anonymous referees for comments that improved the content as well as the presentation of this paper. This work has been supported in part by MOST 104-2221-E-009-101, Taiwan.

References (32)

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