=Paper=
{{Paper
|id=Vol-2843/shortpaper022
|storemode=property
|title=Decision making on the location of the shopping center in a large urban agglomeration (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2843/shortpaper022.pdf
|volume=Vol-2843
|authors=Ildus S. Rizaev,Elza G. Takhavova
}}
==Decision making on the location of the shopping center in a large urban agglomeration (short paper)==
https://ceur-ws.org/Vol-2843/shortpaper022.pdf
Decision making on the location of the shopping center in
a large urban agglomeration*
Ildus S. Rizaev and Elza G. Takhavova
Kazan National Research Technical University named after A.N.Tupolev–KAI, 10, K.Marx
str., Kazan, 420111, Russian Federation
isr4110@mail.ru
Abstract. The paper represents the approach to solve the problem to choose a
place for new commercial centers in large cities. The decision of this problem
depends on many factors and the task belongs to multi criterion problems. Be-
sides that, usually, when the task is stated, input data in this case often has
qualitative type. That is reason, which causes restriction for using classic
mathematical optimization methods. The method of analytical hierarchy analy-
sis is offered to solve the problem. The main stages of the offered approach are
described in the paper. The main information and necessary parameters are rep-
resented which the decision making process is based on. This approach is im-
plemented for the case when four sites were given to choose the best alterna-
tive. Forming estimations that are used to form recommendation are described.
The approach described may be used to solve site placing problem for different
new large objects in the city.
Keywords: Hierarchy Analysis, Criteria, Alternatives Importance Assessment.
1 Introduction
Nowadays modern cities are raising continually due to influx population from villages
and small towns. Large cities attract people with the opportunity to find work or im-
prove their living standards. As a result, to meet supply and demand for products it is
needed to build new shopping centers. To reach high efficiency when constructing
new shopping centers many factors should be taken into account [1-2].
Optimal placing of the commercial center is complicated problem when a wide set
of parameters have to be taken into consideration. It includes such factor as life level
of citizens, transport communications, location of concurrent, logistic etc. In general,
we get multi criteria problem. Analytical methods can be used to solve such problems.
Among them moving to some single global criterion may be used, for example, it may
be getting maximal income. The method of compromises or linear programming and
others may be implemented. However, their disadvantage is the inability to take into
*
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribu-
tion 4.0 International (CC BY 4.0).
account various factors, most of which cannot be represented by exact numerical val-
ues. A more appropriate approach in this case is the analytical hierarchy method us-
ing expert judgment [3-4].
2 Materials and methods
Usually, when a set of criterion and vagueness should be taken into account when
decision making, perspective methods are decomposition methods on the base hierar-
chies analysis and fuzzy logics. It is possible to propose such an approach, based not
on exact quantitative methods, but on the opinions of experts who use scales of pref-
erences when making decisions. This is a method for analyzing hierarchies [5-7].
The difficulty in analyzing the hierarchy lies in determining the weights to evaluate
the alternative solution. A pairwise comparison matrix is used in this case. If the
number of criteria at a given level of the hierarchy is n, the pairwise comparison ma-
trix C(nxn) is determined by the elements cij. The numbers from 1 to 9 are used to
represent the grades to assess the importance of the criteria number i relatively to
criteria number j. If the value of cij is equal to 1, it means that criteria number i and
criteria number j have equal importance. More the value of cij, more the importance of
criteria number i in comparison with criteria number j. If the value of cij is equal to 9,
it means that criteria number i is incomparably important in comparison with criteria
number j. Additional condition for element cij is following: if the value of cij is equal
to k, then the value of cji is equal to 1/k. In the general case, there can be several lev-
els of the hierarchy. At each level, the existence of an arbitrary number of criteria and
an arbitrary number of alternatives A1, ..., Ak is admissible. For clarity, a simpler
diagram is shown in Fig. 1.
Hierarchy analysis method assumes decomposition of general problem onto sim-
pler compounds. Hierarchy is being built beginning from setting general problem. The
next levels of the hierarchy goals and criterion are indicated and the lowest level is the
level of alternatives.
Fig. 1. Scheme of a hierarchy (Eij – hierarchy elements, Aj – alternatives).
Hierarchy analysis method assumes decomposition of general problem onto sim-
pler compounds. Hierarchy is being built beginning from setting general problem. The
next levels of the hierarchy goals and criterion are indicated and the lowest level is the
level of alternatives.
Analytic hierarchy method assumes in the given statement implementation of the
following stages [5; 8]. At the first stage, the problem is represented by the hierarchi-
cal structure with levels: goals – criterion - alternatives. The second stage lies in pair
comparison for the elements of every level taking in account the nature of elements of
the previous, higher level of according hierarchy. Comparative significance coeffi-
cients are shown in Table 1, using ten-point estimation scale.
Table 1. Comparative significance coefficients.
Level of significance Value of coefficient
Equal significance 1
Temperate superiority 3
Essential or strong superiority 5
Significant superiority 7
Absolute superiority 9
Thus, the coefficients cij (i,j=1,…,n, cij =1) are set to take into account the com-
parative significance of the criteria. Pair comparison matrix is formed which has the
inverse symmetry feature (1).
сij 1 / с ji (1)
Using cij the eigenvector for each criteria is calculated by means formula (2) and
(3).
n
d i cij i 1,..., n (2)
j 1
ki n d i i 1,..., n (3)
Importance coefficients are calculated using evaluated components of own vectors
for any comparison matrix for the according level of the hierarchy for criterion and
alternatives on formula (4).
k
i n i , i 1,..., n.
(4)
k
i 1
i
Results of these procedures are formed in tables. Under such conditions the consis-
tency of experts’ opinions should be checked.
Let, accordingly to Figure 1, for the first level of the hierarchy the weights p and q
assigned for elements E1 and E2, with conditions p≤1, q≤1, p+q=1. The weights for
the next level of the hierarchy are following: for E3 it is equal p1, for E4 it is p2 and
p1+p2=1. The weights for the level E4 is equal to q1, for E5 it is equal to q2 and
q1+q2=1. When choosing alternatives at the upper level, the criteria are taken into
account at the first level E1, E2 with weights p and q and at the next levels E3, E4 the
weights will be p1, p2. For the E5 and E6 the weight will be q1 and q2, The choice of
alternative A1 at the third lower level is set by the weights p31, p41, q51, q61, alter-
native A2 is set by the weights p32, p42, p52, p62 and alternative A3 - by p33, p43,
q53, q63. Then to choose the alternative the next expressions are used (5).
W ( A1) p( p1 p31 p 2 p 41) q (q1 q51 q 2 q 61)
W ( A2) p ( p1 p32 p 2 p 42) q (q1 q52 q 2 q 62) (5)
W ( A3) p ( p1 p33 p 2 p 43) q (q1 q53 q 2 q 63)
The alternative should be chosen is those that gets maximal weight W.
3 Results
The problem was stated to place a new commercial center, which must serve the set
of smaller seller. It is necessary to choose the appropriate place for the commercial
center. Let, the alternatives “А”, “В”, “С” and “D” are to be analyzed. The following
criterion and were chosen:
─ The medium of salary in the region (с1).
─ Having satisfactory transport communication (с2).
─ Having qualified labor resources (с3).
─ The presence of competitors (с4).
─ Close to warehouses (с5).
─ The volume of sales market (с6).
The goal is to choose the best alternative to place ырщззштп center that provides
the minimal expenditure for logistic under condition of optimal values of listed above
criterion. In this case, the hierarchical structure in Fig. 2 represents the problem. Table
2 shows results of evaluation given by experts.
The similar way is used to assess the results of comparison alternatives of pairs for
every criteria. Table 3 shows results for the criteria C1. Calculated results in Table 4
represent assessment of importance for alternatives
Assessment of alternative priority is calculated by means summarization of produc-
tion criteria importance and of alternative importance coefficient for each alternative.
Let, Wi is alternative priority, i=1,2,3,4.
Fig. 2. The scheme for the problem of choosing place for the shopping center.
Table 2. Evaluation for pair comparison of criteria.
Criteria C1 C2 C3 C4 C5 C6
C1 1 3 1 2 0.5 0.5
C2 0.3333 1 0.5 2 0.3333 0.3333
C3 1 2 1 0.5 0.25 0.1666,
C4 0.5 0.5 2 1 0.25 0.25
C5 2 3 4 4 1 1
C6 2 3 6 4 1 1
Table 3. Pair comparison assessment for criteria C1.
Alternative “A” “B” “C” “D”
Site “A” 1 0.2 0.25 0.1666
Site “B” 5 1 0.3333 0.5
Site “C” 8 3 3 2
Site “D” 6 2 0.5 1
Assessment of alternative priority is calculated by means summarization of produc-
tion criteria importance and of alternative importance coefficient for each alternative.
Let, Wi is alternative priority, i=1,2,3,4.
W1=0.148×4.7+0.797×40+0.814×40.6+0.776×58.2+0.2965×58.2+0.3167×53.2≈46;
W2=0.148×17.7+0.797×43+0.814×40.6+0.776×28.7+0.2965×29+0.3167×31.3≈30;
W3=0.148×48.7+0.797×5.4+0.814×4.9+0.776×5.2+0.2965×8.5+0.3167×6.1≈13;
W4=0.148×28.91+0.797×11.6+0.814×13.9+0.776×7.9+0.2965×4.2+0.3167×9.4≈11;
After evaluation sites “A”, “B”, “C”, and “D” the following results are obtained:
1. Site “А” - 46%;
2. Site “В” - 30%;
3. Site “С” - 13%;
4. Site “D” - 11%.
Therefore, from the view point of using combined criterion, the most appropriate
site to be recommended is site “A”.
Table 4. Evaluation of alternative importance according to criteria.
Criteria C1 C2 C3 C4 C5 C6
Importance 14.8 7.97 8.14 7.76 29.65 31.67
Site “A” 4.7 40 40.6 28.7 29 31.3
Site “B” 17.7 43 40.6 0.5 0.25 0.1666,
Site “C” 48.7 5.4 4.9 5.2 8.5 6.1
Site “D” 28.91 11.6 13.9 7.9 4.2 9.4
4 Discussion
As it is indicated in [1], an urban agglomeration is a compact arrangement of settle-
ments with industrial, transport and cultural links. Each shopping center has its own
service area. Usually, the following types of services take place: microdistrict, district,
regional, distinguished by their service area and availability. Studies of cities with a
million-plus population in the Russian Federation have shown that a number of cities
do not have a sufficient number of shopping centers, with low forms of trade. There
are cities with more developed trading floors. In any case, cities are growing and the
need to create new shopping centers always appears, and accordingly the problem of
location arises. The placement problem cannot be solved by a decree from above,
since an unsuccessful location can lead to unprofitability of the shopping center and,
accordingly, to large losses. Since this task is due to many dependent factors, then a
mathematical approach is required to solve it, the most acceptable is the method of
analyzing hierarchies. A similar approach has been used to choose the location of the
waste incineration plant in Kazan [9-10]. The approach described e can be used when
the construction of any major project: they may be construction of a new factory,
airport, stadium, etc. e construction of any major project: Construction of a new fac-
tory, airport, stadium, etc., etc.
5 Conclusion
The problem of placing new commercial centers in the city agglomeration has been
considered. Different factors, many of which are not exactly evaluated by quantitative
values, influence on decision. They are alternative sites to be available, transport
communication, solvency of the population and others. Moreover, the problem de-
mands considering not a single, but a set of criteria. To solve the stated problem ana-
lytical hierarchy analysis is implemented to choose the most appropriate alternative
between four possible sites. This approach is based on the opinion of experts and
doesn’t guarantee exactly optimal decision, but it provide quite acceptable choice.
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