Delivery Zones Partitioning Considering Workload Balance Using

Clustering Algorithm

Jaruwan Wangwattanakool

1 a

and Wasakorn Laesanklang

1,2 b

Department of Mathematics, Faculty of Science, Mahidol University, Ratchathewi, Bangkok, 10400, Thailand

Centre of Excellence in Mathematics, CHE, Bangkok, 10400, Thailand

Keywords:

Workload Balance, Last Mile Logistics, Zoning, K-Mean.

Abstract:

This research proposes a novel approach for partitioning delivery zones in Bangkok that utilizes a combination

of clustering and iterative algorithms. The approach leverages 30 days of delivery data to create delivery

zones that having balanced workloads for drivers. The study begins by analyzing the delivery data to conﬁrm

the presence of unbalanced workloads across drivers within the 30-day period. To solve this imbalance, we

use iterative k-means to adjust delivery zones considering the number of deliveries within the zone. The

effectiveness of the approach was evaluated using two sets of parameters: geographic coordinates (latitude

and longitude) and actual travel distance to reﬂect real-world scenarios. Regardless of the parameter set

used, the experiments yielded balanced transportation areas with evenly distributed workloads. This approach

demonstrates an improvement in workload equality compared to the original workload distribution.

1 INTRODUCTION

In recent years, the expansion of e-commerce has sig-

niﬁcantly increase the demand for delivery services,

particularly in urban areas. This growth translates to

a substantial daily volume of orders for both delivery

and product pick-up, subsequently elevating the op-

erational costs for delivery companies. This essential

process, known as last-mile logistics, faces signiﬁcant

challenges in urban environments. These challenges

include trafﬁc congestion, unique road networks con-

straints. Additionally, customer-related limitations,

such as limited operating hours of delivery locations

and the availability of the drivers, add further com-

plexity to the process.

Driver assignment plays an important role in en-

hancing operational efﬁciency. The establishment of

delivery zones fundamental for both drivers and route

planners, aiding in the organization of last mile logis-

tics. A driver’s familiarity with an area signiﬁcantly

inﬂuences customer satisfaction; this includes not just

navigating skills, but also an understanding of the spe-

ciﬁc delivery protocols at customer locations.

Efﬁcient route planning can reduce a company’s

transportation costs and contribute to alleviating

https://orcid.org/0009-0009-4510-9126

https://orcid.org/0000-0003-4203-3452

environmental concerns. In addition, maintaining

consistent delivery zones provides planner with an

advantage, especially when faced with tight decision

making timelines, such as executing time-sensitive

delivery.

There are several strategies for generating delivery

zones, including the use of modern optimization algo-

rithms or the development of machine learning mod-

els. In 2022 and 2023, a combination algorithm based

on k-means clustering was utilized (S.H. Huanga,

2023) (El Ouadi et al., 2022). Creating delivery

zones ensuring an equitable distribution of workload

requires the consideration of multiple factors, such

as the total number of delivery destinations, the spe-

ciﬁc delivery time frames assigned to each location.

Although clustering algorithms offer a methodology

for dividing areas, they often fall short due to the

potential for unbalanced clusters. Thus, this project

introduces a two-phase approach that combines the

strengths of clustering algorithm with iterative meth-

ods to establish zones that boast balanced workloads.

This method utilizes a month’s delivery data for gen-

erating equitable zoning strategy.

378

Wangwattanakool, J. and Laesanklang, W.

Delivery Zones Partitioning Considering Workload Balance Using Clustering Algorithm.

DOI: 10.5220/0012803800003758

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2024), pages 378-385

ISBN: 978-989-758-708-5; ISSN: 2184-2841

2 LITERATURE REVIEW

Research focusing on route optimization for urban lo-

gistics often centers around the Vehicle Routing Prob-

lem (VRP), a pivotal challenge due to the VRP’s clas-

siﬁcation as NP-hard. This complexity means that

managing deliveries in urban areas involves navigat-

ing an exceptionally large decision space, making the

efﬁcient resolution of VRP crucial for effective logis-

tics operations.

Recent trends in last-mile logistics research have

shifted towards improving algorithms for ﬁnding ef-

ﬁcient solutions in a short period of computational

timeframe. However, an emerging trends involves

leveraging artiﬁcial intelligence to tackle the prob-

lem. (Demir et al., 2022) is suggested that AI has the

potential to signiﬁcantly reduce the time complexity

of creating delivery routes, particularly when dealing

with large volumes of orders. Partitioning the city into

zones is a crucial preliminary step in this process, as

it can create time efﬁcient solutions when generating

vehicle routes.

The method of zoning prior to routing has gained

popularity in managing last-mile logistics, as high-

light by research presented by (Muhammad et al.,

2023) and (Zhao et al., 2022). The implementation

of the zoning-based pricing strategies for the VRP has

demonstrated effective performance (Shi et al., 2023),

(Afsar et al., 2021). The research exhibits the impor-

tance of zoning in logistic operations, particularly in

the context of last-mile delivery challenges.

K-means is a technique widely utilized in sev-

eral VRP research, especially when dealing with

zoning. K-means groups data points into distinct,

non-overlapping clusters based on certain parameters

(Hartigan, 1975). This method calculates distances

between points and updates cluster centers, thereby

effectively assigning data points to the most suitable

cluster. The process utilizes a speciﬁc formula to

determine the distance metric for this purpose. Al-

though K-means clustering is applied across a broad

range of ﬁelds due to its versatility, it is not without

limitations. One notable drawback is that it is less

likely that the number of data points in every cluster

would be balanced, indicating a potential bias work-

load when assigning areas to drivers.

K-means has found successful application in other

domains, particularly in zoning purposes. (Peder-

sen et al., 2022) implemented a weighted K-means

method to effectively partition delivery zones speciﬁ-

cally designed for drone logistics. Further relevant re-

search includes the introduction of a Clustering-based

Routing Heuristic (CRH) (Prajapati et al., 2023),

aimed at optimizing last-mile logistics for a fresh food

company. (Bruni et al., 2023) investigated the inte-

gration of machine learning with heuristic algorithms

to address similar logistic challenges. (Ouadi et al.,

2020) and (El Ouadi et al., 2022) combined K-means

with time series methods to forecast demand, facili-

tating more effective zoning in urban areas.

The signiﬁcance of zoning for effective workload

planning has been emphasized by the recent research

(Jabbari et al., 2020). (Wang et al., 2022) empha-

size the need to consider driver workload would sus-

tain morale within the courier workforce. Workload

balance emerges prominently in numerous studies fo-

cused on last-mile logistics management, as shown in

(S.H. Huanga, 2023). Further contributing to this dis-

cussion, (Lorenzo-Espejo et al., 2023) reveals a sig-

niﬁcant link between driver workload, their perfor-

mance, and the distances they travel. (LI et al., 2022)

employ K-mean to achieve balanced customer groups,

showcasing the utility of machine learning techniques

for creating balanced workload.

Recently, a study conducted by (Moreno-Saavedra

et al., 2024) showcases a multi-algorithm approach

that combines recursive and evolutionary algorithms

with K-means. This approach aims to optimize the

balancing of operational workload for drivers within

the last-mile urban delivery system. This research

highlights the signiﬁcant advantages of integrating K-

means with other algorithms to derive optimal solu-

tions for logistical challenges. This integration not

only enhances the efﬁciency of workload distribution

among drivers but also contributes to the broader ob-

jective of improving the overall performance of last-

mile delivery operations.

As shown in the literature, clustering algorithms

are commonly used to generate zones for drivers.

Workload balance is also a major focus in several re-

search studies. However, many approaches address

the problem on a day-to-day basis, where the driver’s

zone may change depending on daily delivery de-

mands. On the other hand, our research utilizes a

month’s worth of data to create delivery zone, ensur-

ing driver familiarity to the delivery areas. This pro-

vides a distinctive feature for our research.

3 METHODOLOGY

3.1 Data Information

This subsection focuses on a delivery dataset span-

ning one month, comprising 30,055 rows of delivery

points. There are several columns providing delivery

information such as driver id, delivery date, actual de-

livery time, and geometric coordinates. The ﬁrst row

Delivery Zones Partitioning Considering Workload Balance Using Clustering Algorithm

379

for each driver on each day represents their depot lo-

cation, and workload of each driver is then measured

by considering the total delivery time and the number

of delivery points.

3.2 Partition Algorithm

This subsection presents a novel algorithm that com-

bines k-mean with an iterative approach, structured

as a two-phase process. The initial phase employs k-

mean to partition the urban area into distinct deliv-

ery zones. The second phase of the algorithm takes

into account the distribution of deliveries within each

zone, as determined in the ﬁrst phase, to achieve

workload balance across zones. The workload bal-

ance process is attained thought the use of a statistical

method, which iteratively adjusts the allocation of de-

livery points to ensure that the delivery workload is

evenly distributed.

Data: geographic coordinate, a number of

drivers

Result: area of delivery

Initial step: assign delivery point to area of

delivery using K-mean clustering according

to the number of drivers;

calculate quartiles from the number of

delivery;

Q1 ← the ﬁrst quartile of clusters;

Q3 ← the third quartile of clusters;

; /* classification type of clusters

for cluster ← the number of clusters do

if the number of point in the cluster more

than Q3 then

Over-Zone ← cluster;

end

if the number of point in the cluster lower

than Q1 then

Under-Zone ← cluster;

else

Balanced Zone ← cluster;

end

Algorithm 1: Overall of classiﬁcation clusters algorithm.

Algorithm 1 outlines the initial phase of the work-

load balancing procedure. This initial phase starts

with the importation of delivery data, including the

geographical coordinates of customers. These coor-

dinates served as input for the clustering algorithm.

The number of clusters is set to match the number of

active drivers within the observed month. Utilizing

k-means, each delivery point is allocated to a speciﬁc

cluster based on proximity. Following the clustering

process, the algorithm proceeds to calculate the ﬁrst

and third quartiles. The ﬁrst and third quartiles cal-

culated from the initial phase are retained and used as

zone balancing criteria. Therefore, the algorithm con-

sistently uses Q1 and Q3 from the ﬁrst clustering step

for every iteration. Each cluster is then classiﬁed into

three categories:

1. Over-zone is the zone having delivery points more

than Q3.

2. Under-zone is the zone having delivery points less

than Q1.

3. Balanced zone is the zone having delivery points

between Q1 and Q3.

Data: geographic coordinate, list of

Over-Zone, list of Under-Zone,Q1,Q3

Result: area of delivery

while OverZone and UnderZone is not empty

num over ← the numbers of clusters of

Over-zone cluster;

num under ← the numbers of clusters of

Under-zone cluster;

adjusted num under ← add the number

of points of Under-zone and divided by

Q3;

different ← a round up of

adjusted num under;

if Over-Zone is not empty then

num cluster ← num over +

(num under - different);

assign all delivery points in all

Over-Zone to area of delivery using

K-mean according to num cluster ;

end

if Under-Zone is not empty then

num cluster ← different;

assign all delivery point in all

Under-Zone to area of delivery using

K-mean according to num cluster ;

end

classiﬁcation new clusters in Over-Zone,

Under-Zone and Balanced Zone;

end

Algorithm 2: Overall of re-clustering algorithm.

In the subsequent phase of the workload balanc-

ing process, as detailed in Algorithm 2, the focus

shift to the over-zone and the under-zone. For these

two zones, k-means is repeatedly applied to reﬁne the

cluster until we have balanced workload.

The re-clustering strategy, designed to tackle the

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

380

challenge of a limited number of drivers, on the prin-

ciple of adjusting the number of zones to achieve a

more balanced distribution of workload. Speciﬁcally,

this approach seeks to decrease the number of zones

classiﬁed under the under-zone category while in-

creasing the number of zones classiﬁed as over-zone.

In the ﬁnal step of the process, clusters that have

not yet achieved balance are subject to re-clustering,

with the new number of clusters being determined as

per calculations made in the previous step. After re-

clustering, the balanced of each zone is again deter-

mined by the number of tasks and the quartile values

which retrieve from the initial step. Finally, all the ar-

eas are re-examined to conﬁrm that no zone is entirely

encompassed by another. If there are zones to be in-

tersect or be nested within each other, a further round

of re-clustering is initiated. The number of cluster in

this round corresponds exactly to the total number of

intersecting zones.

3.3 Scenario with Actual Travel

Distance

To craft zoning reﬂects real-world logistics, it is es-

sential to consider the distances between delivery

points. However, calculating all pairwise distances,

especially for a large dataset, can be computationally

expensive. For instance, utilizing a mapping service

like Longdo Map API for this purpose would result in

an operational that could take more than an hour given

the size of the problem at hand. This approach is not

feasible due to the high computational cost and exces-

sive the time requirement. To dealing with this issue

and enhance algorithm efﬁciency, instead of using all

delivery points, we employ representative point strat-

egy. This method selects a subset of points that effec-

tively represent the broader set of delivery locations

within a 500-meter radius. We assume that the 500-

meter is a short distance that is negligible enough not

to signiﬁcantly impact travel time. This approach re-

duces the number of necessary API calls for distance

calculation, improves the computation time of the

zoning process. By focusing on representative points

rather than the entire dataset, the computational bur-

den is lessen without sacriﬁcing the accuracy needed

for practical route planning. However to accommo-

date this approach, there is a need to transition from

a standard k-mean algorithm to a weighted k-mean

variant (Kerdprasop et al., 2005). The weighted k-

mean algorithm adjusts for the density of these repre-

sentative points, ensuring that the clustering process

accounts for the varying importance or frequency of

deliveries within certain areas.

4 RESULTS

4.1 Overview of the Experiment

4.1.1 Data Overview

The investigation of the dataset reveals insights into

the delivery operations of a real-world scenario over a

one-month period. A total of 912 delivery trips were

recorded during this timeframe, which translates to

an average of approximately 30.4 drivers being dis-

patched daily to handle deliveries. Further analysis of

the 30,055 delivery point records indicates that a sig-

niﬁcant majority, 26,669 rows, correspond to deliver-

ies made on weekdays. This distribution suggests that

the bulk of delivery operations are concentrated on

weekdays, reﬂecting typical business operations and

customer ordering patterns. On the other hand, 1,562

points are attributed to weekend deliveries. Notably,

these weekend deliveries do not include depot assign-

ments, which might imply a different logistical setup

or operational protocol for weekend delivery services

compared to weekdays. This breakdown of delivery

data offers valuable insights into the operational dy-

namics and scheduling preferences.

The detailed analysis of weekday delivery opera-

tions reveals that the average number of active drivers

per day stands at 33.14, with a relatively low stan-

dard deviation of 1.06. This indicates a consistent

level of driver deployment on weekdays, demonstrat-

ing a stable demand for delivery services and effective

workforce management. The range of active drivers,

which spans from a minimum of 31 to a maximum of

35 drivers, further underscores this consistency, sug-

gesting that operational needs and capacity are well-

matched on a day-to-day basis. The median of the

number of driver is at 33, indicating that the central

tendency of driver deployment aligns closely with the

average. This support the decision to utilize 33 as the

target number of clusters for the subsequent zoning

process.

4.1.2 Measurement for Drivers Workload

This section focuses on measuring driver workload.

We consider both delivery time and the number of

delivery points per driver. Table 1 presents selected

statistics on driver workloads in term of delivery point

and working time, split into weekend and weekday

categories.

The data presented in Tables 1 highlights a sub-

stantial disparity in the workload between weekdays

and weekends. This shows that the majority of the

operational demands encounter during the weekdays.

Speciﬁcally, the number of delivery points during

Delivery Zones Partitioning Considering Workload Balance Using Clustering Algorithm

381

Table 1: Selected descriptive statistics of delivery point (pt)

and working time (min) in a month on driver workloads split

into weekday and weekend.

Weekend Weekday

pt min pt min

average 33.28 19.23 867.429 431.30

Q2 36 13.06 925 511

SD 17.38 19.33 382.22 171.72

minimum 1 3 2 50

maximum 67 210 1880 736

weekdays is observed to be more than 26 times higher

than those recorded over the weekends. Similarly, the

total delivery time—or working hours—accumulated

on weekdays surpasses that of weekends by approx-

imately 20 times. With the substantially higher

demands on weekdays, it is clear that zoning ef-

forts should primarily focus on weekday data. Fur-

thermore, the variation in workload—reﬂected in

both the delivery time and the number of delivery

points—suggests that relying on average values might

not provide the most accurate representation of a typ-

ical driver’s day. The median offers a more suitable

metric for understanding and planning workloads.

Statistics from Table 1 reveals imbalances in

driver workload, as evidenced by the standard devi-

ation as well as maximum and minimum deliveries

per driver per day. These disparities indicates a need

for more equitable allocation of deliveries.

4.2 Clustering Result Using Geographic

Coordinate

Figure 1 illustrates delivery points plotted over the

map of the Bangkok metropolitan area, derived from

one-month of delivery data.

Figure 2 illustrates the initial zoning generated by

the ﬁrst-phase algorithm. The lines encompass de-

livery areas into distinct zones by k-means algorithm

whose number of clusters was determined as outlined

in Section 4.1.1.

Figure 1: Original delivery points on the map.

Table 2: The quartile of delivery point in each clusters from

ﬁrst clustering.

Quartile Delivery points in clusters (points)

minimum 80

Q1 436

Q2 588

Q3 1198

maximum 2114

Figure 2: The clusters of delivery zone from ﬁrst K-mean

clustering.

Table 2 displays the results of the quartile analy-

sis performed on the list of clusters. When these re-

sults are compared with the initial data from week-

days, both the minimum and the median values of de-

livery points per cluster have increased, indicating a

shift in workload distribution. However, the result

shows that the maximum number of delivery points

within a single cluster has surpassed even the original

maximum value. This suggests that, despite efforts to

redistribute the workload, imbalances still persist with

some clusters being overloaded compared to others as

shown in Table 3.

Figure 3 showcases a line graph that effectively

compares the number of delivery points per area at

different stages of the algorithm’s application. On

the graph, the X-axis categorizes areas in ascending

order based on the number of delivery points they

contain, from the fewest to the most. The Y-axis,

meanwhile, quantiﬁes the number of delivery points

attributed to each area. The result shows the impact of

the re-clustering algorithm, illustrating a trend toward

a more balanced distribution of delivery points across

Table 3: Clusters from the initial clustering into three types.

Type of Zone The number of Zone

Balance 17

Over 9

Under 9

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

382

cluster. At the initial stage, the graph shows signif-

icant variability in the number of delivery points per

area. After two rounds of re-clustering attempts, the

variability diminishes, reﬂecting a progressive equal-

ization of workloads across different areas.

Figure 3: The number of delivery points for each area is

sorted from lowest to highest.

Table 4 presents another innovative metric for as-

sessing workload balance, which is the slope of the

line graph representing the distribution of delivery

points per area, sorted in ascending order. Initially,

the clustering process yield a slope of 34.03, which

serves as a quantitative indicator of the distribution

of workloads among drivers. A steeper slope in the

context would suggest a less balanced plan. After

the ﬁnal re-clustering step, the slope has decreased to

15.16. This enhancement signiﬁes a 55.45% improve-

ment in the balance of driver workloads, demonstrat-

ing the effectiveness of the re-clustering algorithm to

achieving a more equitable distribution. Note that the

slope decreases with each re-clustering step, which is

a positive indication of the adjustment of the driver

workload.

Table 4: Slope of driver’s workload in each iteration.

The number of times for re-clustering Slope

Original zone 34.03

K-Mean clustering 51.86

Re-clustering 1 31.26

Re-clustering 2 15.16

4.3 Clustering Result Using Travel

Distance

For clustering based on distance between delivery

points, minimizing the number of points to calcu-

late distances is a crucial step in reducing the time

required to call distance information from map API.

Figure 4 illustrate the representative points for group

of points that are within 0.5 km of each other. The

Figure 4: Reduce original delivery points on the map.

Table 5: Slope of driver’s workload (capacity) in each iter-

ation.

The number of times for re-clustering Slope

Original zone 34.03

K-Mean clustering 63.58

Re-clustering 1 33.78

Re-clustering 2 27.66

representative points consolidates the other nearby

points. As a result, this method reduces the total

points of 30,055 to 1,352 representative points.

The results based on the distance parameter re-

veals that, the overall balance of driver workloads

does not exhibit signiﬁcant differences when com-

pared to clustering based on geometric coordinates.

Although, the shapes of the resulting delivery zones

do vary. Figure 5 displays line graph comparing

the number of delivery points within the area of de-

livery, generated by the workload balance algorithm

using distance parameter. The result conﬁrms that

re-clustering method make the workload distribution

more equitable.

Figure 5: The number of delivery points (capacity) for each

area is sorted from lowest to highest in distance.

Delivery Zones Partitioning Considering Workload Balance Using Clustering Algorithm

383

Table 6: Slope of driver’s workload (capacity) in each iter-

ation.

The number of times for re-clustering Slope

Original zone 34.03

K-Mean clustering 63.58

Re-clustering 1 33.78

Re-clustering 2 27.66

4.4 Zoning Analysis

Figure 6: Original Zone of Drivers.

Figure 6 showcases the original zone assignments for

delivery driver, highlighting issues such as overlap-

ping areas. These overlaps can lead to inefﬁciencies

in delivery operations, including redundant routes, in-

creased travel times and potential confusion over de-

livery responsibility.

In contrast, Figure 7 displays the outcome of the

algorithm with travel distance parameter. This con-

ﬁguration provides new delivery areas with improve-

ments on workload balance. However, with the visual

observation, the area in the top left still encompasses

two smaller zones within a larger one. These group

of zones are required to have another re-clustering at-

tempt. Additionally, the zone on the right remains

quite large, potentially requires another re-clustering

attempt.

For the top left zones, we can categorize these

zones as under-zone and the large right zone as an

over-zone. Figure 8 illustrates the outcomes of this

Table 7: The number of delivery in clusters from re-new

clustering.

The zones the number of delivery points

Top left1 824

Top left2 1125

Big right1 949

Big right2 491

Figure 7: Partition zone obtained by the algorithm and dis-

tance parameter.

Figure 8: Final workload balance zone.

re-clustering attempt while Table 7 lists the delivery

points for the new clusters. The result zones have

been improved as the right large zone is split into two

smaller zones. Similarly, the top left area, which ini-

tially comprised three overlapping zones, has been re-

designed into two zones. This adjustment not only

reduces overlap but also ensures that the workload is

more evenly spread.

5 CONCLUSIONS AND FUTURE

WORK

This study introduces a two-phase algorithm designed

to strategically zone urban delivery area, with the

primary goal of achieving a balanced distribution of

driver workloads. The methodology combines the use

of a clustering algorithm with quartiles to systemati-

cally organize delivery points into efﬁciently manage-

able zones. This study investigates the effect of the

algorithm when using geographic coordinates and the

travel distance to ensure that the result is practical and

reﬂective of real-world delivery logistics.

As we show in the study, the algorithm practically

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

384

improve the delivery zones by removing overlapping

areas. Re-clustering procedure can also applied to

make more equitable workload, comparing to a sim-

ple clustering method. Thus, this enhancement reﬁnes

the cluster to ensure that the workload is less varied

among drivers.

Future research from this study should concentrate

on the dynamic of daily delivery operations within

the predetermined zones. The challenge of effectively

assigning delivery points to drivers on a daily basis,

while ensuring an equitable distribution of workload,

is central to optimizing last-mile delivery logistics. A

key aspect of this approach involves the development

of a system capable of intelligently managing deliv-

ery orders, potentially by delaying certain deliveries

to subsequent days. This mechanism would aim to

balance workloads more evenly across adjacent days,

addressing the variability in daily delivery demands.

ACKNOWLEDGEMENTS

This research is supported by Development and Pro-

motion of Science and Technology Talents Project

Scholarship and the Department of Mathematics, Fac-

ulty of Science, Mahidol University, Thailand.

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