Advances in Automatic Control

A principal component analysis and entropy value calculate method in SPSS for MDLAP model

ZIPENG ZHANG School of Management science and Engineering, Shandong Normal University, Jinan, China, HONGGUO WANG School of information science and Engineering, Shandong Normal University, Jinan, China [email protected]

Abstract:- In the analysis of MDLAP, this paper creatively combines the mathematical optimization model of cost-based multiple targets distribution location problem into a logistics location selection decision model with a multiple influencing factors, then put forward the method of data standardization processing, entropy weight, the method of principal component analysis and mathematical expressions to solve this model. Finally using SPSS statistical analysis software of the decision model are analyzed weighted linear regression method of influencing factors which based on entropy, similarity analysis system clustering method based on analysis of candidate services area, analysis effect comprehensive scoring factors of service area with factor analysis and principal component regression method , finally culminating in the service area of the 97 candidate in Shandong Province selected 10 service area of Weifang, Qingdao, Pingdu, Qufu as the optimal logistics center development area.

Keywords:-LAP; SPSS; location selection model; principal component regression method

1 Introduction global optimal location of logistics distribution center location scheme lead to the not ideal effect. [1] With the rapid development of China's economy and Logistics location allocation problem (LAP) the logistics and distribution business is more and can be traced back to the 1909 issue of Weber, it more increasing, the distribution center plays a first treat the LAP from a mathematical point of pivotal role in the logistics system. its main targets view, after nearly a century of development, its is that according to different customer requirements theory and application have been greatly enriched, which in the region to make the goods timely, the logistics location allocation problem has accurately and effectively delivered to the hands of produced a network location model(DLAP), a single customers, so the location problem of logistics period model (SLAP), uncapacitated multi stage distribution center is the core of logistics system model(UMLAP), multi product model(MPLAP), research, and has practical value to solve the above dynamic model (DLAP), probability model (PLAP)and multi-objective location model problem. domestic and foreign scholars have [3-5] conducted a lot of research, put forward many (MOLAP) , Most of the people research the location models, a large number of studies show uncapacity-limit single stage model to solve LAP up that, the logistics distribution center location to the present. problem is a multi-objective optimization problem At present，the study of expressway service area with complex constraints, belonging to the NP- hard to expand the function of logistics mainly focus on problem, therefore, the scholars proposed tabu the feasibility analysis and management research. [6] search algorithm, genetic algorithm and ant colony Ceng Zhaogeng (2008) points out that the algorithm and so on, these algorithms have achieved expressway service area in China will develop to 3 certain results ,but these algorithms are heuristic directions: change from rest function to the leisure search algorithm, when the scale is large, the function, part of the service area will become the searching speed of these algorithms is slow and easy logistics node, the expressway service area will to fall into local optimum, thus unable to obtain the become an important platform for commerce and

ISBN: 978-960-474-383-4 137 Advances in Automatic Control

trade circulation. Zheng Zhiping[7] (2011), Miu through the comprehensive evaluation for each [8] Guosheng (2011) analysis of Fujian, Shanghai, factor using SPSS statistical analysis. Nanjing expressway service area development advantages of modern logistics base, pointed out that the highway development of logistics has great 2 Description of the LAP Problem potential and puts forward the preliminary plan to introduction of LAP in logistics industry. Liu Ying[9] (2009) made Shandong Province as the 2.1 Definition of the LAP problem research object, analyzing the third party logistics In the basic LAP problem, there is a highway service area LAP feasibility study based on the network in the range of a certain area (Shandong development of internal relations between the province), we can know that the position of the expressway service area and the development of candidate logistics center (M) and logistics demand modern logistics industry, and put forward the (N) has been fixed, in order to provide finished strategic plan and strategy of LAP in Shandong products for the logistics demand with low cost, expressway service area. storage, transfer, processing, management and other These literature above discussed the services, the system requirement selects one or a development direction of expressway service area, plurality of logistics center from the candidate the feasibility and countermeasures for the logistics nodes. For example, there are 97 development of logistics LAP, in general can be expressway service area of expressway in Shandong summarized as "should do", but there was no answer province within the scope of their size, location, about "how to do", relates to the future under the condition, location and other characteristics are guidance of the theory of logistics function known for each service area, LAP problem demand expansion did not form, especially there are no to determine the number and location of logistics depth research in the expressway service area center in the service area according to the specific logistics function network under the condition of decision method. development of key technologies. In summary, the highway logistics function has some academic research papers but mostly feasible research and 2.2 Mathematical model of the LAP problem management to develop its logistics function, the literature of LAP in expressway service area The LAP problem of logistics nodes in the service logistics node is rarely, only Ge Xijun[10] (2006) area of Shandong province logistics network is analysis and discusses comprehensive evaluation mainly select multiple service representative as the method of alternative nodes by using the principal logistics node from Shandong province expressway component in expressway service LAP problem, service area within the 97 alternatives which based and use the qualitative analysis and quantitative on the total demand for logistics and transport costs, analysis method to discuss the level , location and so as to achieve the lowest total cost of logistics and function of the logistics node service areas. Qin transport in this area. As everyone knows, the goods Lu[11] (2007) applies the method above to the of transport diversity have various kinds, different logistics service area of expressway node partition types of goods have different distribution costs due to achieve good results in the angel of regional to its weight, volume, timeliness and portable logistics and the expressway service area degree caused by transportation, and in the previous integration. research papers, the most models and methods The paper put the reality Shandong province which based on the LRP questions put the total expressway traffic network topological structure as transportation cost and volume as the target, and the a starting point, and put the LAP problem of types of transport goods to the impact of the logistics nodes in a certain region as the target, distribution cost is no related. Based on this creatively combines the mathematical optimization consideration, this paper put up with a LAP model of cost-based multiple targets distribution optimization model which is close to the reality of location problem into a logistics location selection the classification in the position of that the candidate decision model with a multiple influencing factors, logistics center and logistics demand nodes is then put forward the method of data standardization known, without considering the transportation processing, entropy weight, the method of principal storage fee, management fee and transport cost and component analysis and mathematical expressions freight traffic is proportional to the distance. to solve this model. Finally gain the perfect result The model is as follows：

ISBN: 978-960-474-383-4 138 Advances in Automatic Control

l ll l ll ll （ ） MinC = []CXDQCXDQ'' '' '' ''+ ''' ''' QQ''≤ '' 3 ∑∑ ∑∑∑ ij ijk ij ij ' '' jik ji ' '' ∑∑∑∑ ij ij ''''''''∈∈ ji ji ''''''''∈ i∈∈ Giii G j ∈ G jl Lk N i∈∈ Giii G j ∈ G jlL ll ++H''(F SW ' ' Q ' ) QQ' ''≤ ' ' （4） ∑ j jc j jc j （1） ∑∑∑∑ ji i j '' ''''''''∈ jG∈ j i∈∈ Giii G j ∈ G jlL The formula (3) show that the total freight Table1 Symbol and definition in the algorithm volume of goods from the originating station to Symbol Definition logistics center less than transit goods from the originating station to the terminal; the formula (4) ' '' Gi ={ ii / = 1, 2 m } sets of city of vehicle starting nodes represents that the total freight volume of goods G''={ ii '' / '' = 1, 2 m } sets of city of vehicle finishing nodes from the logistics center to finishing node less than i transit goods from the originating station to the ' '' Gj ={ jj / =++ m 1, m 2 mp + } expressway service areas terminal. N ={k/ k = 1, 2 } the set of vehicles • Capacity constraints constraints. ≤ （ ） L={ ll / = 1,2,3,4 ⋅⋅⋅⋅⋅⋅l } Different types of goods ∑∑Qij''Q j ' 5 '''' iGjG∈∈jj Fjc building cost of the logistics center node The formula(5) above means that the capacity of Operating costs of the logistics center node Wjc logistics center can meet the demand of passenger l '' transportation cost of goods from starting rk. Cij l transit freight logistics netwo

node i' to finishing node j' l D '' transportation distance of goods l from ij 3 Realization of the Algorithm starting node i' to logistics node j' The reasonable methods of solving the logistics l LAP problem can save cost, speed up circulation '' transportation traffic of goods from Qij l efficiency of goods, increase social benefits. in the [12] starting node i' to logistics node j' LAP problem in expressway logistics network , in order to determine logistics centers from the l C transportation manage cost of goods l from candidate service areas, we often screening out ji' '' ' '' various influencing factors which associated with logistic node j to finishing nodei the LAP problem (including the subjective factors l [13] D ' '' transportation distance of goods l from and objective factors) according to the actual ji situation and logistics theory, finally obtained ideal ' '' logistic node j to finishing node i results of our through the comprehensive analysis Ql transportation traffic of goods l from logistic about the factors. ji' '' node j' to finishing node i'' 3.1 Collection for the decision data The related data of expressway service area in this S ' the scale of expressway service area j paper are not only taken from the authority of the

Q ' the maximum amount of transit goods of statistical yearbook and the official website, they are j also obtained through the full market investigation, ' logistics node j and this paper makes a rational analysis about the result which based on the actual data of candidate This is the constraints condition about the locations. It is the capital that the ideas of the survey mathematic model of the LAP problem. data analysis concerning the process of deciding on • Decision variables constraints. candidate service area in LAP problem that required cost data, at the same time the candidate service area economy, politics, population, resources, X''''≤∨ HX''' ≤ H （2） ijkjjikj environment and other data. All kinds of statistical We can know from the formula(2) that the data required for this paper mainly include the service area which was not selected for the logistics following aspects: center will not provide transit function for any • We gain the date of each candidate logistics transport service. center about the number of population, the state • Transport capacity constraints of the economy scale, the logistics demand,

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resources by statistical yearbook. same time make the existing statistical data • We can gain the information of Shandong analysis and processing, which can make the province expressway service area date, date which is used to evaluate is closer to the infrastructure, convenient transportation, toll LAP problem of logistics center, finally make station spacing, service area scale and function, the result more convincing. For example, in the the coverage of the candidate service area and decision-making index of the importance of the of distance information of candidate service service route, there is no direct data to display area from the main urban area through the the importance index, which index can only be official website (Shandong province obtained by statistical analysis the route transportation hall website, Shandong high information according to the shortest path speed group website) information between each pair of the cities. • We can also know the policy environment of To sum up, this paper selects 24 information of candidate logistics center, the degree of public expressway service area as the evaluation index approval, the government support and other from the Shandong Expressway Group, which are information from the government work report. shown in the following table 2: logistics center • In order to ensure data reliability and timeliness, location decision factors of Shandong Expressway this paper obtain information from the Group: authoritative statistical yearbook, it also at the table 2 Logistics center location decision factors of Shandong Expressway Group

NUM Candidate W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 Score 1 De’zhou 1915 16 2 10 6563 557 150 13000 10000 1 50 5.00 8.00 2 Xia’jin 1915 5 1 80 6563 557 200 6000 2000 0 40 1.00 7.00 3 De’nan 1915 16 3 30 6563 557 120 3826 4200 2 60 3.00 8.00 4 Gao’tang 1905 5 1 40 7131 579 200 9687 5600 1 80 3.00 7.00 5 Yu’cheng 1915 16 1 50 6563 557 180 12800 15000 1 50 3.00 8.00 6 Tian’qiao 4400 25 4 5 10705 681 120 15691 2625 1 100 7.00 8.00 7 Tai’an 2475 25 4 0 7018 549 130 11042 3625 2 60 7.00 8.00 8 Ning’yang 2475 30 3 40 7018 549 150 6170 5000 1 50 5.00 8.00 9 Qu’fu 2820 30 3 30 6431 808 350 9639 6350 2 50 5.00 8.00 10 Zou’cheng 2820 16 1 20 6431 808 80 5420 4168 1 50 4.00 7.00 11 Teng’zhou 1560 16 1 10 4243 373 100 6000 6000 1 60 4.00 8.00 12 Zao’zhuang 1560 16 3 0 4243 373 130 11000 8000 1 80 5.00 8.00 13 Xue’cheng 1560 16 1 5 4243 373 150 6800 3500 0 20 1.00 8.00 14 Cao’zhou 1440 16 2 20 4836 829 230 7000 3600 1 30 3.00 8.00 15 Zou’ping 3280 22 3 15 12119 453 90 6392 6500 2 60 7.00 8.00 16 Zi’bo 3280 22 4 0 12119 453 192 12000 9830 2 80 8.00 8.00 17 Qing’zhou 3600 42 3 20 11862 909 170 6789 6400 2 70 6.00 8.00 18 Fang’zi 3600 42 2 15 11862 909 246 5168 3800 1 80 4.00 8.00 19 Wei’fang 3600 42 5 0 11862 909 250 12000 12000 3 80 8.00 8.00 20 Gao’mi 3600 15 2 30 11862 909 80 5600 3000 1 30 2.00 8.00 21 Ping’du 4907 20 4 32 15802 697 278 11000 2000 3 30 7.00 7.00 22 Lai’xi 4907 15 3 38 15802 697 225 3054 500 2 30 6.00 7.00 23 Wen’deng 2203 6 2 20 6869 280 170 5000 2700 1 30 3.00 7.00 24 Qing’dao 6608 21 5 0 25371 872 164 16801 13000 1 100 9.00 8.00

In the above table of the decision factors the candidate service area, W9 represents the shows that: W1 represents the economy condition of turnover of the candidate service area, W10 the city which contain candidate service area, W2 represents the accessibility of the candidate service represents the importance of the route in candidate areas. W11 is the cost of transformation and services, W3 defines a influence index of candidate operation of service areas, at the same time the services area, and W4 describes the distance between development prospect of the logistics service area is a candidate service area and its adjacent city, W5 on behalf of W12, W13 describes the infrastructure in explains a index of logistics demand volume of the the service area. (. The data of W1, W5, W6 are regional area which candidate service areas in, W6 is obtained from the economic development situation the population index of city, W7 is the size of the of Shandong Province Statistical Yearbook and the candidate service area, W8 gives the gross area of government work report in 2011; data of W6, W7,

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W8, W11, W13 come from the statistical data which factors in statistics: when a statistical data of each belong to Shandong province transportation hall of evaluation object is larger, the smaller, entropy, official website, W2, W10 are collected from the which is said the information provided by the index expressway network and the dates of W3, W12 are is larger; when a statistical data of each evaluation obtained through investigation and statistics. object is smaller, the larger ,entropy, which describes the effective information index provide is smaller. When the difference between the data of a 3.2 Data standardization and its formula certain evaluation factor is little, entropy tends to there is no doubt that we often encounter a variety maximize the, show that the valid information of the of data types in the process of analysing about LAP index is very low, so we can remove such indicators problem, and the difference between the unit of from the decision model. measure for various statistical data will lead to the • Definition of entropy: final evaluation results for the convenience of 1 X HX= − i ln analysis, in order to make the perfect decision, we ii∑ (8) ln qXiq∈ ∑ i need put the various data model of analysis to be iq∈ normalized. The standard method used in this thesis • Definition of weight: is the standard method of maximum and minimum 1− H value, the following specific standardization WW=i , (0 ≤≤ W 1, = 1) i ii∑ (9) method: pH− ∑ i ip∈ • Positive index (large for optimal index) ip∈ processing method: where p is the number of index data, q is the number of decision-making object decision making ∗ XXi − min X i = (6) problem. XX− max min • Principal component analysis method: • Negative index (small is better index) **** XXXX−−ij processing method: 1 ( ij)( ) Rij = ∑ ∗ XXmax− i − X = (7) 1 qiq∈ SSij i − (10) XXmax min * ∑ X i Where Xi describes all kinds of index value for * * iq∈ the raw data, X I represents all kinds of data index X i = for the normalized value. q (11) * 2 * − 3.4 Determine the weight ∑( XXi i ) ∈ The concept of entropy is proposed by the German S = iq i − physicist Clausius in 1865, which is a function q 1 (12) description for the state of system. Value and This paper got all kinds of data which related to variation of entropy not only commonly carries to decision model of LAP by using Statistics - be used on the analysis and comparison. but also be description function based on SPSS software with used to calculate a disorder of one system. For the the mathematical methods, then itmakes a dates in the model of LAP , which still exist standardization to original data based on differences between each other even after mathematical expressions above. Like the following normalization. the concept of entropy is put forward table: to measure the difference between the same degree Table3 Normalized location factors in decision model of LAP N candidate X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 score 1 Dezhou 0.09 0.30 0.25 0.13 0.11 0.44 0.35 0.72 0.76 0.33 0.38 0.50 1.00 2 Xiajin 0.09 0.00 0.00 1.00 0.11 0.44 0.61 0.21 0.12 0.00 0.25 0.00 0.00 3 Denan 0.09 0.30 0.50 0.38 0.11 0.44 0.20 0.06 0.30 0.67 0.50 0.25 1.00 4 Gaotag 0.09 0.00 0.00 0.50 0.14 0.48 0.61 0.48 0.41 0.33 0.75 0.25 0.00 5 Yucheng 0.09 0.30 0.00 0.63 0.11 0.44 0.51 0.71 1.16 0.33 0.38 0.25 1.00 6 Tianqiao 0.57 0.54 0.75 0.06 0.31 0.64 0.20 0.92 0.17 0.33 1.00 0.75 1.00 7 Taian 0.20 0.54 0.75 0.00 0.13 0.43 0.25 0.58 0.25 0.67 0.50 0.75 1.00 8 Ningyang 0.20 0.68 0.50 0.50 0.13 0.43 0.35 0.23 0.36 0.33 0.38 0.50 1.00

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9 Qufu 0.27 0.68 0.50 0.38 0.10 0.84 1.36 0.48 0.47 0.67 0.38 0.50 1.00 10 Zoucheng 0.27 0.30 0.00 0.25 0.10 0.84 0.00 0.17 0.29 0.33 0.38 0.38 0.00 11 Tengzhou 0.02 0.30 0.00 0.13 0.00 0.15 0.10 0.21 0.44 0.33 0.50 0.38 1.00 12 Zaozhuang 0.02 0.30 0.50 0.00 0.00 0.15 0.25 0.58 0.60 0.33 0.75 0.50 1.00 13 Xuecheng 0.02 0.30 0.00 0.06 0.00 0.15 0.35 0.27 0.24 0.00 0.00 0.00 1.00 14 Caozhou 0.00 0.30 0.25 0.25 0.03 0.87 0.76 0.29 0.25 0.33 0.13 0.25 1.00 15 Zouping 0.36 0.46 0.50 0.19 0.37 0.28 0.05 0.24 0.48 0.67 0.50 0.75 1.00 16 Zibo 0.36 0.46 0.75 0.00 0.37 0.28 0.57 0.65 0.75 0.67 0.75 0.88 1.00 17 Qingzhou 0.42 1.00 0.50 0.25 0.36 1.00 0.45 0.27 0.47 0.67 0.63 0.63 1.00 18 Fangzi 0.42 1.00 0.25 0.19 0.36 1.00 0.84 0.15 0.26 0.33 0.75 0.38 1.00 19 Weifang 0.42 1.00 1.00 0.00 0.36 1.00 0.86 0.65 0.92 1.00 0.75 0.88 1.00 20 Gaomi 0.42 0.27 0.25 0.38 0.36 1.00 0.00 0.19 0.20 0.33 0.13 0.13 1.00 21 Pingdu 0.67 0.41 0.75 0.40 0.55 0.66 1.00 0.58 0.12 1.00 0.13 0.75 0.00 22 Laixi 0.67 0.27 0.50 0.48 0.55 0.66 0.73 0.00 0.00 0.67 0.13 0.63 0.00 23 Wendeng 0.15 0.03 0.25 0.25 0.12 0.00 0.45 0.14 0.18 0.33 0.13 0.25 0.00 24 Qingdao 1.00 0.43 1.00 0.00 1.00 0.94 0.42 1.00 1.00 0.33 1.00 1.00 1.00

4 Decision-making Model of LAP 4.1 Linear regression method in SPSS Method we first through data standardization will In the process of analysis about decision factors, we we were normalized in the location of decision- gradually found that the decision contents (each making related to the data in the model, in order to index of candidate service area) between each other meet the target established at the start of the chapter, have similar results because of the similarity factor that is finding the optimal logistics center in LAP data, so the index of 24 candidates are divided into problem, this paper use various methods based on several categories which have appropriate large- thought and layers of SPSS software to mine scale system clustering method in SPSS, that not effective information. only can reduce the analysis scale, but also make the differences of the index within the categories as 4.1 Linear regression method in SPSS small as possible, difference between categories is Take steps of “Analysis”—“Regression” –“Weight as large as possible. Corresponding analysis of the estimation” in SPSS software to calculate the weight operation as follows: • of influence factors X1, X2, X3……X13 by Step 1: Click the "analysis" -- "classification" -- mathematical expressions. "cluster • Step 2: Make The decision influence factor Table 4 Weight of influence factor "X1", "X2"...... "X12" be selected into Index Weight Index Weight "variables" list box.

X1 0.352 X8 0.119 • Step 3: Select the method: make the conversion

X 0.524 X 0.115 value standard for "Z score", select the button 2 9 X3 0.129 X10 0.893 below "case", "group". • Step 4: select 2-12 in clustering scheme s, X4 0.236 X11 0.265 determine the preservation. X 0.484 X 0.214 5 12 what the cluster number should we select is not X6 0.087 X13 0.923 determined before the above operation, so it will

X7 0.032 require the calculation of all the results of the 2to12 According to the concept of entropy weight, we class, analysis about the date as follows: it can be can clearly find that the value of factor X13 was seen from the chart that it can display good group significantly higher than the other influence factors, and difference group sex if the candidate are divided and close to 1, so this kind of influence factor index into 6,7 or 8categories. X13 from the 24 candidates have no difference, and the global information it contains was significantly less than the rest factors, thus the factors X13 can be 4.2 Comprehensive decision of LAP model listed as a weak correlation factor, and deleted, then 4.2.1Correlation factor decision factors W13 in table3 (red line) has been The method of factor analysis in SPSS software, to removed. be used to make the correlation variables divided into a fewer sets of variables which with high

ISBN: 978-960-474-383-4 142 Advances in Automatic Control

correlation in the same group, and low correlation in 2 1.90 17.29 61.27 1.90 17.29 61.27 different groups，makes all the original variables 3 1.15 10.46 71.74 1.15 10.46 71.74 can be instead by a few factors to solve the original 4 1.01 9.23 80.97 1.01 9.23 80.97 5 .76 6.94 87.91 .76 6.93 87.91 problem by reducing the number of variables 6 .43 3.96 91.87 It should be prove that there is a strong 7 .37 3.44 95.31 correlation between all variables before we apply 8 .20 2.27 97.58 the method of factor analysis to solve LAP problem. 9 .14 1.32 98.90 For example, the 12 variables of index are provided 10 .10 .92 99.82 in table 3 is not independent for each other, in order 11 .02 .17 100 to analysis of the relationship between the original the principal component analysis method variables, we should investigate the correlation between each other. This paper uses the correlation Table6 Component Matrix (Method: Principal Component Analysis) analysis in SPSS to discuss the correlation, and get Component the following variable correlation table below: 1 2 3 4 5 In order to facilitate the layout, this paper only X1 .781 .549 -.274 .123 -.003 discusses the correlation matrix of the first 8 results, X2 .648 .170 .252 -.589 -.168 which are visible that there is strong or weak X3 .891 .025 -.037 -.232 .198 positive correlation between these variables, that is X4 -.515 .409 -.023 .672 .181 to say the information between the above variables X5 .759 .283 -.090 .202 .050 are overlap X6 .490 .540 .082 .298 -.106 4.2.2Factor concentrate by SPSS X7 .253 .331 .554 .301 .331 In a decision problem, there are p decision hypothesis, decision sample in the index X8 .610 -.213 .547 .401 .226 T X9 .426 -.353 .507 .341 .050 ， data, X= ( xxx123,,,, xp ) is random variables X10 .642 .315 .284 -.694 .314 The common factor which the paper search is X11 .640 -.377 .003 .151 -.576 T ， X12 .922 -.116 -.058 -.191 .178 F= ( fff123,,,, fp ) then we can see factor analysis model as: Table 7 Component Score Coefficient Matrix

X1= aF 111 + aF 12 2 ++ a1mm F +ε 1 Component 1 2 3 4 5 X2= aF 21 1 + aF 22 2 ++ a2mm F +ε 2 （13）  X1 -.088 .460 -.087 -.047 -.049 X2 .109 -.238 -.039 .620 -.084 Xp= aF p11 + aF p 2 2 ++ apm F m +ε p X3 .310 .078 -.029 -.131 -.003

A = (aij ) is the loading matrix of the factor， X4 -.269 .169 .010 -.102 .427 X5 -.122 .477 -.028 -.107 -.015 aij describes the load factor ε is the special X6 -.293 .146 -.029 .593 .050 influence factors outside the factor (the actual analysis is negligible). X7 .111 -.122 .117 .009 .680 We can use regression estimation method to X8 -.076 .052 .445 -.205 .154 compute the mathematical model of factor scores X9 -.130 -.130 .498 .018 .177 after calculating the common factor, and then X10 .500 -.122 -.154 -.101 .208 evaluate the case by further calculating the factor X11 -.129 .005 .269 .215 -.217 scores. The formula of factor scores is: X12 .275 .078 .035 -.139 -.046

Fi= bX i11 + bX i 2 2 ++ bXin n ( i =1, 2, 3 m) (14) According to the step of "analysis", "reduction" From the table 5 we can see that the 12 original and "factor analysis", we can have the following factors can be summarized into five components table5: (factors), the cumulative percentage of the first component is 43.9% in the total data, second Table5 Total variance explained component is 17.3%, third, four or five components Extraction Sums of Squared Initial Eigenvalues of the proportion is respectively 10.5%, 9.2%, 6.9%. Loadings C That is to say the importance degree of first Total Variance% Cumulative Total Variance% Cumulative component in the five components is much larger. 1 4.83 43.98 43.98 4.84 43.98 43.98 The cover rate of the five components is 87.91% in

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all data, so we can determine that the principal X4, X10), the principal component Z5 as investment component analysis method have very ideal effect. and operation cost factors (X11). Combined with the component matrix data of 4.2.3To calculate the comprehensive scores table 6, factors of X3, X5, X12 score higher in the in this paper, from Table 7 we can gain the score first principal components, X1, X6 were higher in the coefficient matrix of various components, which can principal component 2, and X7, X8, X9 have high directly gain the main components of each five score in the main components of 3, at the same time expression , the expressions of first composition are X2, X4, X10 have high score in the components of 4, as follows: then X11 scores higher in the main composition of 5. FXXX1=++−+++0.150* 1234 0.125* 0.171* 0.099* X 0.146* X 5 0.094* X 6 So it can be classified the higher scores of factors 0.049*XX+ 0.117* ++ 0.082*X 0.124*X + 0.123*X + 0.178*X （15） into the corresponding principal component, which 7 8 9 10 11 12 It will automatically generate the five new make principal components of Z1 as the logistics influence factors (including X3, X5, X12), the variables like FAC1-1, FAC1-2 ……FAC4-5 principal component Z2 as the factor of economic and the index data of influence factor in the population (size X1, X6), the principal component Z3 mathematical model of 24 candidate service factor as scale of candidate service area (X7, X8, X9), area which based on five variables (principal the main composition of Z4 as convenience degree component) in SPSS software. of the traffic in candidate service area (including X2,

Table 7 Principal component analysis of the LRP model

num candidate Z1 Z2 Z3 Z4 Z5 score

1 Dezhou -.19310 -.23121 .43171 .51615 .35326 -0.18 2 Xiajin -1.70152 .87836 -.52923 1.77392 .46605 -0.46 3 Denan -.53884 .14081 .03075 -1.06185 .01839 -0.31 4 Gaotang -.74439 -.39378 .04199 1.31084 .39227 -0.24 5 Yucheng -.56428 -.89756 1.02267 2.32593 .63897 -0.04 6 Tianqiao 1.00307 -.90986 -1.10385 -.03176 -.67934 0.12 7 Taian .46523 -.61212 .17287 -1.60620 .33403 -0.01 8 Ningyang -.29266 .21194 .25602 -.34314 -.34767 -0.12 9 Qufu .34766 1.14313 2.17930 .61989 .59852 0.68 10 Zoucheng -.65233 .05567 -.70039 -.23620 -1.45890 -0.47 11 Tengzhou -.89195 -1.11230 .01205 -.83744 -.33264 -0.68 12 Zaozhuang -.16508 -1.83325 .36005 -.52998 .24491 -0.38 13 Xuecheng -1.47313 -.55258 -.04661 -.47863 -.27548 -0.81 14 caozhou -.75448 .63854 .91603 .11161 -.28017 -0.13 15 Zouping .30699 -.37888 -.78478 -1.24556 .30603 -0.11 16 Zibo 1.02575 -1.02600 .20725 -.39490 1.11374 0.34 17 Qingzhou .80867 .74105 .62835 -.34144 -1.64334 0.4 18 Fangzi .38277 1.01734 .73070 .26337 -2.34205 0.28 19 Weifang 1.89434 .09325 1.89190 -.24333 -.16831 1.01 20 Gaomi -.56723 .93155 -1.48281 .16544 -1.27883 -0.32 21 Pingdu .92539 1.80661 -.24507 -.31498 2.19353 0.82 22 Laixi .14267 2.09787 -1.27411 -.53466 .97137 0.31 23 Wendeng -1.11234 -.07635 -.57442 -.85497 1.28069 -0.55 24 qingdao 2.34878 -.73223 -2.14036 1.96791 -.10504 0.86

ISBN: 978-960-474-383-4 144 Advances in Automatic Control

official website of the acquisition as the foothold and starting point, and analyze logistics center location problem(MDLAP) in great detail of Shandong expressway through introducing standardized data processing, analysis of the entropy weight, the principal component method. This paper mainly make full used of the method of entropy weight regression, cluster analysis, factor analysis and principal component analysis which are the functions of data analysis of SPSS in SPSS to solve the MDLAP problem. The final decision location problem make 97 service area under the jurisdiction of Shandong Expressway Group in Shandong province as the research object, finally choose ten service area of Weifang, Qingdao, Pingdu, Qufu, East Laiwu, Tai'an West, Ji'nan, Jining, Yishui, Linyi North as the most suitable to expand the service area. Figure1

According to the principal component features References: charts in Table 4 and the component index value in [1]HU X, ZHANG Y, LI Z. The vehicle route Table 5 we use formula: comprehensive score equal scheduling location problem of multiple to principal components variance contribution distribution centers and its solution: An SPSS and rate*principal component coefficients. genetic algorithm based approach[J]. Logistics

Ri=0.43918* Z1 i + 0.17292* Z 2 i + 0.10467* ZZZ 345 iii ++ 0.9233* 0.6938* Technology, 2010, 1: 029. The specific steps as shown in above Figure1, it [2]Ross A, Jayaraman V. An evaluation of new will generate the comprehensive score of decision- heuristics for the location of cross-docks making in raw data generation, see table dotted line. distribution centers in supply chain network When we take the in descending order to the design[J]. Computers & Industrial Engineering, scores of the items, it is easily been found that the 2008, 55(1): 64-79. seven service area logistics center such as Weifang, [3]Hu X H, Lu C Z, Li M, et al. Mathematical modeling for selecting center locations for Qingdao, Pingdu, Qufu, Qingzhou, Zibo, Fangzi, medical and health supplies reserve in Hainan tianqiao are more satisfied the construction of Province[J]. Asian Pacific journal of tropical logistics transit demand in the 24 candidate service medicine, 2014, 7(2): 160-163 area. To make Weifang, Qingdao, Pingdu, Qufu [4]Yao-li Z. The Construction of Evaluation Index build into a logistics center is the most suitable, System of Logistics Service Quality in Online which covering the rest of the 20 service areas of the Shopping with Small B2C and C2C as site. we can take the method extend to 97 service Example[J]. Journal of Anhui Agricultural area of Shandong province, in addition to the above Sciences, 2013, 1: 177 four is out of the service area of East Laiwu, Tai'an [5]Gajšek B, Grzybowska K. A cross-county West, Ji'nan, Jining, Yishui, Linyi North can also be contextual comparison of the understanding of the selected as the alternative service area. term logistics platform in practice[J]. Research in Logistics & Production, 2013, 3 [6]Siller A B, Tompkins L. The big four: analyzing complex sample survey data using SAS®, 5 Conclusion SPSS®, STATA®, and SUDAAN®[C]//Proceedings of the Thirty-first In order to solve the logistics center location (LAP) Annual SAS® Users Group International problem, This paper puts forward a logistics center Conference. 2006: 26-29. location model (MDLAP) of expressway, which [7]Panda S, Padhy N P. Optimal location and based on the minimum transportation and cost, and controller design of STATCOM for power system use the multi factor decision method of location to stability improvement using PSO[J]. Journal of determine the location optimization problem into a the Franklin Institute, 2008, 345(2): 166-181. decision-making problem. in this paper, we take the [8]Holzbeierlein J M, Lopez-Corona E, Bochner B real data which from the statistical yearbook, the H, et al. Partial cystectomy: a contemporary

ISBN: 978-960-474-383-4 145 Advances in Automatic Control

review of the Memorial Sloan-Kettering Cancer Center experience and recommendations for patient selection[J]. The Journal of urology, 2004, 172(3): 878-881. [9]Jiang Z, Wang D. Model and algorithm of location optimization of distribution centers for B2C e-commerce[J]. Control and Decision, 2005, 20(10): 1125. [10]Ji S W, Huang T T, Zhang Y F. Study on Manufacturing Enterprises Distribution Center Location[J]. Advanced Materials Research, 2014, 834: 1938-1941. [11]Li Y, Liu X, Chen Y. Selection of logistics center location using Axiomatic Fuzzy Set and TOPSIS methodology in logistics management[J]. Expert Systems with Applications, 2011, 38(6): 7901- 7908. [12]Alizadeh B, Burkard R E. Uniform-cost inverse absolute and vertex center location problems with edge length variations on trees[J]. Discrete Applied Mathematics, 2011, 159(8): 706-716. [13]Sun W, Tao L. Cloud Logistics Mode-Based Location of Regional Logistics Distribution Center[J]. Bridges, 2014, 10: 9780784413159.360

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