20 10 evaluation of student dormitory design scheme by Topic _D, the national mathematical modeling competition of higher education club cup.

0 student dormitory design scheme evaluation

abstract

Key words:

First, the problem restatement and analysis:

Dormitory is related to the quality of life of students at school, which directly or indirectly affects their life, study and healthy growth. The design of the use area, layout and facilities of student dormitories should not only make students live comfortably, but also facilitate management. At the same time, the balance between costs and fees should be considered, which is also related to the region, location, cultural customs and economic development level of the city. Therefore, the design of student dormitory must consider the issues of economy, comfort and safety.

Economy is mainly affected by the following three aspects: construction cost, operating cost and charging standard;

Comfort is mainly affected by the following aspects: per capita area, convenient use, non-interference, lighting and ventilation;

Security is mainly affected by the following two aspects: the ability to evacuate people and the ability to guard against theft.

This paper aims to solve the following problems:

(1) This question requires a comprehensive quantitative analysis based on the four typical dormitory design schemes listed, analyzing and comparing the advantages and disadvantages of various dormitory schemes, and getting the weight of each influencing factor when choosing one of them. On the basis of synthesizing the national average selection level, the influencing factors of four design schemes are compared and scored, and their respective weight ratios are combined on the basis of evaluation scores, so as to evaluate a more general and economical scheme.

(2) Evaluate the characteristics (advantages and disadvantages) and applicable environment of these four typical student dormitory design schemes.

(3) According to the differences of economic development level, cultural customs and other factors in different regions of the country, the rationality of each design scheme is different in regional cities with different economic levels. We can choose three cities with different levels of economic development, then redistribute the weights of economy, comfort and safety, and analyze the preferences of these three cities in choosing dormitory design schemes.

Second, the basic assumptions:

1) Assume that the national average selection level is based on website survey data;

2) Assume that the economy, comfort and safety of four given design schemes only consider their direct and main influencing factors;

3) Assumption

Third, the symbol description:

: the rationality of the scheme, the objective function used to evaluate the rationality of the scheme ();

: the contribution weight of each influencing factor to rationality;

The influence of various influencing factors on the rationality of dormitory design scheme;

：

Fourth, the establishment and solution of the model:

The comprehensive quantitative comparison of dormitory design schemes mainly includes three aspects: economy, comfort and safety. Among the above three aspects, economy is mainly composed of three influencing factors, comfort is mainly composed of five influencing factors, and safety is mainly composed of two influencing factors. In order to evaluate the relative rationality of four dormitory design schemes, an objective function value is set, and the larger the value, the more reasonable the scheme is.

Because different dormitory design schemes have different choices for the above-mentioned different influencing factors, various factors have different contributions to the rational value. Set the contribution weight of each factor to rationality as:, so as to obtain the accurate rationality objective function for evaluating dormitory design scheme:

The weight values in the model are obtained by analytic hierarchy process (AHP), and the influence values of each influencing factor can be obtained by five-point scoring method with reference to drawings.

(1) When calculating the weight with AHP, the specific algorithm is as follows:

1) after carefully analyzing the relationship between the direct factors (economy, comfort and safety) that affect the rationality of dormitory design scheme, we have established the hierarchical structure of dormitory design scheme:

2) Compare the importance of each factor in the same level relative to a criterion in the previous level, and construct a comparative judgment matrix. In the process of constructing pairwise comparison judgment matrix, the importance is allocated according to the scale of 1 ~ 9.

For any standard, the judgment matrix can be obtained by comparing several compared elements in pairs:

One of them is the proportion of importance relative to.

3) According to the obtained judgment matrix, we use the "characteristic root method" to solve the ranking weight vector of the compared elements in the judgment matrix.

For this model, we think that economy is slightly more important than comfort, and economy is slightly more important than safety.

Safety is a little more important than comfort. According to the above analytic hierarchy process and the assignment of 1-9 scale, the judgment matrix and its corresponding eigenvalue, eigenvector and consistency index of the following levels are calculated by matlab software.

Meaning of scale

1 means that these two factors are as important as each other.

3 means that compared with two factors, one factor is slightly heavier than the other.

5 means that compared with two factors, one factor is more important than the other.

7 means that one factor is more important than the other.

9 means that one factor is more important than the other.

The median of two adjacent judgments above 2, 4, 4 and 8.

The judgment of reciprocity factor and comparison is the judgment of factor and comparison.

Table 1 Scaling method of judging matrix elements

( 1)

Table 1 destination layer judgment matrix

A B 1 B2 B3

B 1 1 3 2 0.5279

B2 1/3 1 1/3 0 1396

B3 1/2 3 1 0.3325

Maximum eigenvalue: =3.0536

Consistency index: = = 0.0268

Table 4 Random one-off indicators

1 2 3 4 5 6 7 8 9 10

0 0 0.58 0.90 1. 12 1.24 1.32 1.4 1 1.45 1.49

Random consistency index: =0.58 (see Table 4)

Consistency ratio: passed the consistency test

(2)

Table 2 Judgment Matrix of Standard Layer B 1

B 1 C 1 C2 C3

C 1 1 5 4 0.6833

C2 1/5 1 1/2 0 1 169

C3 1/4 2 1 0. 1998

Maximum eigenvalue: =3.0246

Consistency index: = 0.0 123

Random consistency index: =0.58 (see Table 4)

Consistency ratio: passed the consistency test

(3)

Table 3 Standard Layer B2 Judgment Matrix

B2 C4 C5 C6 C7 C8

C4 1 2 4 5 5 0 4375

C5 1/2 1 3 4 4 0.2855

C6 1/4 1/3 1 3 3 0. 145 1

C7 1/5 1/4 1/3 1 1 0.0660

c8 1/5 1/4 1/3 1 1 0.0660

Maximum eigenvalue: =5. 1399

Consistency indicator: =

Random consistency index: = 1. 12 (see table 4)

Consistency ratio: passed the consistency test

(4)

Table 4 Judgment Matrix of Standard Layer B3

B3 C9 C 10

C9 1 3 0.7500

c 10 1/3 1 0.2500

Maximum eigenvalue: =2

On this basis, all levels rank the total weights, and the results can be calculated in the following table:

Table 5 Comprehensive classification

C B B 1 B2 B3 total sorting weight

0.5279 0. 1396 0.3325

C 1 0.6833 0 0 0.3607

C2 0. 1 169 0.06 17

C3 0. 1998 0 0

C4 0 0.4375 0.06 1 1

C5 0 0.2855 0 0.0399

C6 0 0. 14565438

C7 0 0.0660 0 0.0092

C8 0 0.0660 0 0.0092

C9 0 0 0.75 0.2494

c 10 0 0.25 0.093 1

The test values of one-off indicators obtained by synthesizing (1) (2) (3) and (4) all meet the requirements, which shows that the weight vectors obtained above are reasonable.

(2) Calculate the values of each influencing factor in the above four design schemes by using the five-point scoring method, as shown in the following table:

Table 1: Scoring of four design schemes

factor

plan

Scheme I 5522115512

Option 2: 225453444

Option 3: 32434455444

Option 4 2 3 2 5 3 2 4 5 5

Using matlab software, the rationality of four design schemes is as follows:

3.0 130 ; 3.29 18; 3.4533 ; 3.36 19 ;

Because 3.4533 is the most reasonable degree among the four schemes, we think that the third scheme is relatively reasonable under the national average level. However, the final rationality of the four schemes is not much different, which shows that the above four design schemes are reasonable.

(2) Now we evaluate these four design schemes according to the proportion of economy, comfort and safety in the whole design scheme:

The proportional results are as follows:

Figure 2

Scheme 1: The scheme has the advantages of small building area, centralized facilities layout, large occupancy, low fees, good economy, poor comfort and poor safety, and is suitable for the environment with large population, economy and limited building area.

Scheme 2: The scheme has a large area, a large number of people and complete infrastructure, but it has high cost, serious waste of facilities, poor economy, good safety performance and comfort, and is suitable for the environment with a large number of people but high requirements for safety and comfort;

Scheme 3: The scheme has a large number of people, complete facilities and relatively concentrated layout, and the layout of stairs, balconies and public facilities is reasonable. Good economy, comfort and safety, suitable for the environment that comprehensively considers the requirements of the three;

Scheme 4: The scheme has the advantages of small number of people, relaxed accommodation environment, independent arrangement of living facilities, good safety, good comfort and poor economy, and is suitable for the environment with small number of people, large building area and high requirements for comfort and safety;

Evaluation and generalization of verb (verb's abbreviation) model;

(a) model assessment

The model compares and evaluates four dormitory design schemes on the basis of synthesizing the national average selection level.

Advantages: the model can clearly describe the weight of economy, comfort and safety in each design scheme, and can roughly analyze the position of the three performances in the scheme;

Disadvantages: Subjective factors have a great influence on the establishment and scale of the matrix, and it is impossible to accurately calculate the weights of the three main factors when studying the economy, comfort and safety of the design scheme.

(B) Model promotion

Table 6 Decision Matrix from Decision Level to Criterion Level

S 1 Shanghai Xi' an Wuhan

Shanghai11/51/30.1095

Xi 'an 5 1 20.5438+05

Wuhan 3 1/2 1 0.3090

Maximum eigenvalue: =3.007

Consistency indicator: =

Random consistency index: =0.58

Consistency ratio: passed the consistency test

Table 7 Decision Matrix from Decision Level to Criterion Level

S2 Shanghai Xi 'an Wuhan