developing statistical optimization models for urban

Research ArticleDeveloping Statistical Optimization Models for UrbanCompetitiveness Index Under the Boundaries ofEconophysics Approach

Cem Ccedilagrı Donmez 1 and Abdulkadir Atalan 12

1Department of Industrial Engineering Marmara University Istanbul Turkey2Department of Mechanical Engineering Bayburt University Bayburt Turkey

Correspondence should be addressed to Cem Ccedilagrı Donmez cemdonmezmarmaraedutr

Received 30 August 2019 Accepted 8 October 2019 Published 20 November 2019

Guest Editor Marco Locurcio

Copyright copy 2019 Cem Ccedilagrı Donmez and Abdulkadir Atalan is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

e purpose of this research was to establish the urban competitiveness index (UCI) by using the statistical optimization methodfor the econophysics approach With this technique economic data regarding urban areas and the factors aecting UCI have beendetermined e research covers 30 urban centres located in 15 countries worldwide Urban centres with the gross domesticproduct per capita of $10000 or more were taken into consideratione signicant levels of the factors were determined with thestatistical optimization method and optimum values were calculated with the developed optimization models Re-index valueswere calculated and compared with the results of PricewaterhouseCoopers andWorld Economic Forum According to the resultsthe high UCI value of these locations depends not only on economic data but also on high values of social factors us thoselocations are becoming the centre of attraction for investments and capital with increasing competitiveness

1 Introduction

During the last forty years new developments in the dy-namics of the urban system in physics the main incentivehas come from mathematicians and physicists mainlyadaptive cognitive systems in the economical perspectivewho started applying their models of emerging properties toengineering then to social sciences which would give aglobal framework for explaining systems dynamics in a widerange of elds of knowledge [1] Economic developmentresearch has been moving to data-driven approaches withinthe methodology of natural science statistical physics andcomplexity sciences [2ndash4] which makes it possible to in-troduce new metrics that surpass the traditional economicmeasures in revealing current economic status and pre-dicting future economic growth with applications to eco-nomic development [5 6] trading behaviour [7] poverty[8 9] inequality [10 11] unemployment [12 13] and in-dustrial structure [5 14] Economists and physicists havealso introduced a variety of nonmonetary metrics to

quantitatively assess the countryrsquos economic diversity andcompetitiveness by measuring intangible assets of the eco-nomic system [15 16] allowing for quantifying the econ-omiesrsquo hidden potential for future development [17 18] innear real time and at low cost [19]

Many economic methods have been used for the analysisof urban economy problems One of these methods is theeconophysics approach Econophysics was rst introducedin India as a word ldquoEconomicsrdquo and ldquoPhysicsrdquo a conferenceon statistical physics in 1995 [20 21] ldquoEconophysicsrdquo is anew discipline insusectciently rooted in economic theory andempirical observation Another peculiarity of new complexsystem theory is to focus on the emergence of properties at amacrolevel resulting from the interactions between indi-vidual behaviour at a microlevel [1] Although this termdeals with the relations between economics physicsmathematics and nance it basically takes into account theinteraction of theories of physics with the economy [20]is method which is generally recommended for macro-economics is intended to be used for microstructures of

HindawiComplexityVolume 2019 Article ID 4053970 11 pageshttpsdoiorg10115520194053970

financial markets Moreover it is seen that the econophysicsmethod is widely used by the statistical method as a result ofresearch studies because in the characteristic structures ofeconomics data financial time series leads to statisticalfeatures and empirical studies [22 23] In this research theeconophysics method was used for statistical physics toaddress urban competitiveness As a matter of fact the dataare measured locally rather than globally Additionallyeconomists and physicists have applied network and sta-tistical methods to reshape the understanding of in-ternational trade that the knowledge about exporting to adestination diffuses among related products and geographicneighbours [24] More recent works on econophysics andcomplexity are summarized by review papers [20 25 26]and books [20 27]

e processes of economic social and political changeconstantly affect the economic balance in the urban centresand reveal the necessity of renewing and planning them interms of competitiveness [28] Not only national changesbut the fact that they have centres that can govern them-selves accelerate and shape this need e European Union(EU) is at the forefront especially for the growing cities ofdeveloping countries to be at a competitive level Accordingto general belief urban areas with less uncertainty andimbalance in the economy are more competitive than othercities [29ndash31] is situation contributes to the rapid changeand development of the urban However it is seen that therapid changes of economic structures lead to uncertaintyand imbalance in the economies of urban areas and un-certainty and imbalance dominate in real economies [32]Within this information it is seen that the economic theoriesused are inadequate to account for sudden changes in theeconomy (fluctuations sudden movements in the parts andmobility in the capital markets etc) [33] e uncertaintyand imbalance of the fluctuations in the economy have led tothe emergence of new concepts and approaches But there isno specificmodel to reduce uncertainty and imbalance in theeconomy and there are only temporarily developed modelse main reason for this is that the economic structures arecomplex and the change in the economy is fast In such casesthe structures that form in the economies are transforminginto stochastic models on a statistical basis [21] In this workwe aimed to solve the problems of uncertainty and imbal-ance in the economy of urban areas by choosing the con-temporary method of the optimization statistical physictechniques to reach the concept of econophysics

Towards quantifying the complexity of a countryrsquoseconomy the pioneering attempt was made by Hidalgo andHausmann [16] who modelled the international trade flowsas ldquoCountry-Productrdquo networks and derived the EconomicComplexity Index (ECI) by characterizing the networkstructure through a set of linear iterative equations couplingthe diversity of a country (the number of products exportedby that country) and the ubiquity of a product (the numberof countries exporting that product) e intuition behindthis new branch of studies is that the cross-country incomedifferences can be explained by differences in economiccomplexity which is measured by the diversity of a countryrsquosldquocapabilitiesrdquo [15 16 19] the statistical properties of

financial markets have begun to apply physics conceptseconomically by attracting physicists [34] Econophysicistshave tried to use the theoretical approach of physical sta-tistics to understand empirical findings [35] Generallymany methods known in statistical physics have been ap-plied to characterize time evolution in stock prices andexchange rates [34] In the first examination econophysicscan be seen as wide physics models in the economy that ismore quantitative approach statistical models conceptsand calculation methods e macroscopic properties ofintrinsic microscopic interactions cause a complex system inthe economy At this point econophysics is associated withphysical complexity (complex structures) reducing un-certainty and imbalance in the economy [36] Immediatelyafter those studies described above Tacchella and researchcolleagues [37] developed a new statistical approach whichdefines a countryrsquos fitness and a productrsquos complexity by thefixed points of a set of nonlinear iterative equations [38]where the complexity of products is bounded by the fitnessof the less competitive countries exporting them FurtherCristelli and research colleagues [18] studied the hetero-geneous dynamics of economic complexity and found in thefitness-income plane strong explanatory power of economicdevelopment in the laminar regime and weak explanatorypower in the chaotic regime Based on this observation theyargued that regressions are inappropriate in dealing with thisheterogeneous scenario of economic development andfurther proposed a selective predictability scheme to predictthe evolution of countries Nevertheless these economiccomplexity indicators are not perfect for example ECIsuffers from criticisms on its self-consistency fitness de-pends on the dimension of the phase space of the hetero-geneous dynamics of economic complexity [17 18] and anew variant of the fitness method called minimal extremalmetric can perform even better for a noise-free dataset [39]Recently Mariani and research colleagues [40] quantita-tively compared the ability of ECI and fitness in rankingcountries and products and further investigated a general-ization of the ldquoFitness-Complexityrdquo metric

In general the uncertainty and imbalance in the econ-omy have been considered to be reduced by the Gaussian law[41] is approach is not enough to reduce uncertainty andimbalance in the economy is law is suitable for the use ineconomically viable microscopic models such as the prin-ciple of randomly proportional effect However with theapplication of microdimension models for the complexstructure of economies healthy results cannot be obtainedIn another study the econometric approach was taken asquantum statistics In this work entropy temperature freeenergy and the Hamiltonian concepts in probability theoryare integrated into the quantum statistical method formathematical financing [42] As a result the uncertainty ofthe phase transitions in mathematical finance has beenfound to depend on the temperature of the distributionalthough the precision of the mathematical financial data isnot known due to the uncertainty of the phase change Inorder to acquire a more tangible result in this statisticalanalysis optimization models with statistical physics havebeen used to obtain information about the competitiveness

2 Complexity

of urban areas and their future competitiveness us it isinevitable to take the econophysics approach with physicalstatistics e recent econophysical approach is that eco-nomic phenomena are related to statistical physics models[43]

Urban competitiveness structures are very difficult todelimitate e trading networks are evolving through timeFurthermore urban structures are open (the exchanges withtheir environment enable for instance the introduction oftechnical or social innovations) and are overlapping as anarticulation of interlocked networks [1] Understanding howeconomies develop to prosperity and figuring out the bestindicators that reveal the status of economic developmentare long-standing challenges in economics [13 44] whichhave far-reaching implications to practical applicationsTraditional macroeconomic indicators like gross domesticproduct (GDP) are widely applied to reveal the status ofeconomic development however calculating these eco-nomic census-based indicators is usually costly resourceconsuming and thus a long-time delay [45]

Other techniques have been used to create urbancompetitiveness index (UCI) besides the statistical physicsmethod e competitiveness index of four UK cities Bir-mingham Liverpool Glasgow and Belfast was establishedusing the Delphi method and analytic hierarchy process withthe multicriteria analysis method In order to assess theurban competitiveness with the method used city com-petitiveness was recommended to be strengthened andrenovated and synergies of business strategies were to beestablished [46] In support of this work the benefits ofurban renewal and change have been discussed through thecreation of new creative industries corporations and in-stitutions in the cities [47] Another study concerningmidsized French cities is aimed at increasing the competi-tiveness of the cities with both the efficient use of metro-politan assets and the resources of the land of the cities [48]One of the different approaches of the study of urbancompetitiveness has measured two factors for examining theurban competitiveness power of Malaysian cities which arethe diminished cultural life aspects of the cities and themarginalized flights to the economic suburbs [49]

On the basis of the studies made for urban competi-tiveness the most important factors affecting the urbaneconomy are considered by the national economy ereason behind this is that the current state of the globaleconomy and capital constraints are increasing the com-petition between them by putting pressure on the cities ofthe world [50] However when urban competitiveness ties tothe factors of the countryrsquos economy it creates a gap in itscompetitiveness [51] is is because the presence of newcompetitors and the variability of targets for cities are linkednot only to the countryrsquos factors but also to the internal andexternal factors For this reason citiesrsquo competitivenessneeds to be understood in terms of the strengths andweaknesses of the factors that affect their competitors Inorder to establish the UCI the econophysics approach hasbeen used considering the internal and external factors ofthe citiese key contribution of this research is to comparethe urban competitiveness of cities with how they are

positively affecting the social lives of the people as well ashow competitive the cities are in attracting investment andcapital to them

Urban competitiveness is structurally complex andmultidimensional and it differs depending on the variety offactors used in the developed methods [52] Generally thefactors derived from Eurostat [53] are taken into consid-eration in such studies However in the work done somerestrictions were applied to the selected cities For exampleSaez and Periantildeez [50] studied that the population of se-lected cities was more than 100000 us differences in thenumber and type of factors used in studies can correlate withthe methods used e number of factors and cities used inthe study varies from 1 to 199 [54ndash56] e cities werestudied with their per capita income which are thought to beinfluenced by urban competitiveness are 10000 dollars andmore are taken into consideration e generated UCI iscompared with the cities based on an artificial index

e main focus of this research is a comparison of howcompetitive big cities are in terms of locating and attractinginvestment Since urban competitiveness is a complexmultidimensional issue it is aimed to develop the UCI bydeveloping optimization statistical method for the econo-physics approach is work contributes to the literature inthe field of countries growing complexity and the UCI wasfirst explored by the econophysics approach in this research

is work consists of four main parts In Section 1 aliterature study was carried out by examining the econo-physics theory and UCI Section 2 underlines the importanceof the factors and responses that constitute the UCI De-velopment of optimization models for UCI is discussed inthis section e results of optimization models by statisticalanalysis for UCI and interpretations of this study arehandled in Section 3 Finally Section 4 includes conclusionsand future research

2 Methodology

21 Urban Competitiveness Factors Econophysics in urbaneconomy has been defined as a new discipline by usingstatistical physics methods on urban competitivenessproblems In this case urban economy with a complexstructure can be understood with a new approach theeconophysicse data obtained in the social economic andcultural fields constituting the urban economy have beeninterpreted by the econophysics approach e results ob-tained by the econophysics methodology are used to evaluatethe complexity of irregular forms and nowadays econo-mists are able to apply them in the field of UC up to urbandevelopment models

Urban economy is the biggest element that constitutesthe macro economy of a country In the structure of theregion where the urban economy is located work forceproductivity education etc are directly connected to thefactors e stability of the UCI depends not only on thesefactors but also on the macroeconomic structure of thecountry where the economy is located Cities which aremetropolises also bring urban competitiveness as they havelarge economies e strength of the economy of

Complexity 3

metropolitan cities depends on many elements In partic-ular urban areasrsquo commercial performance and productivityplay an important role in urban competitiveness because ofits contribution to the urban economy

A number of methods have been developed for themeasurement of UCI and these methods have been used asan indicator system and weight unit and UCI in general Inthe 2011-2012 Global Urban Competitiveness Report amodel of the UC output was created focusing only on theeconomic parameters of cities [57] e model is formulatedaccordingly and the result is achieved e economic sizeefficiency grade quality density and effect of cities aretaken into account in the form [58] For the World Bankthere are four key factors in the evaluation report on the UCwhich were highlighted economic structure human re-sources regional wealth and factors of institutional struc-ture UCI was created by giving some values to these factors[59] In order to calculate the urban competitiveness indicesof the four cities of United Kingdom investment financesocial capital improvement and useoccupantrsquos possibleand physical environment factors were determined esefactors are regarded as operational components in thatstudy Calculated factor scores did not capture any citysuperiority but some cities had the highest scores for certainfactors [46]

In another research nine different factors were con-sidered fewer than three main headings to form the UCIese factors are determined as transportation health basiceducation economy activities labor force higher educationbusiness sophistication knowledge society and informationsociety of the cities [50] As a result of the statistical analysisit was understood that the outcome in the infrastructure notin the singularities belong to these factors However theinadequacies of this study are that the factors should bestudied not as a group but as an interaction and singularityIt can be concluded the factors must be studied individuallyand interactively before the group is formed For examplethe factor ldquoardquo that affects the competence of urban com-petitiveness and the factor ldquobrdquo with little or no effect shouldbe considered as singular and they should be calculated assignificant or insignificant as a result of interactionsMoreover ignoring the elements of the economy from thefactors that influence a cityrsquos competitive power triggers theinadequate results to be achieved It is also said that a cityrsquoscompetitive power is inversely proportional to the economicdevelopment However this proposal does not find a sci-entific infrastructure Basically the fact that the economicactivity factor is statistically significant among the factorscogitated means that the relationship between urban com-petitiveness and the urban economy is strong

In this work 38 indicators were mentioned under sixmain factors (see Table 1) e data employed in this re-search cover the years of 2016 and 2017 [53 55 60 61] It wasdesigned to establish UCI by considering the factors that areexpressed statistically significant in previous studiese factthat there are different factors in one study suggests theexistence a complex structure for UCI and not a linear oneHaving said that it is possible to increase the numbers ofthese factors and indicators the mathematical optimization

model can be obtained and applied to becomemore complexand stochastic e analysis of this model will be very dif-ficult and time consuming resulting in having distance fromoptimum values Statistical analysis is to be maintained bydetermining factors that are important to reduce thiscomplexity and constitute many subunits as the target factorus in order to establish the UCI the econophysics ap-proach has been used by considering the internal and ex-ternal factors of the cities In this model population energyand environmental factors were ignorede study covers 30cities located in 15 countries worldwide In statisticalanalysis to be performed for each factor the gross domesticproduct per capita was used for 30 different cities over$10000 [60]

Table 1 Indicators of the affecting factors of UCI

Factors Indicators Notations

Education health andtraining

Education systemHigher education

Primary and secondarylevel

Information and knowledgesociety

Trained persons rateHealthcare infrastructure

Health policies

ET

Labor and transport

Old person employmentrate

Young person employmentrate

Female employment rateUnemployment rate

Transport infrastructureShipping transport variety

LT

Technology andindustry

Industrial structures andstandard

Technology infrastructureTechnological developmentInformation technologyProduction technology

TI

Market size

Company varietyProduct varietyMarket economy

Market growth rateSales cycles

Company earnings

MS

Product efficiency

Product varietyProduct quality

Product supply-demandlevel

Production speedCost of products

Product consumption timeEasy-to-carry

Product type (portability)

PE

Financial service

Stability of financial systemFinancial development

Bank indexCurrency and credit

Investment convenienceCapital rate

FS

4 Complexity

22 Urban Competitiveness Response Variables Variations inthe economic environmental and social structures areevident in determining urban competitiveness factors Inthis context the urban competitiveness levels of the analysesin the scientific literature are still being modelled From aresearcherrsquos point of view a city can be artificially measuredaccording to its competitive power using different methodsand theoretical models Advantages and disadvantages ofeach method for urban competitiveness are stated and theyconsequently contribute to finding the most reliable system

In this probe a number of ways have been identifiedin determining the factors affecting urban competitive-ness and the affected responses Researchers working onurban competitiveness assume that factors are more di-rectly influenced by the UCI value When computing theUCI value they referred to the values attributed to thefactors and the formation of an artificial index e in-dexes formed in some research are calculated accordingto the Nash theory and Freudenberg method In suchacademic work the relative weights of the indicatorsresulting from the weighting of the factors have beencalculated In other words weighting calculations aremade according to the weight of each indicator to obtainrelative weights

In another case study UCI values were calculated byusing a closed formulation method by giving a certain rangeof values to the factors and comparing the competitivenessof the cities For example in the global competitivenessreport prepared by Ni in 2014 factors were evaluated be-tween 1 and 7 Subsequently the urban competitivenesslatent formula consisting of six different factors was ob-tained [57] In the competitiveness index developed for the24 cities of Lithuania the steps and basic characteristics ofthe composite index were used to measure urban compet-itiveness [62] Similarly the urban competitiveness forces of23 US cities were measured by statistical analysis taking intoaccount only 3 different factors [63]

When we measure the urban competitiveness in ourperspective it is thought that the factors indirectly affect theUCI value not directly e reason for this is that there aresome responses that these factors influence We think thatUCI values will be formed in the direction of the resultsobtained from these responses ere are two main re-sponses to this study ese are the gross domestic product(UGDP) and the gross domestic product per capita (UGDP-PC) of the urban areas considered for the UCI e reasonfor taking these responses into consideration is the com-petitiveness of the cities and the measurement of the cities bytheir economic growth Some researchers have consideredthese responses as factors for the strength of urban com-petitiveness ey have even argued that the economicgrowth of cities and the strength of urban competitivenessare directly proportional [64 65]

23 Development of Optimization Models for UCI e areasof use of mathematical optimization models vary Inparticular these models are used to solve the problems thatcost and benefit dilemmas are taken into consideration

Mathematical modelling is carried out with the aim ofreducing the cost and maximizing the benefits In thisstudy statistical analysis of the mathematical model wasperformed ere are three basic things that make upmathematical models In a mathematical model the ob-jective function constraints and decision-variable signsare considered ere are three stages in the mathematicalmodel created in this study In the first step the equationsobtained as a result of statistical analysis are considered asobjective functionse next step is to obtain the data fromthe lower and upper limits that constitute the constraintse fact that the index values used for the factors aregreater than zero causes the decision variables to be greaterthan zero In the optimization model developed for thisstudy the values of the decision variables will be greaterthan zero

As a final step the optimal values required for a city tohave competitiveness have been calculated A desirabilityfunction was developed to compute UCI scores of cities forthe comparative outcome of the previous urban competi-tiveness index rough these functions comparisons ofcompetitiveness of cities were made

Attention should be paid to the desirability value whenachieving optimum results Before constructing the op-timization models it is necessary to consider the functionof desirability according to the results to be obtained as aresult of statistical analysis e factors affecting the re-sponse function directly affect the desirability function[66] In short it is desirable that the factors affecting themain response values are at the desired values is ismeasured by the value of desirability e best result isobtained as this value goes from zero to one when cal-culating desirability

To find n factorsrsquo values the function of each responsevalue is expressed as

yi fi x1 x2 xk( 1113857 i 1 2 n (1)

e desirability function is specified as

di di yi( 1113857 di yi(x)( 1113857 (2)

where d(y) takes a value between 0 and 1 If di(yi) 1 thisis the desired best value [67 68] but if di(yi) 0 it is theworst and undesirable value

General desirability is expressed as follows

di yi( 1113857 yi minus li

ui minus li1113888 1113889

wi

li leyi le ui (3)

where li and ui are the lower and upper specification limit ofthe responses the power wi corresponds to the weightedfactor and wi is the parameter that determines the shape ofdi(yi) ere are three purposes for the value of desirabilityese are maximum minimum and target values in theobjective function In this study formula (4) was consideredin order to achieve maximum values of the objectivefunctions ere are three different conditions for each ofthese three situations

For maximization problems the desirability functionsare

Complexity 5

dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

For minimization problems the desirability function is

dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)

For target the desirability function is

dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

0 if yi le l andyi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

At the same time for these three cases nominal the best(NTB) for the target smaller the better (STB) for theminimum and larger the better (LTB) for the maximumconditions are defined in previous research studies [69] eoverall desirability function equation to be obtained byconsidering these three conditions is calculated by thegeometric mean (see equation (7)) e use of the geometricmean is due to the fact that more than one dimensionlessindividual desirability scales arisee individual desirabilityscales are merely a whole using a geometric mean andmerges them into one desirability

d d1 lowast d2 lowast d3 lowast lowastdn( 11138571n

(7)

e overall desirability function includes the upper andlower bound values of the factors that have an effect on theresponse UCI was created separately for each factor UCIformula was obtained by geometric mean of these factors

e parameters analyzed as a result of statistical analysiswere global-based so as to construct the UCI

UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)

where UCI is the urban competitiveness index c1 is theregression constant c2 is the normalization constantpi and k are competitiveness parameters rk is the regressionmultiplier UDGPi is the gross domestic product of urbanand (UDGP PC)i is the gross domestic product per capita ofurban

In this investigation optimal UCI for each urban areaneeds to be established in order for cities to have competitivepower Contemplating two objective functions it was aimedto maximize the urban competitiveness of cities Both op-timization models contain the same constraints For thecalculation of GDP belonging to the urban area (closedformula)

maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)

Optimization equation of the UGDP-PC (closed formula)maximize UGDPPCi

subject to

llexj

xj le u

0lexj

(11)

With this objective function the two response variablesare reduced to a single form us whichever response ismaximum is the optimum value for UCI e optimizationmodel that maximizes the urban competitiveness index isformulated as follows

maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPPCi( 1113857 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦ge xij 0lexij

(12)

6 Complexity

where the lower limit score ldquo lijrdquo and the upper limit scoreldquouijrdquo notations are used xij is the competitiveness parametertype (j ET L T MS G F)yi (the first year of data use)and yf (the last year of data use) are symbolizations thatindicate which data match the function

3 Results of Optimization Models by StatisticalAnalysis for UCI

e calculation of the UCI is based on the data of the GDPand GDPPC of the countries they are affiliated with is isbecause taking the factors that affect the power of UCI on acountry basis has a more accurate result e results ofstatistical analysis for UCI indicate that the determination offactors and responses is consistent in the general sense Somechanges and arrangements have been made on the writing ofthe article eMinitab statistical analysis program was usedfor analysis of variance test of data in this research

According to Table 2 it is understood that all the factorsare effective on the UGDP and these factors are meaningfullysignificant In addition the significance values of the factorsare considered to be effective on UGDP-PC From thesefactors only the effect of the ET and FS is less pronounced

Firstly Figure 1 shows how the UGDP-PC is affected by thefactors It is stated that the education factor is a constant effectand that the increase of product productivity especially affectsthe negative direction e line consisting of grey points showsthe average values of UGDP-PC and UGDP in Figures 1 and 2

Figure 2 shows how the UGDP is affected by the pa-rameters As the scores of education employment and fi-nancial factors increase after a certain point the UGDPtends to be negative It is observed that the level of economythe size of the market and the productivity of the productincreased the level of economy of the urban area

In order to have the competitiveness power of the citiesthe factors must have optimum values as in Figure 3 In thisfigure which gives the optimum values it is assumed thatthe parabolic impression of the curves belonging to thefactors has more than one objective function In such casesimproved optimization models are also defined as multi-objective optimization models e reason for the parabolicview is that if one factor takes the maximum value for oneobjective function the other has the minimum value for theobjective function In this case it is difficult for the de-sirability value to be achieved at the optimum level Inaddition the optimization models established in this studyshow that the curves are stochastic as being parabolic ereason for being stochastic is that the next step is unknown(steady state) A stochastic model was observed on the graphand the parabola was observed

According to the optimization models the best results forthe UGDP and UGDP-PC are given in Table 3 e grey areashown in Figure 3 varies with the values taken by the factors Itshows the values that can be taken in the feasible set or area ofobjective functions of decreasing or increasing this field egrey regions represent the settings in which the correspondingresponse variable has a low value or even zero desirabilityMore feasible space (white region) was formed for the UGDPvalue while the grey area in GDPPC was higher e upper

and lower limits of the grey areas depend on the lower andupper limits of the constraints In the direction of optimumresults the UCI power will increase only if the urban averageUGDP-PC is less than $5052350 and the size of the UGDP isover $419 million ese results reveal an urban area needs toapproach these values to compete with other urban areas ineconomic and social areas

Considering the optimum values of the data newcompetitiveness indexes of the cities are established asshown in Table 4 e components of urban structure withthe econophysics approach index (EI) are clearly observedapplied in the emerging UCI research which affects the UCIespecially the human factor e indexes calculated bystatistical physics approach of econophysics for each urbanwere compared with 3 different sources PwC indexesconsidered the economic structures of cities while UN-Habitat data have considered both the economic structureand sustainable development of cities In the study con-ducted for UN-Habitat indexes have been formed in twodifferent areas considering the economic dimensions andsustainable developments of cities In addition to the eco-nomic dimensions of cities biodiversity urban mobilitytechnological structures and urban planning methodswhich constitute the substructure of cities are considered tocreate indexes for cities In our study an index for each citywas created by combining both fields in one area

According to the comparisonmade with UCI it has beendetermined that the method we have developed has a limitedvariation in some cities In cities where changes are ex-cessive some factors are due to low index values belongingto developing countries In general the best results withinthe scope of UCI are spotted in cities for example inEurope Far East Countries and the United States in termsof attractiveness for investment As expected top seats areoccupied by ldquoglobal citiesrdquo Tokyo Madrid Paris OsakaLondon Seoul and New York ese cities are majoreconomic centres and also have significant economicleadership positions around the world Tokyo New YorkLos Angeles London Osaka Paris Washington DC SeoulMadrid and Philadelphia are among the top 10 cities is

Table 2 e analysis of variance test for UGDP and UGDP-PC

Factors Samplesize

UGDP UGDP-PCProb Status Prob Status

ET 300 0011lowast Sig(plt 005) 0995 Not sig

L 300 0003lowastlowast Sig(plt 001) 0007lowastlowast Sig

(plt 001)

T 290 0001lowastlowast Sig(plt 001) 0000lowastlowast Sig

(plt 001)

MS 300 0049lowast Sig(plt 005) 0015lowast Sig

(plt 005)

G 300 0010lowast Sig(plt 005) 0002lowastlowast Sig

(plt 001)

F 280 0000lowastlowast Sig(plt 001) 0397 Not sig

Note lowastlowastplt 001 and lowastp valuelt 005 are significant factors respectivelyotherwise insignificant

Complexity 7

indicates the potential for being economically strong at-tractive and competitive cities for international investmentIn terms of having the index of competitiveness power the

city of Buenos Aires has the lowest competitiveness whilethe city with the highest competitiveness power was definedas Paris

ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030

Figure 1 e main effects of factors for UGDP-PC

ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030

Figure 2 e main effects of factors for UGDP

HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924

Compositedesirability

D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860

Figure 3 e optimum values of both response variables

8 Complexity

4 Conclusions and Future Research

e statistical physics of the econophysics method wasshown as an important approach for UCI in this study isis the first time that the power of UCI has been linked to thesocial and economic factors with the application of statisticalphysics of the econophysics method In order to establish theUCI human industry and technology factors have to betaken into consideration in the economic parameters of theurban area In this research the level of education of peopleurban technology size of urban market and urban eco-nomic development have been statistically evaluated ereason for dealing with factors other than economic factors

is that they are uniquely positioned to provide dynamicenvironments in which the cities operate In addition thevast urban areas of the world are sources of basic knowledgeand innovation is makes them central to the globalizingworld economy However this globalizing context meansincreasing competition between cities in order to secure thelimited resources available

e fact that the factors that are considered to influenceUCI are in large numbers triggers the artificial level of themethods to be developed e main reason for the display ofthe cityrsquos competitive talents is that it makes it attractive forinvestment and capital Most of the work done for urbanregeneration is at the regional level resulting in the weak-ening of the competitiveness of those cities as a result ofglobal changes In this work competitive indexes of big citiesin the world were created e limitation of the factors takeninto consideration is based on the previous studies How-ever among these factors the UCI was formed by ignoringthe political structures of the countries and therefore reg-ulations and laws But it should be noted that the com-petitiveness of the countries is the effect of social andpolitical structures

ere are differences in the results when we take intoconsideration the data of the UCI obtained by the newmethod (econophysical approach method) that we havechosen in this study according to the report of the WorldEconomic Forum in 2014 and PricewaterhouseCoopers(PwC) under the UC report It is evident that the uncertaintyand imbalance in the economies are less in the cities whereUCI is high At the same time it is foreseen that with thisapproach the high index of UC will be strong in futureeconomies At the same time with the use of this approachit is predicted that the future economies of the cities will bestrong by having a high UC index

Nevertheless the fact that the UCI is low can be said tobe a negative one in terms of the economy of the urban areasAs a result social and economic factors are linked to UCItangible results have been obtained with the numerical dataand the methods used for this research for the first time

In the later stages of this research an interactive sta-tistical analysis of parametric and nonparametric factors willbe performed by using the BoxndashBehnken technique which isamong the design of experiment methods by determiningthe different levels of the factors involved in this work ereason for using this method is to show how the optimi-zation models to be achieved are not linear and that thestochasticity and the factors influence the responses in thesuperficial graphs In addition it is aimed to enrich theoptimum results obtained with the optimization mathe-matical models to be created with the scenarios

Data Availability

e numerical data used to support the findings of this studyhave been deposited in the Global Urban CompetitivenessReport 2011-2012 Also we used World Bank urban de-velopment data sources e numerical data used to supportthe findings of this study were supplied by Marmara Uni-versity Scientific Research Institute under project no FEN-

Table 3 Optimum values of factors and response variables

ET L T MS G F UGDP-PC UGDP4381 5591 628 471 564 584 50235 419111

Table 4 Comparisons of ranking of UCI

Urban UCI PwClowastUN-Habitat

lowastlowastUN-Habitat EI

Tokyo 78353 1 7 3 3New York 65580 2 1 1 7Los Angeles 65569 3 2 14 9Chicago 65565 4 15 9 14London 70359 5 4 2 5Paris 93289 6 18 8 1Osaka 78352 7 9 mdash 4Mexico City 34330 8 29 26 27Philadelphia 65568 9 19 17 10Satildeo Paulo 34424 10 6 mdash 26WashingtonDC 65570 11 27 10 8

Boston 65564 12 16 4 16Buenos Aires 09988 13 30 27 30Dallas 65567 14 8 21 12Moscow 46313 15 25 24 24Hong Kong 50950 16 11 11 22Atlanta 65566 17 23 16 13San Francisco 65565 18 5 12 14Houston 65560 19 10 7 19Miami 65562 20 14 23 18Seoul 68346 21 12 6 6Toronto 65271 22 22 15 20Detroit 65568 23 24 25 10Seattle 65563 24 20 13 17Shanghai 50944 25 13 18 23Madrid 83354 26 28 22 2Singapore 35065 27 3 5 25Sydney 62848 28 26 19 21Mumbai 19699 29 17 mdash 29Istanbul 30736 30 21 20 28Notee cities considered for UN-Habitat were selected among the top 200cities e ranking indexes of the cities that are not on the list are written tothe next city in the list of Table 4 PwC PricewaterhouseCoopers [70] lowastUN-Habitat the United Nations Human Settlements Programme Global UrbanEconomic Competitiveness [71] lowastlowastUN-Habitat the United Nations Hu-man Settlements Programme Global Urban Sustainable Competitiveness[71] EI econophysics index

Complexity 9

C-DRP110618-0344 and so cannot be made freely availableRequests for access to these data should be made to MrAbdulkadir Atalan Bayburt University Engineering Fac-ulty Department of Mechanical Engineering Turkeyaatalanbayburtedutr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] A Bretagnolle E Daude and D Pumain ldquoFrom theory tomodelling urban systems as complex systemsrdquo CybergeoRevue Europeenne de GeographieEuropean Journal of Geog-raphy 2006

[2] L Einav and J Levin ldquoEconomics in the age of big datardquoScience vol 346 no 6210 Article ID 1243089 2014

[3] D S Hamermesh ldquoSix decades of top economics publishingwho and howrdquo Journal of Economic Literature vol 51 no 1pp 162ndash172 2013

[4] C A Hidalgo ldquoDisconnected fragmented or united a trans-disciplinary review of network sciencerdquo Applied NetworkScience vol 1 no 1 p 6 2016

[5] J Gao B Jun A Pentland T Zhou and C A HidalgoldquoCollective learning in Chinarsquos regional economic develop-mentrdquo 2017 httparxivorgabs170905392

[6] C A Hidalgo and R Hausmann ldquoA network view of eco-nomic developmentrdquo Developing Alternatives vol 12 no 1pp 5ndash10 2008

[7] T Preis H S Moat and H E Stanley ldquoQuantifying tradingbehavior in financial markets using Google Trendsrdquo ScientificReports vol 3 no 1 p 1684 2013

[8] J Blumenstock G Cadamuro and R On ldquoPredicting povertyand wealth from mobile phone metadatardquo Science vol 350no 6264 pp 1073ndash1076 2015

[9] N Jean M Burke M Xie W M Davis D B Lobell andS Ermon ldquoCombining satellite imagery andmachine learningto predict povertyrdquo Science vol 353 no 6301 pp 790ndash7942016

[10] D Hartmann M R Guevara C Jara-Figueroa M Aristaranand C A Hidalgo ldquoLinking economic complexity in-stitutions and income inequalityrdquo World Developmentvol 93 pp 75ndash93 2017

[11] P Salesses K Schechtner and C A Hidalgo ldquoe collabo-rative image of the city mapping the inequality of urbanperceptionrdquo PLoS One vol 8 no 7 Article ID e68400 2013

[12] A Llorente M Garcia-Herranz M Cebrian and E MoroldquoSocial media fingerprints of unemploymentrdquo PLoS Onevol 10 no 5 Article ID e0128692 2015

[13] J Yuan Q-M Zhang J Gao et al ldquoPromotion and resig-nation in employee networksrdquo Physica A Statistical Me-chanics and Its Applications vol 444 pp 442ndash447 2016

[14] C A Hidalgo B Klinger A-L Barabasi and R Hausmannldquoe product space conditions the development of nationsrdquoScience vol 317 no 5837 pp 482ndash487 2007

[15] R Hausmann C A Hidalgo S Bustos M Coscia A Simoesand M A Yildirim 6e Atlas of Economic ComplexityMapping Paths to Prosperity MIT Press Cambridge MAUSA 2014

[16] C A Hidalgo and R Hausmann ldquoe building blocks ofeconomic complexityrdquo Proceedings of the National Academyof Sciences vol 106 no 26 pp 10570ndash10575 2009

[17] M Cristelli A Gabrielli A Tacchella G Caldarelli andL Pietronero ldquoMeasuring the intangibles a metrics for theeconomic complexity of countries and productsrdquo PLoS Onevol 8 no 8 Article ID e70726 2013

[18] M Cristelli A Tacchella and L Pietronero ldquoe heteroge-neous dynamics of economic complexityrdquo PLoS One vol 10no 2 Article ID e0117174 2015

[19] J Gao and T Zhou ldquoQuantifying Chinarsquos regional economiccomplexityrdquo Physica A Statistical Mechanics and Its Appli-cations vol 492 pp 1591ndash1603 2018

[20] A Chakraborti I M Toke M Patriarca and F AbergelldquoEconophysics review I Empirical factsrdquo Quantitative Fi-nance vol 11 no 7 pp 991ndash1012 2011

[21] R N Mantegna and H E Stanley An Introduction toEconophysics Correlations and Complexity in FinanceCambridge University Press Cambridge UK 2016

[22] D C Montgomery C L Jennings and M Kulahci In-troduction to Time Series Analysis and Forecasting JohnWileyamp Sons Hoboken NJ USA 2015

[23] B W Silverman Density Estimation for Statistics and DataAnalysis Routledge Abingdon UK 2018

[24] B Jun A Alshamsi J Gao and C A Hidalgo ldquoRelatednessknowledge diffusion and the evolution of bilateral traderdquo2017 httparxivorgabs170905392

[25] J-P Huang ldquoExperimental econophysics complexity self-organization and emergent propertiesrdquo Physics Reportsvol 564 pp 1ndash7 2015

[26] V Plerou P Gopikrishnan B Rosenow L A N Amaral andH E Stanley ldquoEconophysics financial time series from astatistical physics point of viewrdquo Physica A Statistical Me-chanics and Its Applications vol 279 no 1ndash4 pp 443ndash4562000

[27] S Sinha A Chatterjee A Chakraborti and B K ChakrabartiEconophysics An Introduction John Wiley amp Sons HobokenNJ USA 2010

[28] N Smith ldquoNew globalism new urbanism gentrification asglobal urban strategyrdquo Antipode vol 34 no 3 pp 427ndash4502002

[29] M Cimoli and J Katz ldquoStructural reforms technological gapsand economic development a Latin American perspectiverdquoIndustrial and Corporate Change vol 12 no 2 pp 387ndash4112003

[30] P R Dickson ldquoToward a general theory of competitive ra-tionalityrdquo Journal of Marketing vol 56 no 1 pp 69ndash83 1992

[31] S Szymanski ldquoe economic design of sporting contestsrdquoJournal of Economic Literature vol 41 no 4 pp 1137ndash11872003

[32] L Nowzohour and L Stracca More 6an a Feeling Confi-dence Uncertainty and Macroeconomic Fluctuations Euro-pean Central Bank Frankfurt Germany 2017

[33] S Adzic and O Sedlak ldquoEconomic modelling and theory offuzzy sets application in macroeconomic planning within theprocess of transitionrdquo Yugoslav Journal of Operations Re-search vol 8 no 2 pp 331ndash342 1998

[34] H E Stanley L A N Amaral D Canning P GopikrishnanY Lee and Y Liu ldquoEconophysics can physicists contribute tothe science of economicsrdquo Physica A Statistical Mechanicsand Its Applications vol 269 no 1 pp 156ndash169 1999

[35] M Gallegati S Keen T Lux and P Ormerod ldquoWorryingtrends in econophysicsrdquo Physica A Statistical Mechanics andIts Applications vol 370 no 1 pp 1ndash6 2006

[36] M Kravchenko ldquoStructural balance as a basis of the economicsustainability of an enterpriserdquoWorld Scientific News vol 57no 6 pp 300ndash308 2016

10 Complexity

[37] A Tacchella M Cristelli G Caldarelli A Gabrielli andL Pietronero ldquoA new metrics for countriesrsquo fitness andproductsrsquo complexityrdquo Scientific Reports vol 2 p 723 2012

[38] G Caldarelli M Cristelli A Gabrielli L Pietronero A Scalaand A Tacchella ldquoA network analysis of countriesrsquo exportflows firm grounds for the building blocks of the economyrdquoPLoS One vol 7 no 10 Article ID e47278 2012

[39] Q Mao K Zhang W Yan and C Cheng ldquoForecasting theincidence of tuberculosis in China using the seasonal auto-regressive integrated moving average (SARIMA) modelrdquoJournal of Infection and Public Health vol 11 no 5pp 707ndash712 2018

[40] M S Mariani A Vidmer M Medo and Y-C ZhangldquoMeasuring economic complexity of countries and productswhich metric to userdquo 6e European Physical Journal Bvol 88 no 11 p 293 2015

[41] B Mandelbrot ldquoe variation of some other speculativepricesrdquo 6e Journal of Business vol 40 no 4 pp 393ndash4131967

[42] V P Maslov ldquoEconophysics and quantum statisticsrdquoMathematical Notes vol 72 no 5-6 pp 811ndash818 2002

[43] C Schinckus ldquoEconomic uncertainty and econophysicsrdquoPhysica A Statistical Mechanics and Its Applications vol 388no 20 pp 4415ndash4423 2009

[44] N Eagle M Macy and R Claxton ldquoNetwork diversity andeconomic developmentrdquo Science vol 328 no 5981pp 1029ndash1031 2010

[45] J-H Liu J Wang J Shao and T Zhou ldquoOnline social activityreflects economic statusrdquo Physica A Statistical Mechanics andIts Applications vol 457 pp 581ndash589 2016

[46] S Singhal S McGreal and J Berry ldquoAn evaluative model forcity competitiveness application to UK citiesrdquo Land UsePolicy vol 30 no 1 pp 214ndash222 2013

[47] T A Hutton ldquoTrajectories of the new economy regenerationand dislocation in the inner cityrdquoUrban Studies vol 46 no 5-6 pp 987ndash1001 2009

[48] S Puissant and C Lacour ldquoMid-sized French cities and theirniche competitivenessrdquo Cities vol 28 no 5 pp 433ndash4432011

[49] J Abdullah ldquoCity competitiveness and urban sprawl theirimplications to socio-economic and cultural life in Malaysiancitiesrdquo Procedia-Social and Behavioral Sciences vol 50pp 20ndash29 2012

[50] L Saez and I Periantildeez ldquoBenchmarking urban competitive-ness in Europe to attract investmentrdquo Cities vol 48pp 76ndash85 2015

[51] M Lu and Z Chen ldquoUrbanization urban-biased policies andurban-rural inequality in China 1987ndash2001rdquo 6e ChineseEconomy vol 39 no 3 pp 42ndash63 2006

[52] L Salvati and P Serra ldquoEstimating rapidity of change incomplex urban systems a multidimensional local-scaleApproachrdquo Geographical Analysis vol 48 no 2 pp 132ndash1562016

[53] P Annoni L Dijkstra and N Gargano EU Regional Com-petitiveness Index 2016 Italy 2017

[54] R Huggins and N Clifton ldquoCompetitiveness creativity andplace-based developmentrdquo Environment and Planning AEconomy and Space vol 43 no 6 pp 1341ndash1362 2011

[55] N Pengfei and H Qinghu ldquoComparative research on theurban competitivenessrdquo Chinese Academy for Social Science2017

[56] J Shen ldquoCross-border urban governance in Hong Kong therole of state in a globalizing city-regionrdquo Professional Geog-rapher vol 56 no 4 pp 530ndash543 2004

[57] N Pengfei and P K Kresl Global Urban CompetitivenessReport (2011-2012) Edward Elgar Publishing CheltenhamUK 2014

[58] N Pengfei and H Qinghu Comparative Research on theGlobal Urban Competitiveness 2018

[59] E D Viorica Urban Competitiveness Assessment in De-veloping Country Urban Regions6e Rod ForwardeWorldBank Washington DC USA 2000

[60] Klaus Schwab ldquoe global competitiveness report 2018rdquo WorldEconomic Forum Reports 2018 httpwww3weforumorgdocsGCR201805FullReporteGlobalCompetitivenessReport2018pdf

[61] N Pengfei M Kamiya R Ding M Kamiya and R DingldquoGlobal urban competitiveness comparative analysis fromdifferent perspectivesrdquo in Cities Network along the Silk Roadpp 51ndash64 Springer Singapore 2017a

[62] J Bruneckiene A Guzavicius and R Cincikaite ldquoMeasure-ment of urban competitiveness in Lithuaniardquo EngineeringEconomics vol 21 no 5 pp 493ndash508 2010

[63] P Kresl and B Singh ldquoUrban competitiveness and USmetropolitan centresrdquo Urban Studies vol 49 no 2pp 239ndash254 2012

[64] S Iyer M Kitson and B Toh ldquoSocial capital economicgrowth and regional developmentrdquo Regional Studies vol 39no 8 pp 1015ndash1040 2005

[65] Z Yuan X Zheng L Zhang and G Zhao ldquoUrban com-petitiveness measurement of Chinese cities based on astructural equation modelrdquo Sustainability vol 9 no 4 p 6662017

[66] F-C Wu ldquoOptimization of correlated multiple qualitycharacteristics using desirability functionrdquo Quality Engi-neering vol 17 no 1 pp 119ndash126 2004

[67] N R Costa J Lourenccedilo and Z L Pereira ldquoDesirabilityfunction approach a review and performance evaluation inadverse conditionsrdquo Chemometrics and Intelligent LaboratorySystems vol 107 no 2 pp 234ndash244 2011

[68] Z Hu M Cai and H-H Liang ldquoDesirability function ap-proach for the optimization of microwave-assisted extractionof saikosaponins from Radix Bupleurirdquo Separation and Pu-rification Technology vol 61 no 3 pp 266ndash275 2008

[69] B John ldquoApplication of desirability function for optimizingthe performance characteristics of carbonitrided bushesrdquoInternational Journal of Industrial Engineering Computationsvol 4 no 3 pp 305ndash314 2013

[70] PricewaterhouseCoopers ldquoWhich are the largest city econ-omies in the world and how might this change by 2025rdquo2009

[71] N Pengfei M Kamiya and W Haibo ldquoe global urbancompetitiveness report 2017-2018ndashhousing prices changingworld citiesrdquo 2017 httpsunhabitatorgglobal-urban-competitiveness-report-2017-2018-launched

Complexity 11

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

financial markets Moreover it is seen that the econophysicsmethod is widely used by the statistical method as a result ofresearch studies because in the characteristic structures ofeconomics data financial time series leads to statisticalfeatures and empirical studies [22 23] In this research theeconophysics method was used for statistical physics toaddress urban competitiveness As a matter of fact the dataare measured locally rather than globally Additionallyeconomists and physicists have applied network and sta-tistical methods to reshape the understanding of in-ternational trade that the knowledge about exporting to adestination diffuses among related products and geographicneighbours [24] More recent works on econophysics andcomplexity are summarized by review papers [20 25 26]and books [20 27]

e processes of economic social and political changeconstantly affect the economic balance in the urban centresand reveal the necessity of renewing and planning them interms of competitiveness [28] Not only national changesbut the fact that they have centres that can govern them-selves accelerate and shape this need e European Union(EU) is at the forefront especially for the growing cities ofdeveloping countries to be at a competitive level Accordingto general belief urban areas with less uncertainty andimbalance in the economy are more competitive than othercities [29ndash31] is situation contributes to the rapid changeand development of the urban However it is seen that therapid changes of economic structures lead to uncertaintyand imbalance in the economies of urban areas and un-certainty and imbalance dominate in real economies [32]Within this information it is seen that the economic theoriesused are inadequate to account for sudden changes in theeconomy (fluctuations sudden movements in the parts andmobility in the capital markets etc) [33] e uncertaintyand imbalance of the fluctuations in the economy have led tothe emergence of new concepts and approaches But there isno specificmodel to reduce uncertainty and imbalance in theeconomy and there are only temporarily developed modelse main reason for this is that the economic structures arecomplex and the change in the economy is fast In such casesthe structures that form in the economies are transforminginto stochastic models on a statistical basis [21] In this workwe aimed to solve the problems of uncertainty and imbal-ance in the economy of urban areas by choosing the con-temporary method of the optimization statistical physictechniques to reach the concept of econophysics

Towards quantifying the complexity of a countryrsquoseconomy the pioneering attempt was made by Hidalgo andHausmann [16] who modelled the international trade flowsas ldquoCountry-Productrdquo networks and derived the EconomicComplexity Index (ECI) by characterizing the networkstructure through a set of linear iterative equations couplingthe diversity of a country (the number of products exportedby that country) and the ubiquity of a product (the numberof countries exporting that product) e intuition behindthis new branch of studies is that the cross-country incomedifferences can be explained by differences in economiccomplexity which is measured by the diversity of a countryrsquosldquocapabilitiesrdquo [15 16 19] the statistical properties of

financial markets have begun to apply physics conceptseconomically by attracting physicists [34] Econophysicistshave tried to use the theoretical approach of physical sta-tistics to understand empirical findings [35] Generallymany methods known in statistical physics have been ap-plied to characterize time evolution in stock prices andexchange rates [34] In the first examination econophysicscan be seen as wide physics models in the economy that ismore quantitative approach statistical models conceptsand calculation methods e macroscopic properties ofintrinsic microscopic interactions cause a complex system inthe economy At this point econophysics is associated withphysical complexity (complex structures) reducing un-certainty and imbalance in the economy [36] Immediatelyafter those studies described above Tacchella and researchcolleagues [37] developed a new statistical approach whichdefines a countryrsquos fitness and a productrsquos complexity by thefixed points of a set of nonlinear iterative equations [38]where the complexity of products is bounded by the fitnessof the less competitive countries exporting them FurtherCristelli and research colleagues [18] studied the hetero-geneous dynamics of economic complexity and found in thefitness-income plane strong explanatory power of economicdevelopment in the laminar regime and weak explanatorypower in the chaotic regime Based on this observation theyargued that regressions are inappropriate in dealing with thisheterogeneous scenario of economic development andfurther proposed a selective predictability scheme to predictthe evolution of countries Nevertheless these economiccomplexity indicators are not perfect for example ECIsuffers from criticisms on its self-consistency fitness de-pends on the dimension of the phase space of the hetero-geneous dynamics of economic complexity [17 18] and anew variant of the fitness method called minimal extremalmetric can perform even better for a noise-free dataset [39]Recently Mariani and research colleagues [40] quantita-tively compared the ability of ECI and fitness in rankingcountries and products and further investigated a general-ization of the ldquoFitness-Complexityrdquo metric

In general the uncertainty and imbalance in the econ-omy have been considered to be reduced by the Gaussian law[41] is approach is not enough to reduce uncertainty andimbalance in the economy is law is suitable for the use ineconomically viable microscopic models such as the prin-ciple of randomly proportional effect However with theapplication of microdimension models for the complexstructure of economies healthy results cannot be obtainedIn another study the econometric approach was taken asquantum statistics In this work entropy temperature freeenergy and the Hamiltonian concepts in probability theoryare integrated into the quantum statistical method formathematical financing [42] As a result the uncertainty ofthe phase transitions in mathematical finance has beenfound to depend on the temperature of the distributionalthough the precision of the mathematical financial data isnot known due to the uncertainty of the phase change Inorder to acquire a more tangible result in this statisticalanalysis optimization models with statistical physics havebeen used to obtain information about the competitiveness

2 Complexity









2 Methodology



Complexity 3













Health policies

ET

Labor and transport





LT




TI

Market size



Company earnings

MS

Product efficiency






PE

Financial service




FS

4 Complexity










yi fi x1 x2 xk( 1113857 i 1 2 n (1)


di di yi( 1113857 di yi(x)( 1113857 (2)




ui minus li1113888 1113889

wi

li leyi le ui (3)



Complexity 5

dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)


dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)


dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)



(7)



UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)



maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)


subject to

llexj

xj le u

0lexj

(11)


maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi


yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873


(12)

6 Complexity













Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018
















2 Methodology



Complexity 3













Health policies

ET

Labor and transport





LT




TI

Market size



Company earnings

MS

Product efficiency






PE

Financial service




FS

4 Complexity










yi fi x1 x2 xk( 1113857 i 1 2 n (1)


di di yi( 1113857 di yi(x)( 1113857 (2)




ui minus li1113888 1113889

wi

li leyi le ui (3)



Complexity 5

dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)


dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)


dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)



(7)



UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)



maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)


subject to

llexj

xj le u

0lexj

(11)


maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi


yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873


(12)

6 Complexity













Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018




















Health policies

ET

Labor and transport





LT




TI

Market size



Company earnings

MS

Product efficiency






PE

Financial service




FS

4 Complexity










yi fi x1 x2 xk( 1113857 i 1 2 n (1)


di di yi( 1113857 di yi(x)( 1113857 (2)




ui minus li1113888 1113889

wi

li leyi le ui (3)



Complexity 5

dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)


dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)


dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)



(7)



UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)



maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)


subject to

llexj

xj le u

0lexj

(11)


maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi


yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873


(12)

6 Complexity













Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018

















yi fi x1 x2 xk( 1113857 i 1 2 n (1)


di di yi( 1113857 di yi(x)( 1113857 (2)




ui minus li1113888 1113889

wi

li leyi le ui (3)



Complexity 5

dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)


dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)


dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)



(7)



UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)



maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)


subject to

llexj

xj le u

0lexj

(11)


maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi


yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873


(12)

6 Complexity













Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018








dmax

0 if yi le l

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

1 if yi ge u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)


dmin

0 if yi ge u

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l

1 if yi le l

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(5)


dtarget

yi minus l

u minus l1113888 1113889

wi

if yi le u yi ge l

u minus yi

u minus l1113874 1113875

wi

if yi le u yi ge l


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)



(7)



UCI c1 + 1113936

ni1pikrk1113872 1113873UGDPi1113960 1113961

c2 (8)

and

UCI c1 + 1113936

ni1pikrk1113872 1113873(GDPPC)i1113960 1113961

c2 (9)



maximize UGDPi

subject to

llexj

xj le u

0le xj

(10)


subject to

llexj

xj le u

0lexj

(11)


maximizeUCI 1113944

yf

yi

c1 + 1113936ni1pikrk1113872 1113873 UDGPi( 11138571113872 1113873 c2( 11138571113960 1113961

yf minus yi

⎡⎣ ⎤⎦ 1113944

yf

yi


yf minus yi

⎡⎣ ⎤⎦⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

subject to1113936

yf

yimin l

yi

ij lyf

ij1113966 11139671113872 1113873

yf minus yi1113872 1113873⎡⎢⎣ ⎤⎥⎦lexij

1113936yf

yimax u

yi

ij uyf

ij1113966 11139671113872 1113873


(12)

6 Complexity













Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018




















Factors Samplesize




(plt 001)


(plt 001)


(plt 005)


(plt 001)



Complexity 7



ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018










ET L T MS G F

0

25

50

75

100

125

Mea

n of

GD

P pe

r cap

ita

5 64 4 53 45 6030 6 75 4 53 45 6030


ET L T MS G F

0

200

400

600

800

1000

Mea

n of

UG

DP

5 64 4 53 45 6030 6 75 3 54 45 6030


HighCurLow

OptimalD 09994

Predict

GDP pertarg 50510y = 505235d = 099962

UGDPtarg 41830

y = 4191111d = 099924


D 09994

L5690

[55912]2970

T6280

[6280]2750

MS6940

[4710]4710

G5640

[5640]3140

F5840

[5840]3040

ET6090

[43814]3860


8 Complexity








Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018















Data Availability









Complexity 9




References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018











References





































10 Complexity




































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018











































Complexity 11








Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








developing statistical optimization models for urban

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