Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
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A hybrid modeling approach for parking assignment in urban areas
Hanae Errousso a,b,c, Jihane El Ouadi a,b,c, El Arbi Abdellaoui Alaoui c,d,⇑, Siham Benhadou a,b,
Hicham Medromi a,b
a
Research Foundation for Development and Innovation in Science and Engineering, Casablanca, Morocco
National and high school of electricity and mechanic, HASSAN II University, Casablanca, Morocco
c
EIGSI, Casablanca, Morocco
d
Faculty of Sciences and Technologies, My Ismail University, Errachidia, Morocco
b
a r t i c l e
i n f o
Article history:
Received 23 August 2020
Revised 22 October 2020
Accepted 9 November 2020
Available online 19 November 2020
Keywords:
Urban parking management
Fuzzy logic
Freight transport
Conflict handling
a b s t r a c t
Finding a parking space is a daunting task that frustrates drivers, affects the economic efficiency of carriers and impacts city sustainability. Between meeting the needs of deliverers (location, accessibility,
proximity...) and individuals (price, duration, closeness...), transport and urban traffic planners find themselves in a conflict of interest. Hence the importance of a tool that manages the entire urban parking system in real time. This paper presents, in this perspective, a solution that allocates parking spaces to
carriers and individuals under uncertain conditions. Its principle is founded on two allocation levels.
The first distributes parking requests on the city areas by considering three characteristic indicators.
The second ranks, for each driver, the available spaces in the designated area according to their decreasing non-dominated degree. It additionally includes a conflict management approach for dealing with the
assignment of multiple drivers to the same place. It is deployed and its performance is tested by administering parking in a city with four urban areas.
Ó 2020 The Authors. Published by Elsevier B.V. on behalf of King Saud University. This is an open access
article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Freight transport contributes significantly in strengthening the
socio-economic dynamism of a city. It not only connects companies with their suppliers and customers, but also ensures necessary
provision for citizens’ lives and sustains industrial or commercial
activities as well as associated jobs. However, it generates many
problems and challenges that amplified with the increasing density of residential and economic activity.
Goods are carried by vehicles of different gauges that share the
road network and parking infrastructure with private vehicles.
Consequently, these vehicles reduce road capacity, slow down traffic speeds, lead to longer journey times, increase street congestion
and ultimately induce additional expenditure. They thus bring out
environmental nuisances, such as emissions of air pollutants espe⇑ Corresponding author at: EIGSI, Casablanca and Faculty of Sciences and
Technologies, My Ismail University, Errachidia, Morocco.
E-mail address: elarbi.abdellaoui@eigsica.ma (E.A.A. Alaoui).
Peer review under responsibility of King Saud University.
Production and hosting by Elsevier
cially greenhouse gases (carbon dioxide, methane, nitrous oxide,
sulfur hexafluoride. . .), noise, ugly streets, foul odors. . . which negatively impact on the quality of human life in urban areas.
Traditionally, public authorities have not tackled issues related
to the transportation of goods in the city, except through the regulation on parking, street access, hours of operations, and so on
(Crainic et al., 2004). They simply identify parking spaces dedicated
to freight carriers by yellow marking a portion of the road. These
fixed logistics facilities on open terrain, named delivery bays,
improve goods transit and their relations between the road network and the operating site (Boudouin, 2006).
Nonetheless, delivery drivers still point out a lack of parking
facilities, inadequate management and non-optimal allocation of
existing ones (difficult access, small size, narrow sidewalk, different road levels, mismatch between demand and supply). They furthermore underline that delivery bays are mostly illegally occupied
by individuals or other deliverers who do not comply with parkingtime limits. That’s why they no longer hesitate to double park in
order to shorten delivery times and meet deadlines.
Cities are experiencing a significant number of freight deliveries
that continue to grow at a rapid pace. This growth implies a commensurate increase in the number of delivery areas, which
involves a reduction in public space and private car parking. It
therefore prompts an unbalanced sharing of these resources in
https://doi.org/10.1016/j.jksuci.2020.11.006
1319-1578/Ó 2020 The Authors. Published by Elsevier B.V. on behalf of King Saud University.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
walking distance to destination, driving and waiting time, parking
prices, availability, and accessibility (Badii et al., 2018).
Numerous papers address carriers’ parking problems by
proposing tools to dimension delivery area layouts. The authors
of Pinto et al. (2016) optimized, by a mixed analytic-Monte Carlo
simulation approach, the distribution of delivery areas depending
on the demand and location of the business activities. They identified the best locations of lay-by areas by applying a discrete covering model. They defined the most suitable size (i.e.. number of
parking stalls) of each activated lay-by area to reach a compromise
between space occupation and parking availability. In Tamayo
et al. (2017), a framework for delivery spaces location and evaluation is suggested. It consists in gathering real and up-to-date information about cartography, delivery parking demand and existing
delivery spaces. It quantifies the generated flow of loadings and
deliveries for each business with a statistic-based estimation or
with a local survey. It determines the location of new delivery
spaces based on an optimization model that considers real distances, influence radius and physical constraint.
Other authors dealt with this issue through approaches to organizing delivery areas. Roca-Riu et al. (2015) allocated parking
spaces to freight carriers by several alternative models designed
as mixed integer problems and distinguishable by their objective
function (satisfaction of all carriers’ time window requests, earliness/tardiness minimization, minimization of number of requests
scheduled outside the time window. . .). They quantified the degree
of non-accomplishment of requests with different criteria. A model
for dynamic assignment of loading bays is suggested in Letnik et al.
(2018). It provides the optimal number and locations of delivery
areas by employing fuzzy k-means clustering of receivers in combination with a routing algorithm. It manages these logistics
infrastructures in two different ways, a carrier is assigned only to
the delivery area closest to its destination or to the second-best
possible place if the first one is occupied.
Some works are interested in more global tools for sizing, localization and management of delivery areas. A methodology split
into a quantification phase and a location-allocation process is
described in Muñuzuri et al. (2017). It estimates the needed number of loading zones on a given street as a ratio between the average daily carrier parking demand and the capacity of each loading
zone. It solves a specific location-allocation problem that considers
the delivery characteristics of the retailers involved. In Comi et al.
(2018), the authors developed a solution to model temporal transportation demand, simulate delivery area schemes depending on
the features of commercial operations, evaluate these scenarios
by means of some performance indicators and adopt the most optimal one. They also proposed an advanced trip planner that assists
transport and logistic operators in managing their deliveries, during pre-tour and on-route phases.
Several scientific contributions elaborate optimization models
for distributing parking spaces to individuals. Abidi et al. (2015)
mathematically formulated the parking slot assignment problem
for groups with time restriction. They sought to minimize the
sum of the walking distances and the fees that the vehicles have
to pay. They developed, to solve this combinatorial optimization
problem, a hybrid genetic assignment search procedure by combination of a genetic algorithm and a greedy randomized adaptive
search procedure. The problem of dynamic assignment for parking
slots is approached in Ratli et al. (2019). The goals are to provide a
global satisfaction to all customers and to maximize the parking
lots occupancy. A penalty term is introduced in the objective function in order to make parking spaces with low future demand more
attractive. Its values are calibrated through a learning process
using the estimation of distribution algorithm. The authors of
Geng et al. (2011) put forward a smart parking system founded
on a dynamic resource allocation approach. It solves a mixed
favor of transport operators. To restore this balance, we propose an
urban parking management approach that helps both carriers and
individuals to easily find a parking space near their destination.
Several proposals address urban parking problems by concentrating either on parking for individuals or for transporters without
combining these two issues despite being closely related. These
solutions differ considerably in their architecture (with or without
physical infrastructure, nature of components, technologies
deployed, etc.) and functionality. In most instances, they simply
collect data on parking space availability from sensor networks (ultrasonic, magnetic, thermal or acoustic sensors . . .) (Tang et al.,
2006; Cheung et al., 1917; Alkheder et al., 2016; Lee et al., 2008)
or driver networks (Bechini et al., 2013; Chen et al., 2012;
Villalobos et al., 2015), and disseminate it via information technology applications. Their implementation implies high investment
and maintenance costs or strong involvement of drivers. They only
display parking availability maps or tables in an urban area at a
given time, which creates competition between drivers for a parking spot. Resulting in many drivers forced to look for another parking space, wasting more time, consuming more fuel and losing
good mood, hence the importance of an assignment approach.
Our proposed assignment approach allocates parking spaces to
both carriers and individuals. It aims to adjust the parking offer if
necessary and is structured in two levels. The first level is a sizing
problem. The delivery activity is highly concentrated in the day. It
starts around 06:00 am and ends around 11:30 am. It is therefore
necessary to provide professionals with a sufficient number of
well-positioned delivery areas to support their activity and avoid
double parking. The second level is a management problem to
adapt the supply of parking to the needs of the city. Beyond
01:00 pm, logistic activity decreases and the number of delivery
areas can be reduced which implies a change of status for these
infrastructures.
Our main contribution is to develop an integrative approach
that addresses the parking problem of all road users, professionals
and individuals. With such a solution, the notion of a delivery area
will automatically be surpassed as any available and suitable parking space can accommodate a carrier. All parking spaces will be
able to switch their status (delivery area vs. parking space) in real
time and autonomously. In other words, a parking space can
receive a freight vehicle or a private one according to the demand
during the time period concerned. Rather than focusing on a single
urban area like most research, the proposed method processes
parking requests from all areas of a city. Moreover, it redistributes
them to balance the occupancy-load of the different regions. Conventional approaches deal with parking space allocation while
assuming that the problem parameters are fixed and known in
advance. In contrast, the suggested approach effectively handles
inaccurate and vague nature of language evaluation through fuzzy
theory.
The rest of the paper is organized into five sections. Section 2
presents a literature review outlining our proposal’s contributions.
Section 3 briefly summarizes basic concepts of fuzzy logic. Section 4
illustrates the architecture of the proposed approach and describes
the principle of each phase. Section 5 reports the results of applying the proposed approach to a decision problem. Section 6 sets out
conclusions and further developments.
2. Related works
From our vision, the selection of appropriate car parks, for both
carriers and individuals, can be classified as a combination of parking space assignment problem, delivery bay allocation problem,
logistics centers location problem and loading/unloading areas
localization. It could be influenced by multiple factors, e.g.. the
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Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
ing mathematical models, thus assuming that the parameters of
the programs developed were fixed numbers known in advance.
However, these parameters, particularly the qualitative ones, are
often imprecisely and accurately defined. To deal with such issues,
numerous authors resort to fuzzy theory.
The authors in Bouhana et al. (2013) suggested a multi-criteria
decision-making approach to address the urban distribution center
location/allocation problem under uncertain environment. It
defines a set of qualitative and quantitative location criteria and
selects the best locations on using the fuzzy theory and the pairwise fuzzy preference relation approach. In Chen (2001), a new
fuzzy multiple criteria decision-making method is proposed to
choose the best sites for setting up urban distribution centers. A
fuzzy preference relation matrix is built to reflect the degree of
preference of one plant location relative to another. And then, a
stepwise ranking procedure is employed to rank all candidate locations. Hashim et al. (2014) mainly examined a multi-objectives
programming model with fuzzy coefficients for locating logistics
distribution centers. Uncertain parameters (transportation cost,
setup cost and demand) are supposed to be fuzzy variables and
characterized by triangular fuzzy numbers. Fuzzy expected values
are calculated by means of a new fuzzy measure with an
optimistic-pessimistic fit index to transform the uncertain model
into a deterministic one. In Lee and Lin (2008), a fuzzy quantitative
SWOT method is presented to assess the adequacy and preferability of locations as transshipment type’s international distribution
centers. It integrates multiple criteria decision-making concept
and fuzzy analytic hierarchy method. It includes 10 steps starting
with the selection of alternatives, continuing with the standardization of performance values for various criteria and concluding with
the display of all candidate locations on the 4-quadrant coordinate
in the SWOT matrix. The authors in Chu (2002) selected strategic
locations for logistics facilities by a fuzzy TOPSIS model under
group decisions. They evolved the membership function of two
positive trapezoidal fuzzy numbers by applying interval arithmetic
and a-cuts of fuzzy numbers. They performed the ranking method
of the averaged integral values to aid in inferring the ideal and
negative-ideal fuzzy solutions.
The methodologies aforementioned are either predominantly
concerned with optimizing delivery bay layouts, allocating parking
spaces to private vehicles or assigning delivery bays to carriers.
Hence, the suggested approach explores this research opportunity
and tackles all three issues simultaneously. To highlight the concrete advances brought by our proposal, it is compared with
related works on several criteria (Table 1):
integer linear program problem at every decision point such that
each solution constitutes an optimal allocation. It assigns and
reserves for a driver a space that best meets his preferences in
terms of proximity to destination and parking cost, while ensuring
the efficient utilization of overall parking capacity. The solution
described in Venkataramanan and Bornstein (1991) is a networkbased decision support system for assigning parking spaces. This
integrated optimization system generates the model as a pure network problem, which minimizes the weighted sum of priority, cost
and distance to go. It optimizes the resulting program with a primal simplex network optimizer and produces a report for each
car park.
However, few papers propose algorithmic architectures instead
of mathematical models to manage household parking. Hakeem
et al. (2016) presented a cost-effective and adaptive parking system, a system for assigning free curbside parking spaces to drivers.
It uses a parking assignment algorithm, FPA, that minimizes the
total travel time among all drivers and incorporates the effect of
unsubscribed drivers competing with subscribed ones for parking
spaces. This algorithm draws on a modified version of the compound laxity algorithm to determine how long a request can be
delayed before it must be assigned. To increase the processing
speed of new parking requests, they provide, in Hakeem et al.
(2017), a distributed version of their centralized parking assignment algorithm. They structured the parked drivers in a K-D tree
where a node can play two roles either parking manager or region
manager. Each car park manager regularly executes the FPA algorithm to satisfy the pending requests transmitted to it. The authors
in Mejri et al. (2013) suggested an efficient semi-centralized parking slot assignment system where each parking lot, in a given
urban zone, is monitored by a parking coordinator. They distinguished two variants: with or without complete knowledge of
neighboring authorities’ decisions. They used the mathematical
programming solver for linear programming CPLEX to allocate
spaces while optimizing each coordinator’s social welfare.
Logistics platforms location is an issue overly covered and
widely documented in the literature. In Guyon et al. (2012), an
integer linear programming model is proposed to optimize sustainably the location and sizing of logistics facilities in urban
zones. This model, to be properly used by local authorities of
large cities, is integrated in an optimization tool that enables to
edit data, to find a feasible solution and to visualize it. Fei et al.
(2007) studied a strategy of locating distribution centers with
maximum utility and minimum sum of inbound transport cost,
outbound transport cost, management cost and fixed investment
cost. They resolved this discrete model with a genetic algorithm
adapted to the field constraints. A possible organizational and
technological framework for the integrated management of urban
freight transportation is introduced in Crainic et al. (2004). It consists of mini platforms whose main role is to collect goods from
various points outside the city and consolidate them in ecological
vehicles suitable for usage in dense urban areas. It is designed as
a location-allocation model in a multi-echelon distribution setting
that is solved by the branch-and-bound procedure of CPLEX. The
authors in Costa et al. (2013) presented a methodology to locate
logistics platforms with the help of geographic information systems. It is composed of five phases, where the two firsts determine the ideal locations to implement the logistics platforms.
The next two phases check whether or not inadequate transport
flows exist and adjust, if necessary, the mathematical model
defining the candidate locations and the one assaying the transportation cost. The last phase reports all facilities located, the
transportation modes utilized, the transportation routes and the
costs involved.
In most previous research works, the problems of locating logistics platforms or allocating parking spaces are studied by formulat-
Optimization of delivery area number (D_N) locations (D_L) and
sizes (D_S);
Parking space allocation to individuals (P_I) and carriers (P_C);
Spatial (O_S) and temporal (O_T) simulation of obstructions
derived from carriers’ double parking;
Consideration of unclear qualitative parameters (C_L);
Exploitation of real-time information related to parking space
availability (R_P);
Centralized (C_M) or distributed (D_M) nature of the model;
Utilization of empirical data (E_U) or simulation of driver parking operations (P_S).
Our methodological framework integrates real-time information on parking space availability acquired from telematic devices
and the parking occupancy prediction mechanism developed and
tested in Errousso et al. (2020). It cascades from macro level of
cities by allocating drivers’ requests to areas that can accommodate them to micro level of city zones by assigning parking lots
to drivers. It relies on a hybrid approach that combines fuzzy logic
and mathematical optimization.
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H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
Table 1
System comparison.
Reference
D_N
Pinto et al., 2016
Tamayo et al., 2017
Roca-Riu et al., 2015
Letnik et al., 2018
Muñuzuri et al., 2017
Comi et al., 2018
Abidi et al., 2015
Ratli et al., 2019
Geng et al., 2011
Venkataramanan and Bornstein, 1991
Hakeem et al., 2016
Hakeem et al., 2017
Mejri et al., 2013
Delaitre, 2009
Our proposal
–
–
–
p
p
p
–
–
–
–
–
–
–
–
p
D_L
p
p
–
p
p
p
–
–
–
–
–
–
–
–
p
D_S
p
–
–
–
–
–
–
–
–
–
–
–
–
–
p
P_I
P_C
O_S
O_T
C_L
R_P
–
–
–
–
–
–
p
p
p
p
p
p
p
–
–
p
p
–
–
–
–
–
–
–
–
–
–
–
–
–
p
–
–
–
–
–
–
–
–
–
–
–
–
–
p
–
–
–
p
–
–
–
–
–
p
–
–
–
p
–
–
–
–
–
–
–
–
p
–
p
Fuzzy logic studies reasoning systems in which the notions of
truth and falsehood are considered in a graded fashion, in contrast
with classical mathematics where only absolutely true statements
are considered (Spada, 2009). It is the theory of fuzzy sets, sets that
are defined over some universe of discourse.
In recent years, fuzzy set theory has been used for handling
fuzzy decision-making problems. Broadly speaking, fuzzy sets are
the mathematical models for extensions of vague notions
(Gottwald, 1979). If X is a collection of objects denoted generically
x; lA ðxÞjx 2 X
ð1Þ
lA ðxÞ is called the membership function (generalized characteristic function) which maps each element x in X to a real number in
the interval [0,1]. The closer the value of l ðxÞ is to unity, the
A
greater the membership of X to A.
lA ðxÞ ¼
8
0;
if x < n1
>
>
>
>
< xn1 ; if n1 6 x 6 n2
n2 n1
n3 x
>
; if n2 6 x 6 n3
>
n3 n2
>
>
:
0;
if x > n3
A
–
p
–
–
p
p
–
–
–
p
–
p
p
p
p
–
–
p
–
p
P_S
–
–
–
p
–
p
–
p
–
–
p
p
–
p
–
Linguistic term
Membership function
Very poor (VP)
Poor (P)
Medium poor (MP)
Fair (F)
Medium good (MG)
Good (G)
Very good (VG)
ð0; 0; 1Þ
ð0; 1; 3Þ
ð1; 3; 5Þ
ð3; 5; 7Þ
ð5; 7; 9Þ
ð7; 9; 10Þ
ð9; 10; 10Þ
Linguistic term
Membership function
Very low (VL)
Low (L)
Medium low (ML)
Medium (M)
Medium high (MH)
High (H)
Very high (VH)
ð0; 0; 1Þ
ð0; 1; 3Þ
ð1; 3; 5Þ
ð3; 5; 7Þ
ð5; 7; 9Þ
ð7; 9; 10Þ
ð9; 10; 10Þ
4. Proposed approach principle
ð2Þ
The proposed parking space allocation approach is based on
fuzzy logic. It is complemented by a strategy to manage conflicts
arising from the assignment of drivers to the same space. It helps
both carriers and individuals to find a free parking space close to
their destination. It thus considers that individuals transport a zero
quantity of goods. Our solution’s methodological framework
(Fig. 1) consists of three major phases (Macro-assignment, Microassignment and Conflict handling), each of which includes several
steps.
where n1 ; n2 ; n3 are real numbers and n1 < n2 < n3 . This triplet
ðn1 ; n2 ; n3 Þ define a triangular fuzzy number. The maximum value
of l ðxÞ is equal to 1 and obtained for an X value of n2 . The minimum value of
–
p
p
p
–
–
–
–
–
–
–
–
–
–
–
p
p
E_U
p
p
p
Table 3
Linguistic terms for criteria ratings.
by x, then a fuzzy set A in X is a set of ordered pairs (Zimmermann,
2010).
–
–
p
D_M
Table 2
Linguistic terms for objective ratings.
3. Preliminary about fuzzy logic
A¼
–
–
–
–
–
–
–
–
–
–
p
C_M
p
p
p
p
p
p
p
p
p
p
p
lA ðxÞ corresponds to 0 and achieved for a value of
X of n1 or n3 .
Linguistic variables are variables whose values are represented
in words or sentences in natural or artificial languages (Chu, 2002).
They are characterized by a quintuple
x; T; U; G; M
4.1. Phase 1: macro-assignment
(Zimmermann, 2010), in which x is the name of the variable, T
denotes the term set of x, that is, the set of names of linguistic values of x. Each of these values is a fuzzy variable, denoted generically by X and ranging over a universe of discourse U, which is
associated with the base variable u. G is a syntactic rule (which
usually has the form of a grammar) for generating the name, X,
The goal of this first phase is to equitably spread parking
demands across all zones while considering their capacity and also
ensuring that all parking demands are met. Its main concern is to
avoid a parking request being accepted by several zones while
other vehicles do not receive any response to their demand.
In our proposal, a parking space is characterized by an identifier, its coordinates and its status (occupied or unoccupied). Similarly, a parking request is typified by an identifier, the
coordinates of its destination, its delivery time slot, its radius of
influence, its coverage ratio, the mass to be transported, the
time-sensitivity of goods, a ranking of available spaces according
of values of x. M is a fuzzy subset of U.
In this paper, we adopt a scale from 0 to 10 to evaluate criteria
and alternatives. Table 2 presents linguistic values and their corresponding fuzzy numbers attributed for each alternative and Table 3
shows linguistic variables and their respective fuzzy ratings for
each criterion.
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Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Correspondence matrix
calculation
Macro assignment
Coverage indicator
computation
Solicitation ratio calculation
Allocation of parking requests
to areas
Solicitation rate ranking
Extending influence radius of
unsatisfied drivers
No
Ranking the mass to be
transported
Complete driver
satisfaction
Assignment of parking spaces
to drivers
Conflict handling
Delaying deliveries by 15 min
Yes
Evaluation of alternatives'
relevance
Criterion weighting
Fuzzy preference relation
matrix construction
Fuzzy strict preference relation
matrix establishment
Aggregating fuzzy rating of
alternative
Aggregating fuzzy weights for
criteria
Two fuzzy final evaluation
values comparison
Calculation of degrees of nonnomination
Normalized fuzzy decision
matrix calculation
Weighted normalized
alternatives computation
Final fuzzy evaluation value
calculation
Alternative usefulness ranking
Micro assignment
Fig. 1. Parking space allocation architecture.
ing parking requests, it affects, firstly, all demands with a coverage
rate equal to 1, then those with a ratio strictly greater than 1. Unassigned drivers, either because they have a zero-coverage indicator
or because there are no more places in their destination area, can
either report their arrival at the next time slot (i.e. delay them by
15 min) if they have some flexibility, or extend their radius of influence Ri . If the second option is chosen, all parking requests for this
decision point are reassigned by re-running the algorithm.
to their degree of non-nomination and the spot to which it will be
assigned. In turn, an area is modelized by an identifier, its solicitation rate, the number of available spaces, their characteristics, the
number of assigned parking requests and their properties. These
data are represented using the composite data type variables with
several objects (structure).
For each time slot (i.e. every 15 min), parking requests are collected, areas with available parking spaces are selected and free
space coordinates are identified. Considering the walking distance
between the parking space and the driver’s final destination, a cor respondence matrix C ¼ C ij VZ is established with Z (number of
zones) columns and V (total number of requests) rows. It stipulates
the relevant parking requests for each zone.
(
C ij ¼
0; d Di ; pj < Ri
1; Otherwise
Algorithm 1 Macro-assignment
Input:
Let v j 2 Vbe a parking request
Let pi 2 P i be an available parking space within zone zi
Let VNi be the number of available parking spaces in zone
zi
1: Calculate correspondence matrix C ¼ C ij VZ
2: Compute coverage rate Gj for each request v j
3: Calculate solicitation rate Si of each urban area zi
4: Rank areas Z of a city in ascending order of their
solicitation rate
5: Update Z
. to be a sorting of urban zones
Output: V i parking requests assigned to zone zi 2 Z
6: for each zone zi 2 Z do
7: ANi 0
. Initialize the number of parking
requests assigned to zone zi
8: end for
9: Rank parking requests V in increasing order of their
coverage rate
10: Update V
. to be a sorting of parking requests
11: for each request v j 2 V do
12: if (Gj P 1) then
. Affect parking
13:
for each zone zi 2 Z do
requests with a coverage rate equal to or greater than 1
14:
if (C ij ¼ 1 and ANi < VNi ) then
15:
Assign parking demand v j to zone zi
16:
Update V i
17:
ANi ANi þ 1
18:
Break
19:
end if
20:
end for
21: end if
ð3Þ
C ij ¼ 1 if and only if the distance between the final destination
of a carrier i and a parking place in zone j is less than the driver’s
radius of influence Ri . It means that driver i can be greeted by
zone j.
To calculate the distance between a driver’s destination and a
parking space, we apply Euclidean distance which depends on
the coordinates of these two points.
On the basis of this matrix, two indicators are calculated,
namely the solicitation ratio and the coverage rate. The first Sj corresponds to the number of requests that can be accommodated by
a zone j. The second Gi represents the number of zones that can
receive a driver i (Fig. 1).
Sj ¼
V
X
C ij ;
j ¼ 1; . . . ; Z
ð4Þ
i ¼ 1; . . . ; V
ð5Þ
i¼1
Gi ¼
Z
X
C ij ;
j¼1
Taking into account these two metrics and the number of available spaces in each zone, parking demands are assigned to the
most appropriate areas of the city. They are allocated, in priority,
to the least solicited areas. Similarly, the least covered requests
are prioritized and affected first (Algorithm 1).
To that end, the Macro-assignment algorithm arranges the
urban areas’ solicitation rate in ascending order to begin searching
for assignment opportunities in less attractive zones. After classify-
(continued on next page)
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H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
4.2.1. Evaluating the importance of criteria and relevance of
alternatives
Assuming that a committee of l decision-makers
ðDk ; k ¼ 1; . . . ; lÞis responsible for assessing n parking spaces
ðP i ; i ¼ 1; . . . ; nÞunder each of m attributes C j ; j ¼ 1; . . . ; m .
wjk ¼ w1jk ; w2jk ; w3jk is the weight of criterion j assigned by the deci
sion maker k. aijk ¼ a1ijk ; a2ijk ; a3ijk is the rating of a decision maker k
22: end for
23: for each request v j 2 V do
24: if (Gj ¼ 0 or v j R V i ) then
25:
for each zone zi 2 Z do
26:
Write ‘‘Would you like to delay your arrival for
15 min”
27:
Read Ans
28:
if Ans ¼ 1 then
29:
T j T j þ 1
. Report the arrival of driver v j
to the next time slot T j
30:
else
31:
Write ‘‘Please extend your maximum walking
distance”
32:
Read Rj
33:
end if
34:
end for
35: end if
36: end for
for alternative i against criteria j.
4.2.2. Aggregating fuzzy ratings for alternatives and criteria
~ j ¼ w1j ; w2j ; w3j and rating of
The aggregated criteria weights w
~ij ¼ a1ij ; a2ij ; a3ij are
alternatives with respect to each criterion a
defined as follows.
~j ¼
w
~ij ¼
a
4.2. Phase 2: micro-assignment
Once completed, the second phase involves attributing a specific parking space to each driver. It processes the parking requests
targeting different zones in parallel to ensure speedy calculation.
It considers multiple criteria (Table 4) that represent qualitative
and quantitative parameters against which alternatives are compared and judged.
It relies on a fuzzy decision-making based approach containing
several steps. It starts with scoring criteria and alternatives and
ends by ranking available parking spaces according to their
appropriateness.
Type
1
mina1ijk ;
k
l
l
X
k¼1
!
w2jk ; maxw3jk
k
l
X
a2ijk ; maxa3ijk
k¼1
ð6Þ
!
ð7Þ
k
4.2.3. Calculating the fuzzy decision matrix and normalizing it
The objective attributes are measured in different units and
must be transformed into dimensionless indices to ensure compatibility with the linguistic ratings of the subjective attributes (Chu,
2002). To this end, the linear scale transformation is employed and,
therefore, the normalized fuzzy decision matrix is obtained
R ¼ ~rij nm .
~rij ¼
Table 4
Criteria for parking assignment.
Criteria
1
minw1jk ;
k
l
!
a1ij a2ij a3ij
;
; ;
aj aj aj
aj ¼ maxa3ij ;
i
8i ¼ 1; . . . ; n 8j ¼ 1; . . . ; m
ð8Þ
8j ¼ 1; . . . ; m
ð9Þ
Definition
Walking distance ðC 1 Þ
4.2.4. Computing the final fuzzy evaluation value
~i of alternative P i is computed
The final fuzzy evaluation value p
as the sum of their normalized fuzzy ratings weighted by the
importance of each criterion.
Quantitative Walking distance from the parking
space to the delivery point
Driving distance ðC 2 Þ
Quantitative Driving distance between the supply
point and the parking space
Survival probability ðC 3 Þ Qualitative
Likelihood that the parking space
will remain free until the driver
arrives
Parking rate ðC 4 Þ
Qualitative
Unit rate for parking during the
delivery slot
Accessibility ðC 5 Þ
Qualitative
Easy access to the parking space by
different types of vehicles
Parking space
Qualitative
Convenience between the size of the
convenience ðC 6 Þ
parking space and that of the vehicle
to be accommodated
Infrastructure
Qualitative
Absence of obstacles (street
adaptability ðC 7 Þ
furniture, road level differences,
sidewalk widths) on the carrier’s
path to the delivery point
Quality of service ðC 8 Þ
Qualitative
Ability to help drivers meet their
obligations on time, taking into
consideration traffic conditions and
area’s frequentation rate
Security ðC 9 Þ
Qualitative
Parking space security against
accidents, theft and violence
Compliance with
Qualitative
Capacity to comply with sustainable
sustainable freight
freight constraints mandated by
regulations ðC 10 Þ
public authorities (limited delivery
hours, used vehicle size, specific
delivery area . . .)
Space usage rate ðC 11 Þ
Qualitative
Balanced allocation of parking
demands among the different
resources
~i ¼
p
m
X
~ j;
~rij w
8i ¼ 1; . . . ; n
ð10Þ
j¼1
4.2.5. Comparing two fuzzy final evaluation values
To decide on the preferability of the alternative P i over the alter
native Pj , we compare the membership function of Z ij with zero.
The triangular fuzzy number Z ij is the subtraction between the
~i and p
~j . The alternative Pi is certainly prefertwo fuzzy numbers p
able to the alternative Pj if and only if Z ij is strictly positive.
~i p
~j ¼ p1i p3j ; p2i p2j ; p3i p1j
Z ij ¼ p
ð11Þ
4.2.6. Establishing the fuzzy preference relation matrix
If it is unclear whether Z ij is positive or negative, we define the
degree of preference eij of alternative Pi over alternative P j by a for
mula based on the membership function l ðxÞof Z ij . Subsequently,
Z ij
we construct the fuzzy preference relation matrix E ¼ eij nn .
2410
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
R
eij ¼ R
lZ ðxÞdx
ij
R
l ðxÞdx þ x<0 lZ ðxÞdx
x>0 Z
x>0
ij
with
R
x>0
12:
13:
14:
value
15:
16:
17:
18:
19:
20:
ð12Þ
ij
lZ ðxÞdx þ
R
x<0
ij
lZ ðxÞdx > 0
ij
If eij > 0:5, then alternative Pi is preferable to alternative P j .
Moreover, eij < 0:5 means that alternative Pj is preferential to alternative Pi . If eij ¼ 0:5, we cannot discriminate between the two
alternatives.
4.2.7. Constructing the fuzzy strict preference relation matrix
To overcome this flaw, we calculate the degree of strict dominance esij of alternative Pi over alternative Pj according to the degree
of preference eij . The fuzzy strict preference relation matrix is proh i
vided by Es ¼ esij
.
21:
22:
end for
23:
end for
24:
for each available parking space pi 2 Pi do
25:
for each available parking space pj 2 P i do
26:
if i ¼ j then
27:
eij 0:5
. Degree of preference between
pi and pj
28:
else if i > j then
29:
eij 1 eji
nn
esij ¼
eij eji ; eij P eji
0;
ð13Þ
Otherwise
4.2.8. Calculating the degree of non-nomination
The non-dominated degree lND ðPi Þ of each alternative P i is
given by a function of the degree of strict dominance esij as shown
in the following equation.
l ðPi Þ ¼ min
1
16j6n
ND
esij
¼1
j–i
maxesij
16j6m
end for
for each available parking space pi 2 Pi do
pr i 0
. Initialize the fuzzy evaluation
of alternative pi
for each criterion cu 2 C do
pr i pr i þ riu
end for
end for
for each available parking space pi 2 Pi do
for each available parking space pj¼iþ1 2 P i do
pr ij pr i pr j
. pr ij ¼ pr 1ij ; pr 2ij ; pr 3ij
else if pr 2ij < 0 then
30:
pr 3ij pr3ij
S1 31:
2 pr 3ij pr2ij
ð14Þ
32:
j–i
S2 4.2.9. Ranking alternatives regarding their suitability
Among all possible parking spaces, we select the one with the
highest non-dominated degree and remove it from the set of alternatives. We delete, consequently, the row and the column corresponding to this alternative in the fuzzy strict preference relation
matrix. Then, we recalculate the non-dominated degree for the rest
of the alternatives and repeat the last two instructions until the
dimension of this matrix is one.
The micro-assignment phase with its different steps described
above are synthesized in Algorithm 2.
pr 2ij pr 2ij þpr 1ij pr 1ij 2 pr2ij
2 pr 3ij þpr2ij pr2ij
þ
2 pr 2ij pr 1ij
33:
2 pr 3ij pr2ij
else
pr 1ij pr1ij
S2 34:
2 pr 2ij pr1ij
35:
S1 36:
pr 2ij pr 2ij þpr 3ij pr 3ij 2 pr2ij
2 pr 3ij pr 2ij
þ
2 pr 1ij þpr2ij pr2ij
2 pr 2ij pr1ij
1
eij S1SþS
2
37:
end if
38:
end for
39:
end for
40:
for each available parking space pi 2 P i do
41:
for each available parking space pj 2 P i do
42:
if eij > eji then
. Degree of strict
43:
esij eij eji
preference between pi and pj
44:
else
45:
esij 0
46:
end if
47:
end for
48:
end for
49:
k 0
50:
A VNi
51:
while A P 1 do
52:
for each available parking space pi 2 P i do
53:
Determine mi the highest degree of strict
dominance esij
54:
UNDi ¼ 1 mi
55:
end for
56:
Select the alternative ph with the highest UNDh
non-dominated degree
57:
Insert the alternative ph to position k in the ranking
for driver v ij of available spaces P ij
Algorithm 2 Micro-assignment
Input:
Let v ij 2 V i be a parking request assigned to zone zi 2 Z
Let pi 2 P i be an available parking space within zone zi
Let VNi be the number of available parking spaces in zone
zi
1: Evaluate the importance of criterion cu as decision-maker
dk
2: Aggregate the fuzzy weight wu of criterion cu
Output: Pij ranking for driver v ij of available spaces in
descending order of their degree of non-nomination
3: for each zone zi 2 Z do
4: for each request v ij 2 V i do
5:
Score alternative pi against criteria cu as decision
maker dk
6:
Aggregate the fuzzy rating xiu of alternative pi with
respect to criterion cu
7:
for each criterion cu 2 C do
8:
Determine the maximum mu of the largest possible
value of fuzzy ratings of alternatives
9:
for each available parking space pi 2 P i do
u
. Normalize the fuzzy rating of
10:
r iu xiumw
u
alternative pi
11:
end for
(continued on next page)
2411
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
58:
k k þ 1
59:
Delete the corresponding row and column of ph
from the fuzzy strict preference relation matrix
60:
A A 1
61:
end while
62: end for
63: end for
17: end for
18: for each time-sensitivity type t do
19:
for each request v ij 2 K it do
20:
for each place pijk 2 Pij do
21:
if pijk is not yet assigned to a driver then
. Assign space pijk to
22:
ASSijk pijk
driver v ij
23:
Sijk 1
. Change the status of pijk to
occupied
24:
Break
25:
end if
26:
end for
27:
end for
28: end for
29: end for
4.3. Phase 3: conflict handling
To avoid several drivers being assigned to the same space in an
area, the quantities of goods to be transported are classed according
to their heaviness and the parking spaces according to their degree
of non-domination. Moreover, the specific characteristics of goods
are taken into consideration. The freight is classified under three
modalities representing its time-sensitivity: non-sensitive (2), sensitive (1), very sensitive (0). Drivers are affected by decreasing timesensitivity of the goods they carry. For each freight category, the
driver carrying the heaviest quantity has priority to be assigned
to the best parking spot, the carrier delivering the second largest
quantity is assigned to the second-best spot, and so on. If two drivers convey the same quantity or they are private cars, the one having the smallest radius of influence is assigned first.
For this purpose, parking spaces are first sought for deliverymen
carrying first the most time-sensitive and then the heaviest goods.
Each parking request is characterized by a rank of available spaces,
from the most suitable to the least suitable, in the area to which it
is assigned. For each parking request, a check is performed to verify
if its parking space classed first is available, if so, it will be assigned
to this place. If not, the available spaces are searched until the first
best available space (according to the previously established rating) is found. This is the job of Algorithm 3 summarized in as
follows.
5. Simulation results
We simulate the assignment of 38 parking requests from 38 different carriers delivering 4 zones in the same time slot. At the time
of their arrival, there will be 5 available parking spaces in zone 1,
17 spaces in zone 2, 10 spaces in zone 3 and 13 spaces in zone 4.
Coordinates of parking spaces (Table 5) and store locations
(Table 6) are obtained from OpenStreetMap and Google Maps
(Google Places API).
5.1. Phase 1: macro-assignment
The first stage algorithm starts by calculating the distance (in
meters) between each parking space in an urban area and each driver’s destination (Table 7).
Taking into account the walking distance between the parking
space and the driver’s final destination, the following mapping
matrix (Table 8) is established. The distance between parking
space 1 in zone 2 and the destination of driver 3 (19,1597 m) is less
than its radius of influence (20 m), therefore the corresponding
coefficient is equal to 1. The distance between parking space 13
in zone 4 and the destination of driver 35 (37.2645 m) is greater
than its radius of influence (20 m), therefore the corresponding
coefficient is equal to 0.
Based on this matrix, the solicitation rate (Table 9) is calculated
as the number of requests that can be accommodated by an area
Algorithm 3 Conflict handling
Input:
Let v ij 2 V i be a parking request for zone zi 2 Z
Let K it be parking requests of time-sensitivity t in zone
zi 2 Z
Let Pij be a ranking for driver v ij of available spaces in
descending order of their degree of non-nomination
Output: ASSij assigned parking space to driver v ij
1: for each zone zi 2 Z do
2: Cluster parking requests V i by time-sensitivity type
3: Update K it
. to be a classification of requests
following the three modalities
4: end for
5: for each zone zi 2 Z do
6: for each time-sensitivity type t do
7:
Reorder parking requests K it in descending order
according to the amount of goods to be transported
8:
if v ij and v ik carrying the same quantity then
9:
Rank the driver with the smallest radius of influence
first
10:
end if
11:
Update K it
. to be a sorting of parking requests
12: end for
13: end for
14: for each zone zi 2 Z do
15: for each available parking space pijk 2 P ij do
. Initialize the status of pijk with
16:
Sijk 0
available
Table 5
Parking supply.
2412
Zone
Place
X
Y
1
1
...
5
33.5804733
...
33.5787562
7.6344472
...
7.6341231
2
1
2
...
16
17
33.5876577
33.5883381
...
33.5832514
33.5830743
7.6341124
7.637158
...
7.6346329
7.6348695
3
1
2
...
10
33.572046
33.5725151
...
33.5721193
7.6303607
7.6313245
...
7.6312312
4
1
...
12
13
33.5903378
...
33.5902204
33.5901671
7.6285974
...
7.6334884
7.6336776
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Table 6
Parking demand.
Request
X
Y
R
Quantity
1
2
3
...
18
19
20
...
35
36
37
38
33.5860906
33.5871949
33.5860382
...
33.5750402
33.5721729
33.5737448
...
33.5921199
33.591267
33.5929312
33.5927511
7.6359154
7.6381138
7.6351362
...
7.6354132
7.6332434
7.6351676
...
7.6305038
7.6287605
7.6286261
7.627597
25m
30m
20m
...
25m
30m
20m
...
20m
20m
25m
20m
280kg
135kg
440kg
...
72kg
0kg
300kg
...
230kg
180kg
100kg
190kg
Table 7
Distance between each parking space and each delivery destination.
1
1
2
3
4
5
6
...
22
23
24
25
...
35
36
37
38
2
3
4
1
...
5
1
...
17
1
...
10
1
...
13
58.060
76.566
56.073
52.089
51.113
50.433
...
76.511
84.443
86.638
97.327
...
122.960
122.001
137.508
140.595
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
75.502
93.347
73.521
69.457
68.433
67.898
...
59.170
67.819
70.206
81.372
...
138.451
136.116
152.035
154.417
23.888
40.280
19.159
29.577
31.253
24.474
...
146.272
151.288
152.779
161.496
...
57.387
64.552
76.098
82.700
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
31.924
52.445
29.758
26.353
25.621
24.087
...
102.685
109.862
111.849
121.969
...
100.440
102.196
116.678
121.049
151.031
170.176
147.846
145.430
144.568
142.588
...
21.649
9.306
8.154
11.737
...
200.744
192.875
209.571
208.887
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
147.356
165.723
144.563
141.558
140.618
139.175
...
14.313
9.963
11.804
20.282
...
200.138
193.064
209.743
209.494
84.612
100.219
78.257
89.293
90.866
82.019
...
175.625
175.287
175.617
180.775
...
26.096
9.434
25.935
26.124
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
46.503
53.3983
43.7896
53.0248
54.6859
49.4353
...
170.761
175.007
176.313
184.460
...
37.264
50.386
57.582
66.068
Table 8
Correspondence matrix.
1
1
2
3
4
5
6
...
22
23
24
25
...
35
36
37
38
2
3
4
1
...
5
1
...
17
1
...
10
1
...
13
0
0
0
0
0
0
...
0
0
0
0
...
0
0
0
0
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
0
0
0
0
0
0
...
0
0
0
0
...
0
0
0
0
1
0
1
1
0
1
...
0
0
0
0
...
0
0
0
0
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
0
0
0
1
1
1
...
0
0
0
0
...
0
0
0
0
0
0
0
0
0
0
...
1
1
1
1
...
0
0
0
0
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
0
0
0
0
0
0
...
1
1
1
1
...
0
0
0
0
0
0
0
0
0
0
...
0
0
0
0
...
0
1
0
0
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
0
0
0
0
0
0
...
0
0
0
0
...
0
0
0
0
Table 9
Solicitation rate for each zone.
Zone
Solicitation rate
1
24
2
88
3
81
4
53
appropriate areas of the city (Table 11). Demands 14 and 21 are
assigned first since they have a coverage rate equal to 1. Zone 1
is the first reception possibility that the algorithm checks because
of its minimum solicitation rate. Requests 29 and 30 are not
and the coverage rate (Table 10) is computed as the number of
areas that can accommodate a driver.
Considering these two metrics and the number of available
spaces in each zone, parking demands are assigned to the most
2413
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
Table 10
Coverage rate of each request.
Request
Coverage rate
1
3
2
3
...
...
7
2
8
11
9
9
18
14
21
38
15
7
20
31
17
1
19
35
16
2
25
37
3
3
...
...
14
1
15
4
...
...
16
8
36
8
37
6
38
4
Table 11
Parking requests assigned to each zone.
Zone
Number of available places
1
2
3
4
5
17
10
13
Parking requests
9
3
26
32
10
22
34
13
23
36
5
24
33
11
27
6
28
8
4
12
Table 12
Linguistic assessments for the eleven criteria.
Criteria
Decision makers assessments
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
D1
D2
D3
D4
VH
VH
VH
H
VH
VH
VH
H
H
VH
ML
VH
H
VH
H
VH
VH
VH
VH
H
VH
H
VH
H
VH
M
VH
VH
H
H
H
VH
ML
VH
VH
VH
MH
H
VH
VH
H
H
VH
M
0
0
B
B 0:02
B
S
E ¼B
B0
B
@0
0
affected because zone 3 (their corresponding zone) is completely
occupied.
5.2. Phase 2: micro-assignment
Demand 18 is assigned to zone 1, according to phase 1. A committee of four decision-makers D1, D2, D3 and D4 is responsible for
ranking the available parking spaces in this zone by their adequacy
to demand 18. They provide linguistic ratings for the five candidates under all criteria (Table 13) that are themselves linguistically
assessed (Table 12).
Based on Tables 12 and 13, the fuzzy weight for criteria
(Table 14) as well as the rating of alternatives regarding each criterion (Table 15) are computed and then aggregated.
Table 16 represents the normalized fuzzy decision matrix elaborated using Eqs. (8) and (9).
The weighted normalized ratings for each alternative and its
final fuzzy evaluation value are calculated by Eq. (10) and given
in Table 17.
The difference between each two final fuzzy evaluations separately are summarized in Table 18 and calculated as previously
explained.
The next two matrixes are fuzzy preference relation matrix E
0:5
0:49 0:55 0:53 0:57
1
C
0:08 0:16 C
C
0 0
0
0:06 C
C
C
0 0:02 0
0:08 A
0 0
0
0
0 0:1
ð16Þ
lND ðP1 Þ ¼ 1 0:02 ¼ 0:98
lND ðP2 Þ ¼ 1 0 ¼ 1
lND ðP3 Þ ¼ 1 0:1 ¼ 0:9
lND ðP4 Þ ¼ 1 0:08 ¼ 0:92
lND ðP5 Þ ¼ 1 0:16 ¼ 0:84
These values indicate that the alternative P2 has the highest
non-dominated degree. This is why it is deleted from the fuzzy
strict preference matrix and the new fuzzy strict preference matrix
is established.
0
0 0:1
0:06 0:14
B0 0
0
B
ES ¼ B
@ 0 0:02 0
1
C
B
0:55 0:54 0:58 C
B 0:51 0:5
C
B
B
E ¼ B 0:45 0:45 0:5
0:49 0:53 C
C
C
B
0:54 A
@ 0:47 0:46 0:51 0:5
0:06 0:14
The penultimate step of this phase corresponds to the calculation of the non-dominated degree of each alternative, the results
of which are as follows.
and fuzzy strict preference relation matrix ES constructed on the
basis of Eqs. (12) and (13).
0
0 0:1
0 0
ð15Þ
0
1
0:06 C
C
C
0:08 A
ð17Þ
0
Considering this new matrix, the new non-dominated degree
values are computed.
0:43 0:42 0:47 0:46 0:5
lND ðP1 Þ ¼ 1 0 ¼ 1
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Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Table 13
Linguistic assessments for alternatives.
Criteria
Alternatives
Decision makers assessments
D1
D2
D3
D4
C1
P1
P2
P3
P4
P5
VG
G
MP
VG
G
VG
MG
P
VG
G
G
G
P
VG
F
G
F
P
VG
G
C2
P1
P2
P3
P4
P5
G
F
VG
P
MG
G
F
VG
F
G
VG
F
VG
F
MG
G
F
VG
P
MG
C3
P1
P2
P3
P4
P5
VG
F
G
MP
G
VG
F
G
F
G
VG
G
G
MP
MG
VG
MG
F
MG
F
C4
P1
P2
P3
P4
P5
MP
G
MP
VG
F
MP
G
MG
VG
F
MP
G
F
G
G
MP
VG
G
VG
MP
C5
P1
P2
P3
P4
P5
G
VG
F
VG
G
G
VG
G
MG
VG
G
VG
F
G
MG
MG
G
F
G
F
C6
P1
P2
P3
P4
P5
G
MG
VG
G
F
MP
F
VG
VG
MG
P
F
G
G
F
F
F
VG
G
G
C7
P1
P2
P3
P4
P5
F
G
VG
G
P
F
G
VG
F
P
F
MG
G
F
MP
F
G
G
MG
MP
C8
P1
P2
P3
P4
P5
MG
VG
MG
G
VG
MG
VG
MG
G
G
G
VG
MG
G
VG
MG
G
G
G
VG
C9
P1
P2
P3
P4
P5
F
F
G
VG
F
G
F
G
VG
MG
G
G
G
G
MG
G
MG
VG
VG
F
C10
P1
P2
P3
P4
P5
G
VG
F
F
VG
G
VG
MG
F
G
VG
VG
MG
F
VG
G
VG
MP
F
VG
C11
P1
P2
P3
P4
P5
VG
F
G
MP
G
VG
F
G
P
G
VG
G
G
F
MG
VG
MG
F
VP
F
lND ðP3 Þ ¼ 1 0:1 ¼ 0:9
5.3. Phase 3: conflict handling
lND ðP4 Þ ¼ 1 0:06 ¼ 0:94
5 drivers are assigned to zone 1 containing 5 available parking
spaces. The parking spaces are classified according to their degree
of non-domination (output of the micro-assignment phase). The
goods transported by these conductors are not time-sensitive.
Therefore, only the quantity is used to settle disputes. Parking
requests are ranked by their heaviness. Requests 15, 17 and 18
have the same top-ranked place (place 5), so demand 17 is
assigned to place 5, 15 to place 4 and 18 to place 1 (Table 19).
lND ðP5 Þ ¼ 1 0:14 ¼ 0:86
The alternative P1 gets the highest non-dominated degree. We
delete it from the fuzzy strict preference matrix and repeat the last
two steps until getting the ranking order to the five alternatives
that is P2 > P 1 > P 4 > P 3 > P5 .
2415
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
Table 14
Aggregation of fuzzy weight for the 11 criteria.
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
~
w
Decision makers assessments
D1
D2
D3
D4
(9,10,10)
(9,10,10)
(9,10,10)
(7,9,10)
(9,10,10)
(9,10,10)
(9,10,10)
(7,9,10)
(7,9,10)
(9,10,10)
(1,3,5)
(9,10,10)
(7,9,10)
(9,10,10)
(7,9,10)
(9,10,10)
(9,10,10)
(9,10,10)
(9,10,10)
(7,9,10)
(9,10,10)
(7,9,10)
(9,10,10)
(7,9,10)
(9,10,10)
(3,5,7)
(9,10,10)
(9,10,10)
(7,9,10)
(7,9,10)
(7,9,10)
(9,10,10)
(1,3,5)
(9,10,10)
(9,10,10)
(9,10,10)
(5,7,9)
(7,9,10)
(9,10,10)
(9,10,10)
(7,9,10)
(7,9,10)
(9,10,10)
(3,5,7)
(9,10,10)
(7,9.5,10)
(9,10,10)
(3,7.5,10)
(7,9.75,10)
(9,10,10)
(7,9.75,10)
(7,9.25,10)
(7,9,10)
(9,10,10)
(1,5,10)
Table 15
Aggregation of fuzzy weights for alternatives.
Criteria
Alternatives
~
a
Decision makers assessments
D1
D2
D3
D4
C1
P1
P2
P3
P4
P5
(9,10,10)
(7,9,10)
(1,3,5)
(9,10,10)
(7,9,10)
(9,10,10)
(5,7,9)
(0,1,3)
(9,10,10)
(7,9,10)
(7,9,10)
(7,9,10)
(0,1,3)
(9,10,10)
(3,5,7)
(7,9,10)
(3,5,7)
(0,1,3)
(9,10,10)
(7,9,10)
(7,9.5,10)
(3,7.5,10)
(0,1.5,5)
(9,10,10)
(3,8,10)
C2
P1
P2
P3
P4
P5
(7,9,10)
(3,5,7)
(9,10,10)
(0,1,3)
(5,7,9)
(7,9,10)
(3,5,7)
(9,10,10)
(3,5,7)
(7,9,10)
(9,10,10)
(3,5,7)
(9,10,10)
(3,5,7)
(5,7,9)
(7,9,10)
(3,5,7)
(9,10,10)
(0,1,3)
(5,7,9)
(7,9.25,10)
(3,5,7)
(9,10,10)
(0,3,7)
(5,7.5,10)
C3
P1
P2
P3
P4
P5
(9,10,10)
(3,5,7)
(7,9,10)
(1,3,5)
(7,9,10)
(9,10,10)
(3,5,7)
(7,9,10)
(3,5,7)
(7,9,10)
(9,10,10)
(7,9,10)
(7,9,10)
(1,3,5)
(5,7,9)
(9,10,10)
(5,7,9)
(3,5,7)
(5,7,9)
(3,5,7)
(9,10,10)
(3,6.5,10)
(3,8,10)
(1,4.5,9)
(3,7.5,10)
C4
P1
P2
P3
P4
P5
(1,3,5)
(7,9,10)
(1,3,5)
(9,10,10)
(3,5,7)
(1,3,5)
(7,9,10)
(5,7,9)
(9,10,10)
(3,5,7)
(1,3,5)
(7,9,10)
(3,5,7)
(7,9,10)
(7,9,10)
(1,3,5)
(9,10,10)
(7,9,10)
(9,10,10)
(1,3,5)
(1,3,5)
(7,9.25,10)
(1,6,10)
(7,9.75,10)
(1,5.5,10)
C5
P1
P2
P3
P4
P5
(7,9,10)
(9,10,10)
(3,5,7)
(9,10,10)
(7,9,10)
(7,9,10)
(9,10,10)
(5,7,9)
(5,7,9)
(9,10,10)
(7,9,10)
(9,10,10)
(3,5,7)
(7,9,10)
(5,7,9)
(5,7,9)
(7,9,10)
(3,5,7)
(7,9,10)
(3,5,7)
(5,8.5,10)
(7,9.75,10)
(3,5.5,9)
(5,8.75,10)
(3,7.75,10)
C6
P1
P2
P3
P4
P5
(7,9,10)
(5,7,9)
(9,10,10)
(7,9,10)
(3,5,7)
(1,3,5)
(3,5,7)
(9,10,10)
(9,10,10)
(5,7,9)
(0,1,3)
(3,5,7)
(7,9,10)
(7,9,10)
(3,5,7)
(3,5,7)
(3,5,7)
(9,10,10)
(7,9,10)
(7,9,10)
(0,4.5,10)
(3,5.5,9)
(7,9.75,10)
(7,9.25,10)
(3,6.5,10)
C7
P1
P2
P3
P4
P5
(3,5,7)
(7,9,10)
(9,10,10)
(7,9,10)
(0,1,3)
(3,5,7)
(7,9,10)
(9,10,10)
(3,5,7)
(0,1,3)
(3,5,7)
(5,7,9)
(7,9,10)
(3,5,7)
(1,3,5)
(3,5,7)
(7,9,10)
(7,9,10)
(5,7,9)
(1,3,5)
(3,5,7)
(5,8.5,10)
(7,9.5,10)
(3,6.5,10)
(0,2,5)
C8
P1
P2
P3
P4
P5
(5,7,9)
(9,10,10)
(5,7,9)
(7,9,10)
(9,10,10)
(5,7,9)
(9,10,10)
(5,7,9)
(7,9,10)
(7,9,10)
(7,9,10)
(9,10,10)
(5,7,9)
(7,9,10)
(9,10,10)
(5,7,9)
(7,9,10)
(7,9,10)
(7,9,10)
(9,10,10)
(5,7.5,10)
(7,9.75,10)
(5,7.5,10)
(7,9,10)
(7,9.75,10)
C9
P1
P2
P3
P4
P5
(3,5,7)
(3,5,7)
(7,9,10)
(9,10,10)
(3,5,7)
(7,9,10)
(3,5,7)
(7,9,10)
(9,10,10)
(5,7,9)
(7,9,10)
(7,9,10)
(7,9,10)
(7,9,10)
(5,7,9)
(7,9,10)
(5,7,9)
(9,10,10)
(9,10,10)
(3,5,7)
(3,8,10)
(3,6.5,10)
(7,9.25,10)
(7,9.75,10)
(3,6,9)
C10
P1
P2
P3
P4
P5
(7,9,10)
(9,10,10)
(3,5,7)
(3,5,7)
(9,10,10)
(7,9,10)
(9,10,10)
(5,7,9)
(3,5,7)
(7,9,10)
(9,10,10)
(9,10,10)
(5,7,9)
(3,5,7)
(9,10,10)
(7,9,10)
(9,10,10)
(1,3,5)
(3,5,7)
(9,10,10)
(7,9.25,10)
(9,10,10)
(1,5.5,9)
(3,5,7)
(7,9.75,10)
C11
P1
P2
P3
P4
P5
(9,10,10)
(3,5,7)
(7,9,10)
(1,3,5)
(7,9,10)
(9,10,10)
(3,5,7)
(7,9,10)
(1,3,5)
(7,9,10)
(9,10,10)
(7,9,10)
(7,9,10)
(3,5,7)
(5,7,9)
(9,10,10)
(5,7,9)
(3,5,7)
(5,7,9)
(3,5,7)
(9,10,10)
(3,6.5,10)
(3,8,10)
(1,4.5,9)
(3,7.5,10)
2416
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Table 16
Normalized fuzzy decision matrix for alternatives.
Criteria
j
a
cj
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
0
0
1
1
3
0
0
5
3
1
1
10
10
10
10
10
10
10
10
10
10
10
Normalized ratings
P1
P2
P3
P4
P5
(0.7,0.95,1)
(0.7,0.925,1)
(0.9,1,1)
(0.1,0.3,0.5)
(0.5,0.85,1)
(0,0.45,1)
(0.3,0.5,0.7)
(0.5,0.75,1)
(0.3,0.8,1)
(0.7,0.925,1)
(0.9,1,1)
(0.3,0.75,1)
(0.3,0.5,0.7)
(0.3,0.65,1)
(0.7,0.925,1)
(0.7,0.975,1)
(0.3,0.55,0.9)
(0.5,0.85,1)
(0.7,0.975,1)
(0.3,0.65,1)
(0.9,1,1)
(0.3,0.65,1)
(0,0.15,0.5)
(0.9,1,1)
(0.3,0.8,1)
(0.1,0.6,1)
(0.3,0.55,0.9)
(0.7,0.975,1)
(0.7,0.95,1)
(0.5,0.75,1)
(0.7,0.925,1)
(0.1,0.55,0.9)
(0.3,0.8,1)
(0.9,1,1)
(0,0.3,0.7)
(0.1,0.45,0.9)
(0.7,0.975,1)
(0.5,0.875,1)
(0.7,0.925,1)
(0.3,0.65,1)
(0.7,0.9,1)
(0.7,0.975,1)
(0.3,0.5,0.7)
(0.1,0.45,0.9)
(0.3,0.8,1)
(0.5,0.75,1)
(0.3,0.75,1)
(0.1,0.55,1)
(0.3,0.775,1)
(0.3,0.65,1)
(0,0.2,0.5)
(0.7,0.975,1)
(0.3,0.6,0.9)
(0.7,0.975,1)
(0.3,0.75,1)
Table 17
Weighted normalized alternatives.
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
~i
p
Normalized ratings
P1
P2
P3
P4
P5
(6.3,9.5,10)
(4.9,8.7875,10)
(8.1,10,10)
(0.3,2.25,5)
(3.5,8.2875,10)
(0,4.5,10)
(2.1,4.875,7)
(3.5,6.9375,10)
(2.1,7.2,10)
(6.3,9.25,10)
(0.9,5,10)
(38,76.5875,102)
(2.7,7.5,10)
(2.1,4.75,7)
(2.7,6.5,10)
(2.1,6.937,10)
(4.9,9.506,10)
(2.7,5.5,9)
(3.5,8.287,10)
(4.9,9.018,10)
(2.1,5.85,10)
(8.1,10,10)
(0.3,3.25,10)
(36.1,77,106)
(0,1.5,5)
(6.3,9.5,10)
(2.7,8,10)
(0.3,4.5,10)
(2.1,5.3625,9)
(6.3,9.75,10)
(4.9,9.2625,10)
(3.5,6.9375,10)
(4.9,8.325,10)
(0.9,5.5,9)
(0.3,4,10)
(32.2,72.6375,103)
(8.1,10,10)
(0,2.85,7)
(0.9,4.5,9)
(2.1,7.3125,10)
(3.5,8.53125,10)
(6.3,9.25,10)
(2.1,6.3375,10)
(4.9,8.325,10)
(4.9,8.775,10)
(2.7,5,7)
(0.1,2.25,9)
(35.6,73.13125,102)
(2.7,8,10)
(3.5,7.125,10)
(2.7,7.5,10)
(0.3,4.125,10)
(2.1,7.55625,10)
(2.7,6.5,10)
(0,1.95,5)
(4.9,9.01875,10)
(2.1,5.4,9)
(6.3,9.75,10)
(0.3,3.75,10)
(27.6,70.675,104)
Evaluated scenario where our solution is deployed to manage
urban parking.
Table 18
Difference between two final fuzzy evaluations values.
p~1
p~1
p~2
p~2
p~3
p~2
p~3
p~3
p~5
p~5
(-68,-0.5125,65.9)
(-65,3.95,69.8)
(-66.9,4.4625,73.8)
(-67.9,6.425,78.4)
(-71.8,1.9625,75.4)
p~1
p~1
p~1
p~3
p~4
p~4
p~5
p~4
p~4
p~5
(-64,3.45625,66.4)
(-66,5.9125,74.4)
(-65.9,3.96875,70.4)
(-69.8,-0.49375,67.4)
(-68.4,2.45625,74.4)
In compliance with the outcome of the macro-assignment
phase, two drivers out of the thirty-eight will not be assigned during the required time slot and thereafter the satisfied demand rate
is 94.73684 %. On the other hand, if drivers are solely responsible
for finding a parking space, this performance indicator has a value
of 78.94737%. Our proposal thereby reduces the number of unsatisfied parking requests fourfold.
The total walking distance is calculated considering that drivers’
flexibility is zero, i.e. all drivers must park upon arrival and cannot
wait. It is equal for the reference scenario to 861 meters and for the
evaluated scenario to 544 meters. It is thus decreased thanks to our
solution by more than 300 meters.
Our approach is also compared to other related methods adopting the same performance measures. The demand satisfaction rate
reaches 60% in Mejri et al. (2013), 75% in Mejri et al. (2014) and
90% in Mejri et al. (2016) against 95% in our study. It is improved
by 16.7% with respect to the baseline scenario in Comi et al.
5.4. Performance evaluation
Our solution’s performance is evaluated by two metrics: satisfied demand rate defined as the ratio of assigned parking requests
to received ones and total walking distance given by the sum of
distances from the parking spaces to the delivery points.
Keeping the data described above, two scenarios are simulated:
A baseline scenario that represents the current situation in the
study area where drivers, by nature, park in the nearest space to
their destination;
Table 19
Parking space assigned to each request of zone 1.
Request
Quantity in kg
18
15
17
16
9
72
150
410
173
300
Ranking of parking spaces
5
5
5
3
2
4
4
4
2
3
2417
1
1
1
1
1
Place
3
3
3
4
4
2
2
2
5
5
1
4
5
3
2
H. Errousso, Jihane El Ouadi, El Arbi Abdellaoui Alaoui et al.
Journal of King Saud University – Computer and Information Sciences 34 (2022) 2405–2418
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by 10% with regard to the current situation in Muñuzuri et al.
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6. Conclusion
In this paper, we propose an urban parking management tool
that addresses problems encountered by drivers when looking
for a free parking space. It allocates available parking spaces to
all road users, with the aim to provide the most appropriate places
for deliverers without compromising the possibility of parking an
individual vehicle. It is centered on fuzzy theory and supplemented
by two algorithms, the first distributes parking requests over the
city’s zones and the second manages conflicts related to assigning
several drivers to the same place. It introduces transparent and
equitable rules for urban parking operations, contributes to mitigating their negative environmental effects and increases revenues
from private parking.
The proposed tool can be enhanced with algorithms for delivery
trip planning, dynamic city zoning (clustering of parking spaces
and shops according to their proximity) and time-dependent variable parking pricing. It can be incorporated into a decision-support
software for urban logistics management already used by municipalities. It may be rendered more efficient by exploiting information and communication technologies.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
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