An Order-Picking Problem in a Medical Facility Using Genetic Algorithm

Abstract

Storage operations, order-picking, and product-handling processes have become increasingly important in today’s industrial environment. These operations are a huge burden for businesses in terms of time and cost, but they often do not add direct value to products or services. Therefore, it has become essential to improve the storage operations to the highest quality, reduce the costs arising from storage, and increase customer satisfaction. This study compared genetic algorithm (GA) and simulated annealing (SA) methods with existing real results and operations in order to minimize the distance traveled by the picker in order-picking systems, optimize routes, and increase operational efficiency in the medical textile industry. In the analyses conducted on product-based, list-based, and order-based strategies, real data sets were used to examine the performance of both methods in detail. The study results revealed that GA reduced the total travel distance by 50% and reduced the total number of tours from 51 to 32. In addition, the SA method provided efficient results in certain scenarios, but GA showed superior performance in terms of minimizing the distance and number of tours. While the product-based strategy provided the best results regarding travel distance and number of tours, the list-based approach showed a balanced performance. The study offers significant improvement potential in logistics operations by reducing distances by up to 37% and increasing operational efficiency by up to 50% in order-picking processes.

Full text

Academic Editors: Chia-Nan Wang,
Nhat Luong Nhieu, Phan Van-Thanh,
Hector Tibo and Jun-Qiang Wang
Received: 25 November 2024
Revised: 17 December 2024
Accepted: 23 December 2024
Published: 25 December 2024
Citation: Denizhan, B.; Yıldırım, E.;
Akkan, Ö. An Order-Picking Problem
in a Medical Facility Using Genetic
Algorithm. Processes 2025,13, 22.
https://doi.org/10.3390/
pr13010022
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
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Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
Article
An Order-Picking Problem in a Medical Facility Using
Genetic Algorithm
Berrin Denizhan * , Elif Yıldırım and Öznur Akkan
Department of Industrial Engineering, Engineering Faculty, Sakarya University, 54050 Sakarya, Türkiye;
elifyildirim@sakarya.edu.tr (E.Y.)
*Correspondence: denizhan@sakarya.edu.tr
Abstract: Storage operations, order-picking, and product-handling processes have become
increasingly important in today’s industrial environment. These operations are a huge
burden for businesses in terms of time and cost, but they often do not add direct value to
products or services. Therefore, it has become essential to improve the storage operations to
the highest quality, reduce the costs arising from storage, and increase customer satisfaction.
This study compared genetic algorithm (GA) and simulated annealing (SA) methods with
existing real results and operations in order to minimize the distance traveled by the picker
in order-picking systems, optimize routes, and increase operational efficiency in the medical
textile industry. In the analyses conducted on product-based, list-based, and order-based
strategies, real data sets were used to examine the performance of both methods in detail.
The study results revealed that GA reduced the total travel distance by 50% and reduced
the total number of tours from 51 to 32. In addition, the SA method provided efficient
results in certain scenarios, but GA showed superior performance in terms of minimizing
the distance and number of tours. While the product-based strategy provided the best
results regarding travel distance and number of tours, the list-based approach showed
a balanced performance. The study offers significant improvement potential in logistics
operations by reducing distances by up to 37% and increasing operational efficiency by up
to 50% in order-picking processes.
Keywords: travel distance optimization; warehouse operations; order picking optimization;
genetic algorithm; simulated annealing
1. Introduction
Order picking constitutes a vital element of warehouse operations, representing
roughly 50% to 55% of the total time utilization and 65% of overall operational costs [
1
].
Healthcare systems worldwide face mounting pressure to minimize waste and cut unnec-
essary costs while enhancing the quality of patient care. For instance, the supply chain
function oversees most of a health system’s external spending, which accounts for up to
40 percent
of total costs [
2
]. As a result, healthcare logistics and supply chain management
are increasingly scrutinized by both practitioners and researchers [
3
–
6
]). Manual order
picking is employed in small and medium enterprises. The storage process is overseen
by warehouse personnel who manually choose items from shelves and generate orders.
Despite technological advancements, many firms have favored manual order selection due
to its diminished technological requirements and lower costs. There are several categories
of order-picking systems. Picker-to-parts systems are the most common, where workers
move through shelves to pick products. This system can include low-level picking and
Processes 2025,13, 22 https://doi.org/10.3390/pr13010022

Processes 2025,13, 22 2 of 24
high-level picking, where workers use lifting mechanisms to reach high shelves. Order
picking is divided into and detailed as picking operations performed by humans or ma-
chines. For humans, picking policies are determined according to who is moving in the
picking area (picker or product) and whether a conveyor system is used. In cases where a
picker moves, picking can be performed according to the order or product, while in cases
where a conveyor system is used, order, product or piece-based picking policies are applied.
There are also automatic picking methods for operations performed by machines. This type
of classification helps to select an appropriate picking method to increase the efficiency of
warehouse operations [7].
The types of order picking, which are tailored to different operational scales and
efficiency goals, include single order picking, best suited for small businesses where indi-
vidual orders are processed independently [
8
]; batch order picking, ideal for consolidating
multiple orders to minimize picker travel [
9
–
11
]; zone order picking, designed for large
businesses to divide picking tasks by warehouse zones [
12
,
13
]; pick-and-pass, where items
are sequentially picked and passed along a predefined route [
14
]; cluster order picking,
focused on grouping similar orders to optimize picking time [
15
]; and wave order picking,
used to coordinate picking schedules with outbound shipping times [
16
]. Order-picking
systems have also been categorized, including sorting systems for the automated organiza-
tion of items [
17
]; pick-to-box systems, which streamline the packing process by picking
items directly into order-specific boxes [
18
–
20
]; picker-to-part systems, where pickers move
to retrieve items from storage locations (this study); and part-to-picker systems, where
items are brought to pickers via automated solutions for increased efficiency [21,22].
Given these classifications, order picking can be performed by humans or machines,
and each system offers different operational benefits and barriers. According to the lit-
erature, four main sub-problems are identified in order picking: order grouping, group
assignment, group sorting, and picker routing [
23
]. Optimizing order picking is crucial
for improving a company’s logistics performance. Careful planning and execution are
necessary to avoid inefficiencies and to reduce costs [
24
]. Otherwise, inefficient order
picking can lead to wasted time and under-utilization of resources [25].
In this study, the manual order-picking process of medical textile products operating
as a labor-intensive factory in Türkiye is discussed. Our aim is to improve the manual
order-picking process and develop a fast, forward-looking solution that can be adapted to
all similar applications by optimizing it with meta-heuristic techniques.
Moreover, recent research has explored advanced optimization techniques for improv-
ing order picking. He and Chen [
26
] proposed a dynamic routing algorithm for manual
order picking that adapts to real-time changes in the warehouse environment, reducing
overall travel time. In a study by Petersen and Aase [
27
], the effects of slotting optimization
were analyzed, revealing that well-planned product placement can significantly enhance
order-picking efficiency. Additionally, Grosse et al. [
28
] discussed the integration of au-
tonomous robots in parts-to-picker systems, highlighting the potential of collaborative
robots (cobots) in reducing human workload and increasing operational speed. Finally,
Boysen et al. [
29
] explored the benefits of zone-picking systems, where workers focus on
specific warehouse areas, leading to better workload distribution and increased throughput.
This study focuses on the picker-to-parts system, specifically low-level picking. How-
ever, this approach has drawbacks, such as higher error rates, slower processes, and
reduced productivity. Factors such as workforce fatigue and incorrect order selection
negatively impact productivity. Businesses can improve manual order picking by improv-
ing inventory organization, providing employee training, and developing optimization
strategies, especially in industries such as textiles, which still rely heavily on manual labor
for manufacturing and warehouse tasks.

Processes 2025,13, 22 3 of 24
Coruzzolo et al. [
30
] developed a joint model for batching, assignment, sequencing,
and routing in order picking to minimize completion time and tardiness in picker-to-part
systems. Using multi-start heuristics, iterated local search, and constructive heuristics, their
study demonstrated a 57% reduction in picking time compared to the single-order strategy,
contributing significantly to the literature on integrated optimization in order-picking
systems. Similarly, Czerniachowska et al. [
31
] introduced a model for order picking using a
one-way conveyor system with buffer zones to optimize travel and resource allocation in
high-demand e-commerce environments. Their study employed a CPLEX solver, which
effectively optimized small instances but revealed limitations in medium and large-scale
scenarios. Focusing on ergonomics in manual order picking, Kapou et al. [
32
] proposed a
slot allocation algorithm designed to improve layout and storage assignments, reducing
physical fatigue for workers. The study achieved a 14.9% increase in productivity and a 31%
reduction in the order-picking difficulty index, emphasizing the importance of ergonomic
considerations in warehouse operations. Li, Zhang, and Jiang [
33
] provided a literature
review summarizing advancements in picker-to-parts and parts-to-picker systems, focusing
on e-commerce warehouses.
As seen in the literature, rigid mathematical models reduce flexibility and become
difficult or impossible to solve as the number of parts increases—they are called NP-hard
problems. However, order picking is a problem with a dynamic structure, and techniques
that will increase this dynamism and flexibility are needed. In this context, meta-heuristic
algorithms like genetic algorithm (GA) and simulated annealing algorithm (SA) provide an
advantage that can be integrated into computer systems and data in today’s conditions,
providing dynamism and flexibility. It also contributes to the data-driven decision-making
process. It is emphasized that smart methods must be utilized to organize tasks effectively,
ensuring that orders can be easily located when placed [
34
]. This study addresses critical
gaps in current order-picking optimization research by combining GA and SA with real-
world data and provides a practical, scalable approach to logistics efficiency. It provides
travel length, pallet utilization rate, and picking mode flexibility in the context of real
orders.
By Ou et al. [
35
], a literature review from 2018 to 2023 has closely examined how GA
has been applied to optimize order-picking systems in picker-to-part environments. It has
been further investigated that various optimization techniques such as GA, meta-heuristics,
cluster analysis, and hybrid approaches have been proposed to address order assignment,
grouping, and sorting problems. Some of these studies have partially developed GA-based
methods targeting efficiency improvements in different warehouse systems through storage
location assignment. In most studies, GA is applied to optimize multiple objectives, such
as travel distance and resource utilization.
Casella et al. [
36
] studied 269 journal papers published between 2007 and 2022, and
the studies focused primarily on trends in order-picking research, particularly in manual
picker-to-parts systems, identifying the minimization of travel distance and ergonomic
considerations as key priorities. Real-world applications in e-commerce and warehousing
are emphasized, with suggestions for integrating emerging technologies to optimize picking
systems. While traditional research prioritizes reducing travel distances and ergonomic
improvements in manual picking systems, our study uniquely integrates GA with adaptive
constraints, emphasizing real-world warehouse operations and focusing on dynamic order
clustering to enhance practical applicability and efficiency.
Our study stands out by applying GA to optimize order picking in a real-world
medical warehouse across three distinct picking scenarios, thereby advancing practical
solutions in warehouse management as seen in Figure 1.

Processes 2025,13, 22 4 of 24
Classical metrics such as “travel distances”, “ergonomic pickers’ movements”, “num-
ber of orders” and “storage space limitations” have been frequently studied in the literature.
We minimize the travel distance and number of tours of the pickers, while also increasing
the pallet usage. In this respect, it offers a multi-purpose solution. In addition, by consider-
ing the order change dynamically and probabilistically, it can produce solutions even if the
order list becomes more complex or increases in volume, and thus aims to contribute to the
literature. In particular, the interaction between pallet management and order grouping,
which is usually addressed individually or in a limited scope in the existing literature, has
been analyzed comprehensively and flexibly by using GA and SA in accordance with the
structure of the real problem, taking into account high order diversity.
Figure 1. Classification of order-picking systems (OPS). Adapted from [36].
2. Materials and Methods
Order picking involves retrieving items from the warehouse to fulfill customer orders.
The process includes receiving and processing customer orders, determining product
placement and priority, selecting items in sequence, packing the selected products, and
shipping them to customers. Efficient order picking is critical for both customer satisfaction
and business success [
37
]. The order lists of a medical textile manufacturer described above
were searched for best performance using genetic algorithm (GA) and simulation annealing
algorithm (SA). The Manhattan distance was used to calculate the circulation distance
of the orders. In this section, information about GA and SA, their reasons for use in the
research, and Manhattan distance will be given, respectively.
2.1. Genetic Algorithm and Simulated Annealing
Genetic algorithm (GA) optimization techniques are inspired by the principles of
natural selection and evolutionary biology [
38
] firstly introduced by Holland in 1975 [
39
].
These algorithms simulate the process of natural evolution to solve complex optimization
problems [
40
]. The fundamental concept involves representing potential solutions as
“chromosomes” and iterative improving these solutions through genetic operators such
as selection, crossover, and mutation. The GA approach has been successfully applied to

Processes 2025,13, 22 5 of 24
various optimization problems, including vehicle routing, scheduling, and network design,
particularly in scenarios where traditional optimization methods are computationally
infeasible [41].
This paper presents an artificial intelligence approach using a multi-objective GA
solution. The proposed GA method’s performance is compared with the traditional method
using real data from a medical textile manufacturer. The two primary research questions
are: (1) Can a better order-picking sequence be created beyond the fixed lists? and (2) How
does the new GA approach affect the number of tours and distance traveled? Which
algorithm is better for this problem, SA or GA, to meet optimum results?
Although approaches vary, the GA has been used to address order-picking challenges.
For example, GA can optimize make-span in manual order-picking operations. Dalle Mura
and Dini [
42
] utilized GA to address the order-picking problem, emphasizing its application
in optimizing worker health by accounting for variations in energy expenditure influenced
by individual characteristics such as gender, age, and weight. GA has optimized worker
assignments in order-picking systems by considering worker fatigue and spatial character-
istics of order groups [
43
]. Additionally, GA has been applied to balance workloads and
minimize the number of batches required in the picking process [44]. Other GA were also
used to reduce congestion and waiting times during order picking and sorting [45].
Some combined storage location assignment problems with order picking involve
using multi-objective GA to improve warehouse management efficiency. Other methods,
such as meta-heuristics and cluster analysis, have also been tried to improve picker routing,
grouping, and delivery scheduling. It involves the combined problems of order-picking and
sorting problems in low-level picker-to-part systems, where the potential for simplifying
operations using GA-based solutions has been revealed. Overall, this study addresses
the flexibility and efficiency of GA in solving relevant problems related to order-picking
problems. SA and GA are both prominent optimization techniques that can be effectively
combined to enhance their performance in various applications. The SA approach has been
shown to significantly enhance storage assignment strategies, yielding a 21% reduction
in total retrieval times compared to traditional frequency-based methods in multi-level
warehouses [46]. On the other hand, GA has been explored in various contexts, including
optimizing order-picking strategies through simulations that compare multiple algorithms,
including hlGA and ant colony optimization [
47
]. Furthermore, Ardjmand et al.
[48]
demonstrated the effectiveness of combining list-based SA with GA for order batching
and picker routing, leading to improved efficiency in put wall picking systems. Similarly,
Nathania
[49]
highlights the joint optimization of order batching and picker routing through
the SA algorithm, effectively circumventing local optima to achieve superior solutions.
Additionally, Castier and Martínez-Toro
[50]
applied a modified SA method for storage
allocation, integrating advanced computational tools to tackle the pick-to-parts problem.
Collectively, these studies underscore the potential of SA and GA in enhancing operational
efficiency in order-picking systems.
Simulated annealing (SA) is an optimization technique inspired by the annealing
process in materials science and engineering and first introduced by Kirkpatrick in 1983.
This technique carefully heats and cools a material to form the desired structure. The
method uses probabilistic navigation of the solution space from a computational perspective
to address complex optimization problems [51].
SA has been acknowledged for effectively addressing many optimization problems,
including the traveling salesman problem, workshop planning, etc. For example, SA was
successfully used in order picking aimed at reducing CO2 emissions [
52
]. The method
is convenient in scenarios where the search space is significantly large and complex, and
traditional optimization methods are less applicable. Atmaca et al. [
53
] demonstrated

Processes 2025,13, 22 6 of 24
that SA is a viable method for solving complex warehouse management problems by
effectively minimizing costs and improving efficiency in the storage system. Also, in their
paper, Kostrzewski et al. [
54
] employed SA to optimize order-picking policies in automated
storage/retrieval systems. By applying SA, the authors [
54
] aim to minimize order picking
times and costs, enhance process reliability, and support warehouse managers in decision-
making. Kucuksari [
55
] is another study that successfully solves the SA algorithm in
minimizing congestion and travel distance in an automated warehouse. The SA method was
used to obtain an optimal solution, which then, in combination with the COMET method,
provided satisfactory results by determining the relationship between the preferences of
the initial alternatives and newly identified alternatives [56].
This study implements the SA alongside the GA due to the challenges associated
with identifying the optimal solution using conventional approaches in complicated and
expansive solution spaces within warehouse systems. The research categorizes the issue of
manual order picking in a manufacturing facility producing medical textile items, along
with the minimization of trip time and rounds, as NP-hard due to the wide variety of
orders. In this scenario, where identifying the optimal solution inside extensive solution
spaces becomes mathematically infeasible, the SA algorithm was employed as a meta-
heuristic strategy.
In recent years, the SA algorithm has been employed in the literature for warehouse
placement and picking challenges, owing to its capacity to yield results near the global
optimal solution while avoiding entrapment in local optima [
51
]. The SA algorithm was em-
ployed in the study for its capacity to dynamically optimize order selection strategies. The
program generates an appropriate order list of materials based on three distinct scenarios
and product categories. The SA algorithm operated iteratively across varying temperatures,
generating distinct solutions at each temperature, and assessed these solutions using a
probabilistic method. In accepting lower-cost solutions, it also demonstrated the capability
to evade local minima, allowing for the exploration of higher-cost yet broader solution
spaces. GA emulate the mechanisms of diversity and adaptation using genetic opera-
tors like crossover and mutation among individuals (solutions) in a population, drawing
inspiration from natural evolutionary processes [
39
,
41
]. By evaluating several solutions
concurrently (population), GA possess the capacity to enhance diversity while progressing
toward the global optimum. They can offer a wider view on certain issues by concurrently
assessing various solution alternatives [
51
,
57
]. Consequently, the issue was examined using
two methodologies.
The benefits and contributions can be described as follows:
1.
This study concentrates on lightweight and essential medical textile items, particularly
utilizing empirical data.
2.
It enhances the literature by comparing the performance of GA and SA optimization
techniques, addressing the complexities inherent in real-world scenarios characterized
by a variety of products and orders.
3.
By including actual warehouse data, the research enhances the practical relevance
of its findings and bridges the divide between theoretical models and real-world
implementations.
4.
The paper examines the performance of three scenarios classified by dataset size and
order selection procedures, specifically product-based, list-based, and order-based
approaches, offering a comprehensive comparison of GA and SA methodologies.
5.
Concurrently, the order lists in these three scenarios indicate variations regarding
products, volume, and order quantity in alignment with reality.

Processes 2025,13, 22 7 of 24
6.
Incorporating adaptive pallet capacity limits, the model accurately represents real-
world fluctuations in resource availability and operating requirements, hence enhanc-
ing its adaptability to dynamic contexts.
7.
Sensitivity evaluations examine the impacts of variations in order volume and adjust-
ments to genetic algorithm parameters, illustrating the scalability and adaptability of
the offered methodologies.
2.2. Manhattan Distance
The Manhattan distance, also known as the city block distance, Taxicab distance or L1
norm, is a metric used to measure the distance between two points on a rectangular grid.
This method is named after the Manhattan borough of New York City, characterized by its
grid-like street layout. Because the forklifts have to navigate between and around shelves,
determining the Euclidean distance cannot be feasible because it requires maneuvering
over the racks, which is not practicable. As shown in Figure 2, the Manhattan distance is a
more suitable distance metric in this situation.
Figure 2. Possible calculations for picking two consecutive products in the warehouse.
The Manhattan distance is calculated as the sum of the absolute differences between
the coordinates of two points. It represents the path between points using only right-angle
turns, analogous to navigating city blocks [
58
]. Also it calculates the absolute differences
between coordinates of a pair of objects [59].
Specifically, let
A= (a1
,
a2
,
. . .
,
am)
and
B= (b1
,
b2
,
. . .
,
bm)
be two points in
Rm
. Then
the multi-dimensional Manhattan distance can be written as:
DAB =
m
∑
k=1
|ak−bk|(1)
where
| · |
denotes the absolute value function,
m
is the total dimension number, and
DXY
is the Manhattan distance between the two points.
For two points such as a and b, which are from the products to be collected, a
(x1
,
y1)
and
b(x2,y2)in a two-dimensional plane, the Manhattan distance is calculated in Equation (9).

Processes 2025,13, 22 8 of 24
3. Problem Definition
The company’s order fulfillment process involves multiple interrelated activities that
significantly impact operational efficiency and customer satisfaction. The current system
follows a two-tiered approach, depending on the type and volume of incoming orders:
1.
High-volume orders: A production order is generated, and production begins to meet
the demand;
2.
Low-volume orders: The company fulfills demand using existing inventory from the
central warehouse while maintaining production efficiency.
The warehouse management system is the foundation of the order fulfillment process,
which oversees product selection, packaging, and distribution. When an order arrives,
the production planning engineer checks inventory availability through the Enterprise
Resource Planning (ERP) system. If the products are in stock, the warehouse staff initiates
a transfer of goods.
However, the current picking strategy (product-based, list-based, or order-based) lacks
systematic optimization, leading to inefficiencies in travel distances, under-utilized pallet ca-
pacities, and excessive travel times within the warehouse. These inefficiencies directly affect
the speed and accuracy of order fulfillment, ultimately impacting customer satisfaction.
Three primary picking techniques are discussed as potential solutions to these chal-
lenges, as seen in Figure 3.
1.
Product-based picking: Products are arranged and collected based on their prox-
imity within the warehouse to minimize travel distances. This method empha-
sizes grouping items by location while considering capacity constraints, resulting in
169 distinct groups.
2.
List-based picking: Products are picked according to predefined selection lists that
came directly from the company, yielding 10 groups. The company uses this list as a
stable order-picking method for collecting orders.
3.
Order-based picking: Products are gathered based on order sequences to fulfill mul-
tiple orders in a single trip, minimizing overall travel distances and maximizing
efficiency, resulting in 29 groups.
The experiment utilized a dataset from a medical textile company’s actual data,
comprising 169 unique products with varying quantities, volumes, and spatial coordi-
nates within a warehouse. Each product was associated with a specific list number and
order name.
After the input data containing the necessary details for the process calculations
are loaded by the genetic algorithm, a random sequence of routes is generated to create
the initial population. The efficiency of each route is evaluated by calculating the route
distances. The first route is created and changed with genetic operations such as crossover
and mutation (addition, replacement, or substitution of genes), and selection is performed.
Termination criteria determine whether the algorithm should stop after finding a feasible
solution or after a predetermined number of iterations, which is 1000 in our study. Pallet
capacity is managed throughout the process to keep track of picked volumes.

Processes 2025,13, 22 9 of 24
Figure 3. The flowchart of the picking strategies of this study.
This study implemented three different order-picking strategies by using Python 3.12:
product-based, list-based, and order-based approaches. Each strategy was evaluated based
on its performance in terms of the number of trips required, total trip distance, total volume
picked, total products collected, and pallet utilization efficiency, as shown in Table 1. The
study was formulated as a multi-objective optimization model, where the objectives were
first to minimize the total trip distance, and subsequently to minimize the number of trips.
Each trip utilized a single pallet that traversed the warehouse to collect orders, with a
maximum pallet capacity of 1.2 m
3
. A simulated order-picking process was executed for
each strategy, recording key performance indicators during the collection process.

Processes 2025,13, 22 10 of 24
Table 1. Outline of the parameters of the study.
Symbol Description Type
TSet of trips Index
PSet of products Index
OSet of orders Index
i,jProduct indices (specific products in P) Index
kOrder index (specific order in O) Index
xi,yiCoordinates of product iin the warehouse Parameter
x0,y0
Coordinates of the starting and ending point in the
warehouse
Parameter
ViVolume of product iParameter
CMaximum capacity per trip Parameter
dij Manhattan distance between products iand jParameter
di0
Manhattan distance between the starting point and
product i
Parameter
Xt,i
Binary variable indicating if product
i
is collected in
trip t
Decision Variable
Yt,k
Binary variable indicating if order
k
is included in
trip t
Decision Variable
Sk1,k2Set of shared products between orders k1,k2Set
Fitness Functions:
min ∑
t∈T
Distancet(2)
min |T|(3)
Distance Calculation:
Distancet=
|P|−1
∑
i=1
(|xi−xi+1|+|yi−yi+1|) + (|x|P|−x0|+|y|P|−y0|)(4)
Capacity Constraint:
∑
i∈P
Xt,iVi≤C,∀t∈T(5)
Order Inclusion Constraint:
Yt,k≥Xt,i,∀i∈P,∀k∈O(6)
Product Collection Constraint:
∑
t∈T
Xt,i=1, ∀i∈P(7)
Shared Product Constraint:
∑
i∈Sk1,k2
Vi≤C,∀k1,k2∈O(8)
Manhattan Distance Definition:
d(a,b) = |x1−x2|+|y1−y2|(9)

Processes 2025,13, 22 11 of 24
Output Metrics:
∑
t∈T
Distancet(Total Distance) (10)
|T|(Total Number of Trips) (11)
Pallet Utilization =Total Volume
|T| × C(12)
The proposed product-based collection model has been applied to a simulated ware-
house environment to validate its effectiveness in addressing the order-picking problem.
The warehouse layout comprises a double block of parallel racks with four bays. This setup
is in accordance with the product allocation and capacity constraints established in the
model. The process, which involves three distinct orders, is executed manually without the
aid of automated tools. During this process, the picker traverses the warehouse, starting
and ending at a predefined position
(x0
,
y0)
. This point, also known as the order-picking
point or depot, is located in the front left corner of the warehouse.
The travel distances from this starting point to each product
i
(denoted as
di0
) and
between consecutive products
i
and
j
(denoted as
dij
) are determined using the Manhattan
distance metric, as described in objective functions (Equations
(2)
and
(3)
). The objective,
defined by Equations
(2)
and
(3)
, is to minimize both the total distance traveled and the
number of trips made. Equations
(4)
and
(5)
address distance calculations and capacity
constraints, ensuring that the total volume of products collected per trip does not exceed
capacity
C
. Furthermore, Equations
(6)
and
(7)
establish order and product inclusion rules,
while Equation
(8)
manages shared products across multiple orders. Equation
(9)
defines
the distance metric between any two given points. Finally, the overall performance and
utilization metrics are summarized by Equations (10)–(12).
4. Results
The study environment of this paper consists of a double block of parallel racks with
four bays, as seen in Figure 4a. The pallet used for collecting orders is shown in Figure 4b.
The warehouse layout and order placement for List 1 can be seen in Figure 4c.
Through these considerations, the application ensures that the constraints and assump-
tions align with real-world scenarios, providing a robust framework for minimizing travel
distance while respecting operational constraints.
(a) (b)
Figure 4. Cont.

Processes 2025,13, 22 12 of 24
(c)
Figure 4. (a) Shelves of the warehouse. (b) Pallet used in order picking. (c) Product layout of List 1 in
the facility.
4.1. The Real-World Dataset
The total number of separate orders for each list varies between 2 and 6, totaling 29
different orders. The number of unique items varies between 16 and 67 per list, totaling 169
unique items, as shown in Table 2.
Table 2. The study environment of algorithms.
Scenario: List
ID Problem Size
Count of
Unique
Orders
Count of
Unique
Products
Total
Products Total Volume Min Expected
Trip Number
1 Large 6 23 2837 4.017125 4
2 Medium 3 51 920 3.41414 4
3 Medium 2 45 1976 3.67986 4
4 Medium 2 35 660 2.26585 3
5 Large 2 67 2663 9.95921 9
6 Medium 2 39 558 2.53745 3
7 Small 4 24 339 1.664875 2
8 Small 3 23 724 1.6945 2
9 Medium 3 16 1240 4.0205 4
10 Medium 2 34 1605 4.4378 5
11 Very Large 29 169 13,522 37.69131 32
Case studies were studied by considering 11 datasets with unique order configurations
to evaluate the efficiency of the proposed approaches in solving the order-picking optimiza-
tion problem. Table 2provides an overview of the datasets, ranging from small-, medium-,
and large-scale problems, based on the number of orders, volume, and items, which enables
the comparison of the proposed methods in various complexities. Lists 1 through 10 for
different scenarios range in scale from small to medium, while
List 11 combines
all lists
into one large-sized dataset.
Each of the lists possesses different characteristics and can provide insight into how
changes in order and the number of items, along with volume, affect the performance of
the optimization. Problem instances with small sizes, like List 7, have only four distinct
orders and 24 distinct items. These are representatives of sparse picking environments with

Processes 2025,13, 22 13 of 24
small volumes. One large-scale set is List 11, a merged dataset that forms the base on which
one will witness the scalability and robustness of the order-picking strategy with high
volumes. Diversity in the design of the dataset is structured in such a way that it allows
robust testing of the proposed GA-based solutions across different warehouse scenarios,
providing insights into both performance scalability and adaptability under varying levels
of operational demand. Through these considerations, the application ensures that the
constraints and assumptions align with real-world scenarios, providing a robust framework
for minimizing travel distance while respecting operational constraints.
4.2. Comparative Results
This research evaluates the effectiveness of three picking scenarios using GA and
SA algorithms and real models. The methodologies cover product-based, list-based, and
order-based approaches. The evaluation focused on basic operational data such as the
total number of trips, trip distances, total volume picked, and pallet usage rates. In the
application phase, data were collected from a medical device manufacturer. The studies
were carried out by considering the company’s current operational workflow. The results
of the study are summarized in Table 3. Table 3details the results of various order-picking
techniques. The company’s calculated solutions are also provided for comparison.
The performance of the GA was assessed concerning the current warehouse operations
procedure through several scenarios and a comparison. The current method in the company
generates fresh lists with every order arrival without dynamically adjusting to continuous
changes, so it is rather strict. This rigidity causes ineffective grouping and routing as well
as more trips and pallet capacity under-utilization.
Using three different approaches—product-based, order-based, and list-based—the
evaluation concentrated on three key performance indicators (Total Distance Traveled,
Total Number of Trips, and Pallet Utilization) to compare against the actual process and
ascertain relative effectiveness.
In situations with lower order volumes and fewer products, such as Lists 7 and 8, the
GA method found ideal solutions quickly by lowering the number of trips and the distance
covered by over 30% compared to the current process, producing efficiency gains visible
through shortened travel distances. Conversely, the rigidity of the current method resulted
in a doubling of trips due to its tight order processing and long travel paths, reducing pallet
utilization rates.
For medium-sized scenarios, such as Lists 2 and 6, the GA regularly showed efficiency
improvements when handling moderate complexity by achieving a 20–30% reduction in
the number of trips and travel distance, highlighting its capacity to dynamically optimize
routes even with a modest increase in complexity.
In large-scale scenarios, such as Lists 5 and 9, the GA showed its full potential by min-
imizing travel distances while maintaining high pallet usage, attaining a 22–35% reduction
in trips and a 10–15% decrease in travel distances compared to the existing process, which
remained limited by its fragmented list generating, resulting in a higher number of trips,
increased travel distances, and lower pallet utilization.
Scenario 11, which shows the joining of all lists into a single daily order set, demon-
strated the scalability and flexibility of the GA as it dynamically adapted to the large-scale
scenario, achieving a 37.3% reduction in trips and a 12.7% decrease in total travel dis-
tance while maintaining a high pallet utilization rate of 98% compared to 61.5% for the
existing process.

Processes 2025,13, 22 14 of 24
Table 3. Results of GA, SA, and company’s real process.
Scenario Approach Method Total Distance (m) Total Trips
1
List-Based GA 420 4
Order-Based GA 430 4
Product-Based GA 240 4
List-Based Real Process 487 7
List-Based SA 439.5 5
Order-Based SA 435 4
Product-Based SA 288 4
2
List-Based GA 85 3
Order-Based GA 119 3
Product-Based GA 89 3
List-Based Real Process 137.5 5
List-Based SA 124 4
Order-Based SA 130 4
Product-Based SA 124 4
3
List-Based GA 153 4
Order-Based GA 158 4
Product-Based GA 150 4
List-Based Real Process 165.5 5
List-Based SA 150 4
Order-Based SA 174 4
Product-Based SA 126 4
4
List-Based GA 78 2
Order-Based GA 79 2
Product-Based GA 74 2
List-Based Real Process 94.5 3
List-Based SA 103 2
Order-Based SA 95 2
Product-Based SA 93 2
5
List-Based GA 342 9
Order-Based GA 419 9
Product-Based GA 347 9
List-Based Real Process 378.5 11
List-Based SA 359 10
Order-Based SA 347 11
Product-Based SA 359 10
6
List-Based GA 146 3
Order-Based GA 178 3
Product-Based GA 145 3
List-Based Real Process 152.5 3
List-Based SA 154.5 3
Order-Based SA 188.5 3
Product-Based SA 156.5 3
7
List-Based GA 75 2
Order-Based GA 78 2
Product-Based GA 74 2
List-Based Real Process 90 4
List-Based SA 79 2
Order-Based SA 83 2
Product-Based SA 81 2
8
List-Based GA 120 2
Order-Based GA 165 2
Product-Based GA 118 2
List-Based Real Process 154.5 3
List-Based SA 127 2
Order-Based SA 125 2
Product-Based SA 123 2

Processes 2025,13, 22 15 of 24
Table 3. Cont.
Scenario Approach Method Total Distance (m) Total Trips
8
List-Based GA 120 2
Order-Based GA 165 2
Product-Based GA 118 2
List-Based Real Process 154.5 3
List-Based SA 127 2
Order-Based SA 125 2
Product-Based SA 123 2
9
List-Based GA 210 4
Order-Based GA 240 4
Product-Based GA 215 4
List-Based Real Process 215.5 5
List-Based SA 213.5 5
Order-Based SA 234 4
Product-Based SA 225.5 5
10
List-Based GA 125 4
Order-Based GA 132 4
Product-Based GA 124 4
List-Based Real Process 133.5 5
List-Based SA 132.5 5
Order-Based SA 124.2 4
Product-Based SA 126.2 4
11
List-Based GA 1754 32
Order-Based GA 1998 32
Product-Based GA 980 32
List-Based Real Process 2009 51
List-Based SA 1992 36
Order-Based SA 1998 36
Product-Based SA 1723.5 37
With fast convergence to optimal solutions observed in small-scope lists, therefore
reducing travel distances and trips, the size of each list, the number of orders, and the
degree of complexity were fundamental factors of GA efficiency. Simultaneously, the GA
showed steady efficiency improvements with increasing scenario complexity, indicating its
versatility throughout various logistical settings.
Under different conditions, each of the three GA techniques showed capabilities; the
product-based approach was most successful in situations involving many unique items by
lowering the total journey distance through spatial grouping. By contrast, the list-based
approach offered balanced performance for medium-to-large lists. When maintaining order
integrity was a top concern, and enormous order quantities were involved, the order-based
approach performed exceptionally well, providing a flexible toolkit for optimizing logistics
operations depending on scenario-specific criteria.
Where the GA regularly achieved lower distances, fewer trips, and more pallet uti-
lization rates than the actual process across all scenarios, the visual analysis evaluated the
impact of each strategy on total journey distance, number of trips, and pallet usage.
With particularly marked reductions in large-numbered lists, including List 5,
List 9,
and Scenario 11, where total distance dropped by over 50% compared to the current process
(98,000 cm), the GA approach resulted in significantly reduced travel distances compared
to the existing process in almost every scenario, demonstrating its capacity to optimize
routes and lower travel time, thus generating significant operational cost savings and
enhanced efficiency.

Processes 2025,13, 22 16 of 24
Although the GA method concentrated on reducing journey distance, it kept a similar
or lower number of visits than conventional methods, so it efficiently grouped orders and
reduced unnecessary trips without running afoul of capacity limits.
The GA order-picking strategy shows great promise for high usage rates despite less
operational predictability and more variance in journey distances. Consistency is essential;
the list-based GA performs consistently for realistic journey distances. Although the order-
based GA shows effective pallet use, generally it results in longer journey distances. A GA
may be appropriate for flexibility and adaptability due to managing variability. For typical
applications that require consistent and predictable results, list-based GA approaches offer a
balanced solution with satisfactory performance across various criteria. Future work could
focus on combining hybrid methodologies that combine the adaptability of GA with the
robustness of real models, thus achieving optimal travel times and high utilization rates in
various logistics contexts. Moreover, creating complex algorithms that dynamically adapt
to changing layout configurations could increase efficiency and operational robustness. In
contrast, the existing process required additional journeys due to its fragmented processing
of incoming orders, resulting in excessive trips.
Depending on the scenario, the GA consistently achieved higher pallet utilization,
ranging between 70% and 98%. In comparison, the existing process showed significant
under-utilization with rates ranging from 35% to 60%, with higher utilization rates indicat-
ing improved load management, reducing the number of trips required and minimizing
empty pallet spaces, as the GA achieved nearly 98% utilization in the combined scenario
compared to 61.5% for the actual process.
The GA outperforms the current company process in all performance metrics (total
trips, travel distances, and pallet usage), optimizing routes and combining orders efficiently
despite fluctuations in order composition and volumes. This practical applicability in
real-world logistics is demonstrated in this study, with a 37.3% reduction in trips and a
12.7% reduction in distance in the combined scenario. Furthermore, GA is a preferable
solution for contemporary logistics with high pallet usage rates.
Minimizing the travel distance primarily relies on the manual product-based method.
On the other hand, the intuitive order-based strategy maintains a suitable number of trips
and a balanced performance, maintaining a short travel time overall. Regarding travel
distance, the manual order-based strategy outperforms other methods, indicating that it
is unsuitable for reducing travel time even if excellent pallet utilization is achieved. The
results of our study reveal that approach selection can improve warehouse operations. The
goal might be to reduce travel distance, reduce trips, or balance both.
Since the GA product-based approach has the shortest travel distances, the results
prove the success of this method. The study reveals that optimization techniques ap-
plied beyond the organization’s baseline can significantly increase logistics efficiency with
comprehensive analysis and strategic selection.
The datasets were classified into fuzzy categories (Small, Medium, Large, and Very
Large [only for list 11/combined list]) based on Total Volume Size, Number of Discrete
Items, and Number of Discrete Orders. The performance of the datasets divided into these
categories, SA, GA, and the real process, was compared in three approaches: list-based,
order-based, and product-based, as shown in the Figures below.
For example, in Figure 5a, List 7 in the small category showed the minimum total
distance of 74 m from the product-based GA approach, about an 18% reduction from the
real process that took 90 m. All the approaches by both SA and GA recorded two trips,
while the real process made four trips—an indication of how inefficient the real process
is. In general, it was seen that in both approaches, GA provided more efficient distance
reductions than those obtained with SA.

Processes 2025,13, 22 17 of 24
For example, the minimum total distance of 126 m in the Medium List of Scenario 3
was obtained through product-based GA, which achieved about a 24% gain compared to
the real process as shown in Figure 5b. The SA method found the same number of trips but
a slightly higher total distance than GA. GA provided better optimization than SA, with a
consistent reduction in total distance while maintaining comparable trip counts.
For the Large List shown in Figure 5c the best performance was from the product-
based GA approach; it trimmed the total distance by 50% from 487 m, as executed by
the real list-based process, to 240 m. For the instances in which comparable distances
were available, GA was always consistently superior to SA at minimizing distances. The
greatest gap occurred with the product-based approach. All heuristics resulted in fewer
trips compared to the real process. In the Very Large List (Scenario 11), which was created
by combining all the lists, the product-based GA approach showed the highest efficiency,
resulting in a total distance of 980 m, a reduction of over 51% from the real list-based
process of 2009 m. The number of trips was also minimized; GA and SA methods required
only 32 to 37 trips in all approaches, which is significantly fewer than the 51 trips of the
real process. When all the lists were combined, the product-based GA method achieved
an overall minimum distance of 2556 m; this represented a 36% reduction compared to
the actual list-based process (4018 m). GA achieved significantly shorter distances than
SA, particularly in the product-based approach, where the difference exceeded 43%. These
findings demonstrate that the product-based GA approach consistently offers superior
efficiency in minimizing both total distance and trips across all list categories as shown
in Figure 5d. GA demonstrated overall superiority across all approaches, with notable
efficiency gains in reducing both total distance and the number of trips compared to SA.
(a) (b)
(c) (d)
Figure 5. Results for various lists: (a) Small list: List 7 results, (b) Medium list: List 3 results, (c) Large
list: List 1 results, (d) Combined list (Very Large List): List 11 results.

Processes 2025,13, 22 18 of 24
4.3. Sensitivity Analysis Made by Order Amount Increased
Sensitivity analysis shows how each picking strategy adapts to increased order vol-
umes, showing scalability and operational strengths or limitations.
4.3.1. Order-Based Strategy
As shown in Figure 6a, for combined List 11, the distance increases drastically as more
and more orders increase, reflecting the inefficiency in processing each order individually at
high demand levels. From this, it can be seen that since this strategy necessitates a separate
pass through the warehouse for every order, it presupposes lower efficiency in picking
and higher costs of time and labor, as can be seen from notable distance growth in List
5 as orders increase. Sensitivity analysis underlines that this strategy scales poorly with
demand in the case of high-order periods.
As such, it is best averaged for smaller order quantities where the accuracy of each
order individually is more important than travel efficiency.
Figure 6. Sensitivity Analysis on (a) List 9. (b) List 8. (c) Combined List 11. (d) List 5 results.
4.3.2. List-Based Strategy
First, the list-based approach saves travel time by clumping orders together to mini-
mize routes taken. However, as order volumes increase, this approach becomes less flexible.
That can be understood from the list, wherein larger volumes of orders disrupt the planned
routes and cause small inefficiencies in travel. Another weakness of this strategy is its
potential to generate shortages of items when high-demand products have to be shared
among orders, as shown in the list, where the increased order amounts include slight
variability in travel distances. The sensitivity analysis results show that, though effective
under stable demand conditions, the list-based strategy cannot maintain efficiency when
volumes increase substantially. It is more appropriate in moderate and predictable demand.

Processes 2025,13, 22 19 of 24
4.3.3. Product-Based Strategy
The product-based strategy is resilient to higher volumes because the items would be
collected by product location; this means travel distances would remain relatively constant
even at high demand. As shown in Figure 6a–d, distance remains efficient in the various
sized lists despite added orders, underlining the strategy’s capability for effective scaling.
On the other hand, this method needs more significant inventory management since the
shortest travel relies on well-stocked product locations.
The difficulty represented by sorting the items into individual orders after collective
picking for more orders is increased in the combined List 11 profile. Sensitivity analy-
sis reveals that under the product-based strategy, travel efficiency is advantageous but
needs robust stock control to prevent congestion bottlenecks, especially in high-demand
environments.
Sensitivity analysis indicates that the product-based strategy behaves well with in-
creased demand but requires strong inventory practices. By contrast, the order-based
and list-based strategies are more challenged by increased order amounts due to higher
travel distances and reduced flexibility. By understanding these dynamics, warehouses
can choose strategies that match travel efficiency, labor costs, and flexibility for expected
demand variability.
4.4. Sensitivity Analysis of Population Size—Genetic Algorithm Parameter
A sensitivity analysis of the GA concerning the population size is performed in this
work to study the variations in the solution quality. Overall, population sizes ranged from
10 to 150 across multiple lists of complexities described by attributes like distinct orders,
distinct items, total volume, and problem size. The main goal of this analysis is to search
for an appropriate population size that will yield a good balance between the accuracy of
the solution and time efficiency for various scenarios.
4.4.1. Population Size Impact
As can be gathered from Table 1, the objective function values and computation
times generated by GA are sensitive to changes in the size of the population. For small
problem sizes such as Lists 7 and 8, for instance, population size in the 50–70 range gave the
optimum solution with a limited increase in computation time, whereas further increases
have resulted in diminishing returns. Medium-sized problems—exact Lists 1 and 2—have
shown a 10–15% improvement of objective function after increasing the population size
to 70–100 while computation time increases remained manageable. Population size in the
range of 100–150 yielded the best solution quality with as much as a 28% objective function
improvement at large and very large problem sizes, such as lists 5 and 11, respectively.
These gains in solution accuracy had to be weighed against increased computation times,
double or triple those found with smaller populations, indicating an apparent solution
accuracy and computation time trade-off.
4.4.2. Correlation Analysis
Figure 7presents the correlation matrix of the critical parameters. From this figure, it
is observed that computation time is highly correlated with population size (0.89), shown
in the red circle, implying that high population sizes increase computational requirements
significantly. Problem Size is highly correlated with Total Volume 0.85 and Number of
Distinct Items 0.75, implying that these factors together increase complexity. The other
correlations of Best Fitness remain low, testifying to the robustness of the performance of
GA across a wide range of configurations.

Processes 2025,13, 22 20 of 24
Changes in population size led to statistically significant objective improvements,
especially related to complex scenarios. For example, Lists 3 and 5 had solution quality
gains of 20-28% going from baseline to optimal population sizes, which suggests gains
from larger population sizes when dealing with more complex scenarios.
The sensitivity analysis identified general effective population sizes based on the
problem complexities: 50–100 for small- to medium-sized problems, while larger ones
see significant improvements with increased population sizes up to 100–150, although at
increased computational costs. These findings give insights into the more practical tuning
of the parameters of GA in balancing the solution quality with the availability of resources
in adaptable optimization for real applications.
Figure 7. Correlation matrix of the critical parameters.
5. Conclusions
Manual order picking and optimization is an NP-hard problem in real life and leads
to an increase in time and distance to the user as product variety and complexity increase.
In this study, meta-heuristic solutions are proposed to the problem of a medical textile
manufacturer where manual order picking is quite intensive.
In the solution phase, 3 different scenarios and different order lists were run in both
algorithms and the results were compared for GA and SA. In addition, detailed sensitivity
analyses were performed. According to the findings obtained, in cases where GA was
used, the product-based strategy reduced the pallet usage rate by offering the lowest total
distance in many scenarios, and in addition, orders in the entire list were collected with
fewer trips. For example, in Scenario 1, when GA is used, the product-based solution
offers the lowest distance with 240 m, while list-based remains at 420 m and order-based
remains at 430 m. When we look at SA, the product-based approach is still in a relatively
advantageous position with a result of 288 m. List-based SA falls behind with 439.5 m, and
order-based SA falls behind with 435 m. According to the real process results, it is seen that
the list-based application remains at 487 m, which further emphasizes the superiority of

Processes 2025,13, 22 21 of 24
GA and SA-based product-based solutions in this scenario. This superiority is also evident
in different scenarios.
In Scenario 3, the product-based approach with GA is better or at a similar level when
compared to both list-based (GA: 153 m) and order-based (GA: 158 m) solutions with a
result of 150 m. When we look at the SA results, product-based provides a significant
advantage with 126 m (list-based SA: 150 m, order-based SA: 174 m). Here, the real process
falls behind other methods with 165.5 m.
In Scenario 4, while product-based is 74 m, list-based is 78 m, and order-based is
79 m
among the GA results; SA and product-based remains at 93 m, list-based SA is
103 m,
and order-based SA is 95 m. The real process, on the other hand, offers a longer distance
compared to GA and SA solutions, with 94.5 m. This table shows that when GA is applied,
the product-based approach has a slight advantage, while when SA is applied, it maintains
its competitive position.
Scenario 11 reflects a larger volume and a more complex structure. Here, when GA is
used, the product-based strategy provides a remarkable advantage with a total distance
of 980 m. While list-based GA is 1754 m, order-based GA is 1998 m, and the real process
is far behind with 2009 m. In the SA application, product-based is also better than list-
based (
1992 m
) and order-based (1998 m) solutions with 1723.5 m. This shows that the
product-based approach can produce strong results with GA and SA, even in complex and
large-scale scenarios.
In general, it is understood that the product-based approach can offer stable advan-
tages in terms of both distance and number of trips in different scenarios, especially when
GA is used. When compared with SA and real process data, the competitive position
of the product-based strategy is clearly revealed. GA maximizes the potential of the
product-based approach by effectively scanning a multidimensional and dynamic decision
space, but this also brings costs such as increased computational time, software/hardware
requirements, and operational planning requirements.
As a result, the table data shows that the product-based strategy, when supported by
GA and SA, can show high performance even in different and challenging scenarios and
provide significant distance and time savings compared to real processes. In future studies,
it should be aimed to make the product-based approach more sustainable and effective in
both theoretical and practical terms by integrating human factors, equipment limitations,
cost, energy consumption, and environmental effects into the process.
In this context, we advocate the importance of heuristic algorithms that adaptively
evaluate the optimal picking approach based on the descriptive characteristics of the orders
and warehouse design and metrics obtained from real-time interaction. Capturing this
flexibility with the GA is much easier and more adaptable than mathematical models. For
example, even if the lists change in the study, the algorithm can work and produce the
best ordering. In addition, since a single and fixed-sized pallet was used in our problem,
the model was solved accordingly. Still, researchers can produce alternatives that can
reduce the number of rounds in the solution by adding multiple pallets to the model. More
refined picking strategies can be created by comprehensively integrating machine learning
techniques and SA. Doing so can focus on optimizing order-picking operations in a more
balanced and sustainable way through approaches that go beyond a single performance
indicator and include energy consumption, environmental footprint, and labor cost issues.
For new studies, ergonomic considerations and personnel costs can be fully integrated into
the optimization process. Although simulation and theoretical models have guided the
research, and the practical applicability of the proposed strategies is high, companies may
have to pick priorities they can implement. These priorities can be expanded by adding
them to the model.

Processes 2025,13, 22 22 of 24
Author Contributions: Methodology, E.Y.; software, E.Y.; investigation, E.Y.; data curation, Ö.A.;
writing—review and editing, B.D. and E.Y. All authors have read and agreed to the published version
of the manuscript.
Funding: This research received no external funding
Data Availability Statement: The data are unavailable due to privacy restrictions.
Conflicts of Interest: The authors declare no conflicts of interest.
References
1. Coyle, J.J.; Bardi, E.J.; Langley, C.J. The Management of Business Logistics; West Publishing Company: St. Paul, MN, USA, 1992.
2.
Bowen, B.; Galceran Borja, C.; Karim, S.; Weinstein, W. Optimizing Health System Supply Chain Performance; McKinsey & Company:
Chicago, IL, USA, 2023. Available online: https://www.mckinsey.com/industries/healthcare/our-insights/optimizing-health-
system-supply-chain-performance (accessed on 24 November 2024).
3.
Bradley, P. Taking on the Health Care Supply Chain. Available online: https://www.proquest.com/trade-journals/taking-on-
health-care-supply-chain/docview/205962882/se-2 (accessed on 24 November 2024).
4.
Chandra, C. The case for healthcare supply chain management: Insights from problem-solving approaches. Int. J. Procure. Manag.
2008,1, 261. [CrossRef]
5.
Battini, D.; Faccio, M.; Persona, A.; Sgarbossa, F. Healthcare supply chain modeling: A conceptual framework. In Proceedings of
the POMS (Production and Operations Management Society) 20th Annual Conference, Orlando, FL, USA, 1–4 May 2009.
6.
Lewczuk, K.; Kłodawski, M.; Gepner, P. Energy consumption in a distributional warehouse: A practical case study for different
warehouse technologies. Energies 2021,14, 2709. [CrossRef]
7. Dallari, F.; Marchet, G.; Melacini, M. Design of order picking system. Int. J. Adv. Manuf. Technol. 2008,42, 1–12. [CrossRef]
8.
Pan, J.C.H.; Shih, P.H. Evaluation of the throughput of a multiple-picker order picking system with congestion consideration.
Comput. Ind. Eng. 2008,55, 379–389. [CrossRef]
9.
Yener, F.; Yazgan, H.R.; Cömert, S.E.; Kır, S.; Kaya, Y. Solution of Order Batching Problem with Association Rules and Genetic
Algorithm: A Case Study in Pharmacy Warehouse. J. Transp. Logist. 2016,1, 129–142. [CrossRef]
10.
Yang, J.; Zhou, L.; Liu, H.; Wang, Y. Hybrid genetic algorithm-based optimisation of the batch order picking in a dense mobile
rack warehouse. PLoS ONE 2021,16, e0249543. [CrossRef]
11.
Yousefi Nejad Attari, M.; Ebadi Torkayesh, A.; Malmir, B.; Neyshabouri Jami, E. Robust possibilistic programming for joint order
batching and picker routing problem in warehouse management. Int. J. Prod. Res. 2021,59, 4434–4452. [CrossRef]
12.
Ho, Y.-C.; Lin, J.-W. Improving order-picking performance by converting a sequential zone-picking line into a zone-picking
network. Comput. Ind. Eng. 2017,113, 241–255. [CrossRef]
13.
Yu, M.; de Koster, R. The impact of order batching and picking area zoning on order picking system performance. Eur. J. Oper.
Res. 2009,198, 480–490. [CrossRef]
14.
Yu, M.; de Koster, R. Performance approximation and design of pick-and-pass order picking systems. IIE Trans. 2008,40,
1054–1069. [CrossRef]
15.
Lorenc, A.; Burinskiene, A. Improve the orders picking in eCommerce by using WMS data and BigData analysis. FME Trans.
2021,49, 233–243. [CrossRef]
16.
Saylam, S.; Çelik, M.; Süral, H. The min–max order picking problem in synchronised dynamic zone-picking systems. Int. J. Prod.
Res. 2023,61, 2086–2104. [CrossRef]
17.
Yener, F.; Yazgan, H.R. Green order sorting problem in cold storage solved by genetic algorithm. Sustainability 2024,16, 9062.
[CrossRef]
18.
Yener, F. Determination of Picking Policies in Robotic Compact bin Picking Storage Systems with Artificial Bee Colony Algorithm.
Ph.D. Thesis, Sakarya University, Sakarya, Turkey, 2023. Available online: https://acikerisim.sakarya.edu.tr/bitstream/handle/
20.500.12619/101079/T10387.pdf (accessed on 27 November 2024).
19.
Tutam, M. Optimizing order-picking warehouse designs using collaborative robots. Gazi Üniversitesi Mühendislik Mimarlık
Fakültesi Dergisi 2023,39, 203–216. [CrossRef]
20.
Pan, J.C.H.; Wu, M.H. A study of storage assignment problem for an order picking line in a pick-and-pass warehousing system.
Comput. Ind. Eng. 2009,57, 261–268. [CrossRef]
21.
Yener, F.; Yazgan, H.R. Simulation of Re-Arrangement and Healing in Robotic Compact Bin-Storage System. Int. J. Simul. Model.
2023,22, 100–109. [CrossRef]
22. Bolu, A.; Korçak, Ö. Adaptive Task Planning for Multi-Robot Smart Warehouse. IEEE Access 2021,9, 27346–27358. [CrossRef]
23.
Ardjmand, E.; Ghalehkhondabi, I.; Young II, W.A.; Sadeghi, A.; Shakeri, H. A hybrid artificial neural network, GA, and column
generation for minimizing makespan in manual order-picking operations. Expert Syst. Appl. 2020,159, 113566. [CrossRef]

Processes 2025,13, 22 23 of 24
24.
Kumar, S.; Sheu, J.B.; Kundu, T. Planning a parts-to-picker order-picking system with consideration of the impact of perceived
workload. Transp. Res. Part E Logist. Transp. Rev. 2023,173, 103088. [CrossRef]
25.
Loske, D.; Klumpp, M.; Grosse, E.H.; Modica, T.; Glock, C.H. Storage systems’ impact on order-picking time: An empirical
economic analysis of flow-rack storage systems. Int. J. Prod. Econ. 2023,261, 108887. [CrossRef]
26.
He, W.; Chen, J. Dynamic routing algorithm for manual order-picking systems with real-time adjustment. Transp. Res. Part C
Emerg. Technol. 2018,96, 392–407. [CrossRef]
27.
Petersen, C.; Aase, G. Effects of slotting optimization in warehouse order-picking. Eur. J. Oper. Res. 2021,290, 1051–1063.
[CrossRef]
28.
Grosse, E.H.; Glock, C.H.; Sadrnia, A.; Modica, T. Collaborative robots in parts-to-picker systems: A simulation study. Comput.
Ind. Eng. 2019,131, 597–605. [CrossRef]
29.
Boysen, N.; Emde, S.; Hoeck, M.; Kauderer, L. Zone-picking systems: A survey of conceptual variants and their optimization
approaches. Eur. J. Oper. Res. 2020,284, 799–818. [CrossRef]
30.
Coruzzolo, A.M.; Lolli, F.; Balugani, E.; Magnani, E.; Sellitto, M.A. Order-picking problem: A model for the joint optimisation of
order batching, batch assignment sequencing, and picking routing. Logistics 2023,7, 61. [CrossRef]
31.
Czerniachowska, K.; Wichniarek, R.; ˙
Zywicki, K. A model for an order-picking problem with a one-directional conveyor and
buffer. Sustainability 2023,15, 13731. [CrossRef]
32.
Kapou, V.; Ponis, S.T.; Plakas, G.; Aretoulaki, E. An innovative layout design and storage assignment method for manual
order-picking with respect to ergonomic criteria. Logistics 2022,6, 83. [CrossRef]
33.
Li, Y.; Zhang, R.; Jiang, D. Order-picking efficiency in e-commerce warehouses: A literature review. J. Theor. Appl. Electron.
Commer. Res. 2022,17, 1812–1830. [CrossRef]
34.
Çil, ˙
I.; Pınar, D.; Araslı, A.; Kurt, A.; Topcan, A.N. Creating a Lean and Sustainable Warehouse with 5S in E-Commerce Operations
Center: Trendyol Case Study. Int. J. Behav. Sustain. Manag. (JOBESAM) 2023,10, 131–150. [CrossRef]
35.
Ou, S.; Ismail, Z.H.; Sariff, N. Hybrid Genetic Algorithms for Order Assignment and Batching in Picking System: A Systematic
Literature Review. IEEE Access 2024,12, 23029–23042. [CrossRef]
36.
Casella, G.; Volpi, A.; Montanari, R.; Tebaldi, L.; Bottani, E. Trends in order picking: A 2007–2022 review of the literature. Prod.
Manuf. Res. 2023,11, 2191115. [CrossRef]
37.
Yazgan, H.R.; Kir, S.; Yener, F.; Comert, S.E. A new collecting and management proposal under logistics 4.0 and green concept. In
Logistics 4.0: Digital Transformation of Supply Chain Management; Paksoy, T., Kochan, C.G., Ali, S.S., Eds.; CRC Press: Boca Raton,
FL, USA, 2020; pp. 320–337. [CrossRef]
38.
Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial
Intelligence; MIT Press: Cambridge, MA, USA, 1992.
39. Holland, J.H. Adaptation in Natural and Artificial Systems; University of Michigan Press: Ann Arbor, MI, USA, 1975.
40.
Yıldırım, E.; Denizhan, B. A Two-Echelon Pharmaceutical Supply Chain Optimization via Genetic Algorithm. In Recent Advances
in Intelligent Manufacturing and Service Systems; Sen, Z., Oztemel, E., Erden, C., Eds.; Springer: Singapore, 2022;
pp. 77–87.
.
[CrossRef]
41. Goldberg, D.E. Genetic Algorithms in Search, Optimization, and Machine Learning; Addison-Wesley: Reading, MA, USA, 1989.
42.
Dalle Mura, M.; Dini, G. Optimizing ergonomics in assembly lines: A multi-objective genetic algorithm. CIRP J. Manuf. Sci.
Technol. 2019,27, 31–45. [CrossRef]
43.
Gabellini, M.; Calabrese, F.; Regattieri, A.; Loske, D.; Klumpp, M. A hybrid approach integrating GA and machine learning to
solve the order-picking batch assignment problem considering learning and fatigue of pickers. Comput. Ind. Eng. 2024,191,
110175. [CrossRef]
44.
Pan, J.C.H.; Shih, P.H.; Wu, M.H. Order batching in a pick-and-pass warehousing system with group genetic algorithm. Omega
2015,57, 238–248. [CrossRef]
45.
Jiang, X.; Sun, L.; Zhang, Y.; Hu, X. Order batching and sequencing for minimizing the total order completion time in pick-and-sort
warehouses. Expert Syst. Appl. 2022,187, 115943. [CrossRef]
46. Eckrot, A. A Simulated Annealing Approach to Optimal Storing in a Multi-Level Warehouse. arXiv 2017, arXiv:1704.01049.
47.
Jin, H.; Wang, W.; Cai, M.; Wang, G.; Chen, Y. Ant colony optimization model with characterization-based speed and multi-driver
for the refilling system in hospital. Adv. Mech. Eng. 2017,9, 168781401771370. [CrossRef]
48.
Ardjmand, E.; Bajgiran, O.; Youssef, E. Using list-based simulated annealing and genetic algorithm for order batching and picker
routing in put wall-based picking systems. Appl. Soft Comput. 2019,75, 106–119. [CrossRef]
49.
Nathania, F. An Efficient Simulated Annealing Algorithm for the Joint Order Batching and Picker Routing Problem in Manual
Order Picking Systems. In Proceedings of the 8th North American Conference on Industrial Engineering and Operations
Management, Houston, TX, USA, 12–15 June 2023. [CrossRef]
50.
Castier, M.; Martínez-Toro, E. Planning and picking in small warehouses under industry-relevant constraints. Prod. Eng. 2022,17,
575–590. [CrossRef]

Processes 2025,13, 22 24 of 24
51. Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M. Optimization by simulated annealing. Science 1983,220, 671–680. [CrossRef]
52.
Küçüko˘glu, ˙
I.; Ene, S.; Aksoy, A.; Öztürk, N. A memory structure adapted simulated annealing algorithm for a green vehicle
routing problem. Environ. Sci. Pollut. Res. 2015,22, 3279–3297. [CrossRef] [PubMed]
53.
Atmaca, E.; Ozturk, A. Defining order picking policy: A storage assignment model and a simulated annealing solution in AS/RS
systems. Appl. Math. Model. 2013,37, 5069–5079. [CrossRef]
54.
Kostrzewski, M. Sensitivity Analysis of Selected Parameters in the Order Picking Process Simulation Model, with Randomly
Generated Orders. Entropy 2020,22, 423. [CrossRef] [PubMed]
55.
Kucuksari, Z. Optimal Order Batching for Automated Warehouse Picking. Ph.D. Thesis, University of Waterloo, Waterloo, ON,
Canada, 2023. Available online: http://hdl.handle.net/10012/19869 (accessed on 27 November 2024).
56.
Wi˛eckowski, J.; Kizielewicz, B.; Kołodziejczyk, J. Finding an approximate global optimum of characteristic objects preferences by
using simulated annealing. Intell. Decis. Technol. 2020,193, 365–375. [CrossRef]
57. Michalewicz, Z.; Fogel, D. B. How to Solve It: Modern Heuristics; Springer: Berlin/Heidelberg, Germany, 2004. [CrossRef]
58.
Zhao, Y. Manufacturing cell integrated layout method based on RNS-FOA algorithm in smart factory. Processes 2022,10, 1759.
[CrossRef]
59.
Can, Z.; Colak, Z.; Yıldırım, K.; Geli¸sgen, O. A Note on Some Distance Formulae in 3-Dimensional Maximum Space. J. Mahani
Math. Res. 2021,10, 95–102. [CrossRef]
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