A hybrid artificial neural network, genetic algorithm and column generation heuristic for minimizing makespan in manual order picking operations

doi:10.1016/j.eswa.2020.113566

Expert Systems with Applications

Volume 159, 30 November 2020, 113566

https://doi.org/10.1016/j.eswa.2020.113566 Get rights and content

Highlights

•
A soft computing-based column generation heuristic for order picking is proposed.
•
The proposed algorithm is compared against PSA-ACO and an exact method.
•
Based on numerical experiments some managerial insights are proposed.

Abstract

At an operational level, order picking is the main activity in fulfillment centers. Motivated by and through collaboration with a third party logistic company, this study presents a novel hybrid column generation (CG), genetic algorithm (GA), and artificial neural network (ANN) heuristic for minimizing makespan in manual order picking operations. The results of column generation heuristic is compared against a mixed integer programming model solved by Gurobi, and a parallel simulated annealing and ant colony optimization (PSA-ACO) previously proposed in the literature. Through numerical experiments, the superiority of CG heuristic compared to other methods is shown, and some managerial insights regarding the relationship between makespan optimization, workload balance, picking capacity, and number of pickers in order picking operations is presented.

Introduction

Order picking processes shape the foundation of modern fulfillment centers and are a determining factor in the efficiency of retail and e-tail supply chains. Manual order picking operations comprise of labor-intensive activities that can potentially contribute up to 60% of a fulfillment center cost (Ardjmand et al., 2019, Kulak et al., 2012). For this reason, many approaches are proposed to control and improve picking activities (Poon et al., 2009). The main objective of order picking operations is to retrieve stock-keeping units (SKUs) from their location in a warehouse based on the orders received from customers.

Order picking operations are usually preceded by the tactical problem of locating items in a fulfillment center (Chan & Chan, 2011). In the literature of order picking, four sub-problems are recognized: order batching, batch assignment, batch sequencing, and picker routing (Scholz et al., 2017, Ardjmand et al., 2018). In the order batching sub-problem, customer orders are batched in such a way to facilitate the picking process by pickers and optimize a particular criterion such as the total distance traveled to pick the batch. Batch assignment sub-problem is usually relevant when there are more than one, but a limited number of pickers and various assignment scenarios may result in different values of picking makespan or tardiness. Batch sequencing sub-problem deals with determining the sequence of batches assigned to a picker, and is usually considered when tardiness minimization is of interest. Picker routing sub-problem is concerned with minimizing the length of tours that pickers traverse during the order picking operations.

While the order picking problem is extensively studied, still some structural and methodological gaps exist. The majority of the order picking studies focus on order batching, and picker routing sub-problems and the proportion of the studies that go beyond these two sub-problems are relatively low (Ardjmand et al., 2018, Scholz et al., 2017, van Gils et al., 2019, Chen et al., 2015). Moreover, most of the studies in order picking are focused on minimizing total distance traveled or tardiness, which may not be suitable for wave-picking warehouses, as discussed in (Ardjmand et al., 2018). To the best of the authors’ knowledge, there is only one study that deals with minimizing makespan while considering all relevant order picking sub-problems (Ardjmand et al., 2018). Additionally, from a methodological viewpoint and as noted by Gademann and Velde (2005), order picking problems with the objective of makespan minimization do not easily lend themselves to column generation (CG) algorithms. Thus, the research on the application of column generation algorithms to the order picking problems is quite scarce.

Motivated by a collaboration with a third party logistic company and the gaps mentioned earlier, this study aims at proposing a hybrid column generation (CG) heuristic for minimizing makespan in an order picking problem where order batching, batch assignment, and picker routing sub-problems are to be solved simultaneously. For this purpose, a novel methodology based on artificial neural networks (ANNs) and genetic algorithm (GA) for estimating and optimizing reduced costs in the column generation algorithm is proposed. In this methodology, an ANN is trained to estimate the optimum length of a batch and later is utilized as the basis of the fitness function in a GA whose objective is to find the batch with minimum reduced cost. For evaluation purposes, the proposed methods are compared against a mixed integer programming model solved by Gurobi, and a hybrid parallel simulated annealing and ant colony optimization (PSA-ACO) algorithm proposed by Ardjmand et al. (2018).

The contributions of this study are twofold:

•
A novel hybrid CG, GA, and ANN method for minimizing makespan in order picking problems is proposed.
•
The performance of the proposed column generation heuristic is compared against PSA-ACO and an exact method by using real data obtained from a third party logistics company.

The remainder of this paper is organized as follows. In Section 2, the problem is defined. In Section 3, related literature is reviewed. In Section 4, a mathematical model for the problem is introduced. Section 5 is dedicated to the proposed column generation heuristic. In Section 6, numerical experiments are conducted, and managerial insights are discussed. Finally, in Section 7, overall conclusion is stated.

Section snippets

Problem statement

The picking operation starts with grouping the orders into a maximum of Bbatches and assigning them to the pickers. Orders assigned to a batch must not exceed pickers’ capacity C. A picker picks a batch by traversing a tour in the warehouse that begins from the origin O, visits the locations of items in the batch, and returns to O. Fig. 1 depicts an order picking operation where ten orders are to be batched, assigned to pickers, and picked. Note that in the picker routing stage of Fig. 1, only

Literature review

This section presents a review of the order picking operations and its sub-problems. Table 1 summarizes previous studies, order picking sub-problems they have considered, methods, and the objectives they used. As can be observed in Table 1 and discussed by Cergibozan and Tasan (2016), the majority of order picking studies have utilized a heuristic or metaheuristic approach. In terms of objective function, total distance/time traveled, and total tardiness are the most common objectives, which is

Model

In this section, a mixed integer programming model $P$ for minimizing makespan of an integrated order batching, batch assignment, and picker routing problem is proposed. Indices, parameters, and decision variables are defined as follows:

Indexes:

$b \in B = {1, 2, \dots, B}$ : batches.

$r \in R = {1, 2, \dots, R}$ : pickers.

$i \in N = {1, 2, \dots, N}$ : customers/orders.

$j \in M = {1, 2, \dots, M}$ : products.

$O$ : index of the origin point in the warehouse.

Parameters:

$d_{j_{1} j_{2}} = d_{j_{2} j_{1}}$ : minimum traveling time between locations of items $j_{1}$ and $j_{2}$ in the warehouse.

$d_{Oj} = d_{jO}$

Column generation heuristic

In this section, a column generation heuristic for the problem under study is proposed. The main idea behind the column generation algorithm is to solve the linear relaxation of a small subset of decision variables, which is usually referred to as restricted master problem (RMP). For this purpose, it is often necessary to reformulate the original problem as a set partitioning problem. In this study, a variable in the set partitioning formulation is corresponding to a set of orders batched

Numerical experiments

In this section, using real data obtained from a 3PL company is used to investigate and evaluate the efficiency of the proposed column generation heuristic. The warehouse of this study has 23 parallel aisles and 25 bays in each aisle side. The majority of the orders for this warehouse have less than 25 items. The results obtained are compared against the exact solutions of model $P$ solved using Gurobi 8.1 and PSA-ACO algorithm for a similar problem as proposed in (Ardjmand et al., 2018). CPU

Conclusion

Order picking is a central problem in picking operations of fulfillment centers. This study investigates a makespan optimization problem in manual order picking operations where order batching, batch assignment, and picker routing are to be optimized simultaneously. Since minimax optimization problems (including makespan minimization problems) are not structurally suitable for column generation algorithms, a novel CG method is proposed to surmount this problem. Additionally, ANN and GA are

References (52)

E. Ardjmand et al.
Using list-based simulated annealing and genetic algorithm for order batching and picker routing in put wall based picking systems
Applied Soft Computing
(2019)
E. Ardjmand et al.
Minimizing order picking makespan with multiple pickers in a wave picking warehouse
International Journal of Production Economics
(2018)
T. Bódis et al.
Bacterial memetic algorithms for order picking routing problem with loading constraints
Expert Systems with Applications
(2018)
F.T. Chan et al.
Improving the productivity of order picking of a manual-pick and multi-level rack distribution warehouse through the implementation of class-based storage
Expert Systems with Applications
(2011)
M.-C. Chen et al.
Aggregation of orders in distribution centers using data mining
Expert Systems with Applications
(2005)
T.-L. Chen et al.
An efficient hybrid algorithm for integrated order batching, sequencing and routing problem
International Journal of Production Economics
(2015)
C.-Y. Cheng et al.
Using a hybrid approach based on the particle swarm optimization and ant colony optimization to solve a joint order batching and picker routing problem
International Journal of Production Economics
(2015)
P. Cortés et al.
A tabu search approach to solving the picking routing problem for large-and medium-size distribution centres considering the availability of inventory and k heterogeneous material handling equipment
Applied Soft Computing
(2017)
S. Henn
Algorithms for on-line order batching in an order picking warehouse
Computers & Operations Research
(2012)
S. Henn et al.
Metaheuristics for order batching and sequencing in manual order picking systems
Computers & Industrial Engineering
(2013)

S. Henn et al.

Tabu search heuristics for the order batching problem in manual order picking systems

European Journal of Operational Research

(2012)

Y.-C. Ho et al.

Order-batching methods for an order-picking warehouse with two cross aisles

Computers & Industrial Engineering

(2008)

L.-F. Hsieh et al.

New batch construction heuristics to optimise the performance of order picking systems

International Journal of Production Economics

(2011)

C.-C. Lin et al.

Joint order batching and picker manhattan routing problem

Computers & Industrial Engineering

(2016)

M. Matusiak et al.

A fast simulated annealing method for batching precedence-constrained customer orders in a warehouse

European Journal of Operational Research

(2014)

B. Menéndez et al.

General variable neighborhood search for the order batching and sequencing problem

European Journal of Operational Research

(2017)

B. Menéndez et al.

Variable neighborhood search strategies for the order batching problem

Computers & Operations Research

(2017)

T. Öncan

Milp formulations and an iterated local search algorithm with tabu thresholding for the order batching problem

European Journal of Operational Research

(2015)

J.C.-H. Pan et al.

Order batching in a pick-and-pass warehousing system with group genetic algorithm

Omega

(2015)

T. Poon et al.

A rfid case-based logistics resource management system for managing order-picking operations in warehouses

Expert Systems with Applications

(2009)

K.J. Roodbergen et al.

Routing order pickers in a warehouse with a middle aisle

European Journal of Operational Research

(2001)

A. Scholz et al.

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

European Journal of Operational Research

(2017)

C.A. Valle et al.

Optimally solving the joint order batching and picker routing problem

European Journal of Operational Research

(2017)

J. Zhang et al.

On-line scheduling of order picking and delivery with multiple zones and limited vehicle capacity

Omega

(2018)

I. Žulj et al.

A hybrid of adaptive large neighborhood search and tabu search for the order-batching problem

European Journal of Operational Research

(2018)

M. Albareda-Sambola et al.

Variable neighborhood search for order batching in a warehouse

Asia-Pacific Journal of Operational Research

(2009)

Cited by (30)

Order batching problems: Taxonomy and literature review
2024, European Journal of Operational Research
Order Batching is a family of optimization problems related to the process of picking items in a warehouse as part of supply chain management. Problems classified into this category are those whose picking policy consists of grouping the orders received in a warehouse into batches, prior to starting the picking process. Once the batches have been formed, all items within the same batch are picked together on a single picking route. In this survey we review the optimization problems known in this family, focusing on manual picking systems and rectangular-shaped warehouses with only parallel and cross aisles, which is the most common warehouse configuration in the literature. First, we identify the decisions within the strategic, tactical, and operational levels that influence the picking task. Then, we characterize the optimization problems belonging to this family, whose objective function might differ. The identified problems are classified into a taxonomy proposed in this paper, which is designed to host future problems within this family. We also review the most outstanding papers by category and the strategies and algorithms proposed for the most relevant activities: batching, routing, sequencing, waiting, and assigning. To conclude, we outline the open issues and future paths of the topic under study.
Responsive pick face replenishment strategy for stock allocation to fulfil e-commerce order
2023, International Journal of Production Economics
In the rapidly growing e-commerce industry, pallet picking is no longer feasible as the stock keeping units (SKUs) change from the pallet level to the carton or item level. Thus, an effective order-picking process focusing on fast and efficient retrieval of SKUs from shelves is required to fulfil numerous small lot-sized e-commerce orders within a short time. This study investigates a responsive pick face replenishment (RPFR) strategy that divides the high-bay racks in the distribution centres (DCs) into two parts: the upper-deck reserve areas and the pick-face forward areas to improve the operational efficiency in order picking. To address the fluctuating order demand and limited space in the pick-face forward areas, the proposed RPFR system integrates a predictive analytics algorithm with an adaptive network-based fuzzy inference system (ANFIS) and adaptive genetic algorithm-based stock allocation model to generate an optimal stock replenishment plan. By predicting the order demand of each SKU in the next time interval, the types of selected SKUs and their quantities to be loaded into the pick-face forward areas are determined. Numerical experiments are performed to validate the system performance, and comparative analyses are conducted to determine the best parameter settings for the models.
A comprehensive review of batching problems in low-level picker-to-parts systems with order due dates: Main gaps, trade-offs, and prospects for future research
2022, Journal of Manufacturing Systems
Citation Excerpt :
However, literature focuses rather on the high-level picker-to-parts system and/or on the Automated Storage and Retrieval System (AS/RS), leaving many gaps, perhaps because they are NP-hard, to the low-level picker-to-parts system [40,54,56]. Moreover, most order-picking studies focus on order batching and picker routing subproblems [2]. This results from the picking solutions for this type of system including several questions that outstrip the use of algorithms and the agility of the POMs’ Computational Processing Time (CPT) [108].
Literature has shown expressive demands for Picking Optimization Methods (POMs) that are better suited to the manual picking systems and Warehouses (WAs). There are still many gaps and trade-offs between the level of customer service and the WA efficiency for the so-called Joint Order Batching, Assignment and Sequencing, and Routing Problem (JOBASRP). Thus, the objective of this manuscript is to provide a literature review on the POMs proposed for the JOBASRP in WAs that deal with low-level picker-to-parts systems together with the order due dates and Stock Keeping Units. In the total of analyzed manuscripts (from 1960 to 2021), metaheuristics together with constructive heuristics obtained the best solutions for the JOBASRP. The most used technique is the Genetic Algorithm (50 %), followed by the Variable Neighborhood Search (40 %) and Iterated Local Search (10 %). The main performance indicators are Total Picking Time, Tardiness in Customer Orders and Computational Processing Time for POMs. In addition, we present a reflection focused on the main gaps, trade-offs, and prospects for improving the level of adaptation and performance demanded for the POMs. This manuscript provides eminent contributions to WAs management theory and practice and to the application of the so-called POMs. The theoretical framework presented summarizes the state of the art, defining the basic guidelines regarding new research opportunities, and supporting managers, students, and researchers in the optimization processes and decision making in WAs. We conclude that broader views on adaptation taxonomies and multi-objective algorithms will guide the integration between different areas of the WAs and the development of better POMs.
In-store order fulfilment in omni-channel supermarkets with heterogeneous workforce: A bi-objective optimisation approach
2022, Computers and Industrial Engineering
The development of omni-channel retailing brings both opportunities and challenges to conventional supermarkets. Utilising local establishments to complete online customer orders is critical to providing timely and seamless omni-channel shopping experiences. We propose a bi-objective mixed-integer non-linear order batching and assignment optimisation model with the objectives of minimising person-hours, earliness and tardiness penalties, and workload imbalance. We apply a multi-objective genetic algorithm-based heuristic to obtain the Pareto frontier solutions in an omni-channel supermarket case, demonstrating the effectiveness of the proposed model and trade-offs among objectives. By conducting extensive numerical experiments, we discuss the influences of unique operational attributes in omni-channel supermarkets, namely workforce heterogeneity and store crowding, on the performance of in-store order fulfilment. Results suggest that the proposed model are relatively robust to workforce heterogeneity and coordinating online/offline channel traffic in peak hours is of importance. Overall, the research highlights the essence of bi-objective optimisation in order fulfilment and the importance of incorporating the operational attributes in omni-channel retail stores. We lastly provide managerial insights for in-store order fulfilment in omni-channel supermarkets.
Order batching and sequencing for minimising the total order completion time in pick-and-sort warehouses
2022, Expert Systems with Applications
Citation Excerpt :
Blocking and starving will seriously delay the total order completion time in warehouses and threaten the timeliness of order fulfilment. Most previous studies (Arbex Valle & Beasley, 2020; Ardjmand et al., 2020; Hwang & Kim, 2005; Ruben & Jacobs, 1999; Yang, Zhao, & Guo, 2020) generally focused on the order picking process under the sort-while-pick strategy (Fig. 1(a)). They mainly studied the order batching problem (OBP) to minimise the total order picking time.
Under the pick-and-sort order batch processing strategy, orders successively go through an order picking process, a buffer area, and an order sorting process in the form of batches. Owing to the difference in order batches and the limitation of the buffer capacity, blocking in the picking and starving in the sorting often occurs. This leads to a longer order completion time. Therefore, to minimise the total order completion time, this study investigates the order batching and sequencing problem under this strategy to reduce or even eliminate the blocking and starving phenomena. We formulate this problem as a mathematical model. By analysing the model, two useful properties and a lower bound are obtained. Based on these properties, we propose a situation-based seed (SBS) algorithm to solve the problem, which provides the intelligence of coordination for the classical seed algorithm. Numerical experiments demonstrate the superiority, effectiveness and optimality of the proposed algorithm. The proposed algorithm can save 8.359% of the total order completion time compared with the real-life algorithm applied in pick-and-sort warehouses, and its performance is close to the lower bound (only 1.105% gap). In addition, we also provide some management insights on how to coordinate the picking and sorting processes in practical pick-and-sort warehouses.
Mitigating the risk of infection spread in manual order picking operations: A multi-objective approach
2021, Applied Soft Computing
Citation Excerpt :
This section examines the existing order picking literature that is most relevant to the subject of this study. Structurally, and from an operational standpoint, order picking problems are composed of four sub-problems of order batching, batch assignment, batch sequencing, and picker routing [15–17], among which order batching and picker routing are the subjects of this study. Order batching is primarily revolving around grouping a set of customer orders in such a manner to achieve a set of operational objectives such as total travel time or tardiness minimization [18–20].
In the aftermath of the COVID-19 pandemic, supply chains experienced an unprecedented challenge to fulfill consumers’ demand. As a vital operational component, manual order picking operations are highly prone to infection spread among the workers, and thus, susceptible to interruption. This study revisits the well-known order batching problem by considering a new overlap objective that measures the time pickers work in close vicinity of each other and acts as a proxy of infection spread risk. For this purpose, a multi-objective optimization model and three multi-objective metaheuristics with an effective seeding procedure are proposed and are tested on the data obtained from a major US-based logistics company. Through extensive numerical experiments and comparison with the company’s current practices, the results are discussed, and some managerial insights are offered. It is found that the picking capacity can have a determining impact on reducing the risk of infection spread through minimizing the picking overlap.

View all citing articles on Scopus

View full text

A hybrid artificial neural network, genetic algorithm and column generation heuristic for minimizing makespan in manual order picking operations

Highlights

Abstract

Introduction

Section snippets

Problem statement

Literature review

Model

Column generation heuristic

Numerical experiments

Conclusion

Applied Soft Computing

International Journal of Production Economics

Expert Systems with Applications

Expert Systems with Applications

Expert Systems with Applications

International Journal of Production Economics

International Journal of Production Economics

Applied Soft Computing

Computers & Operations Research

Computers & Industrial Engineering

European Journal of Operational Research

Computers & Industrial Engineering

International Journal of Production Economics

Computers & Industrial Engineering

European Journal of Operational Research

European Journal of Operational Research

Computers & Operations Research

European Journal of Operational Research

Omega

Expert Systems with Applications

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

Omega

European Journal of Operational Research

Variable neighborhood search for order batching in a warehouse

Asia-Pacific Journal of Operational Research