Multiattribute Supply and Demand Matching Decision Model

Research ArticleMultiattribute Supply and Demand Matching Decision Model forOnline-Listed Rental Housing An Empirical StudyBased on Shanghai

Lingyan Li 1 Jiangying An1 Yan Li 2 and Xiaotong Guo1

1School of Management Xirsquoan University of Architecture and Technology Xirsquoan 710055 China2School of Management Xirsquoan Polytechnic University Xirsquoan 710048 China

Correspondence should be addressed to Yan Li sayidlixpueducn

Received 22 April 2020 Revised 10 June 2020 Accepted 23 June 2020 Published 1 August 2020

Guest Editor Chi-Hua Chen

Copyright copy 2020 Lingyan Li et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e mismatch between the supply and demand of online-listed rental housing (ORH) is an important factor restricting theoperational efficiency of online rental service platforms However extant literature pays little attention to this problemis studyproposes an ORH multiattribute supply and demand matching decision model based on the perceived utility of matching bothsides of this market e model considers the multiattribute information of ORH such as area transportation rent room andinterior decoration and quantifies their perceived utility values based on the theory of disappointment ereafter we constructthe matching decision model and verify it for feasibility by applying it to Shanghairsquos ORH supply and demand informationmdashourempirical case e results show that this method can be applied to online rental housing platforms and meet the supply anddemand matching requirements to the greatest extent e constructed model takes into account the perceptions of both supplyand demand parties may promote the effective matching of ORH supply and demand and bears theoretical implications for theimprovement of rental housing matching in ORH platforms

1 Introduction

Matching supply and demand (SAD) directly affects thesuccess of online trading However regarding rentalhousing efficiency in matching SAD is not high [1] manycountries around the world have rental housing marketscharacterized by mismatches in SAD [2] In terms of rentalexpenses the USrsquo traditional housing market for exampleoffers properties with higher rental prices than residents canafford [3] Other examples are Germany where rentedhomes do not match regional SAD [4] and Nigeria wherethe speed and scale of housing supply are smaller than thedemand causing inefficiency in the countryrsquos ability to meetthe housing needs of low-income earners [5] Similarly inChina the rental housing SAD structure is incongruent[6 7] is shows that traditional rental housing supplystructures are incapable of matching personalized demandsand the mismatch between the quality and quantity of ORH

leads to this discrepancy between the rental housing mar-ketrsquos SAD which seriously hinders the efficiency of rentalhousing service platforms erefore not only can thecreation of an effective matching method for online rentalhousing platforms solve the operational inefficiency of therental housing market but can also promote the rapid de-velopment of the rental market

To promote the effective matching of rental housingonline some scholars have made various attempts to studythe SAD matching of ORH So far the matching model ofORH is mainly a balanced search model whose purpose is toreduce search costs [8 9] ere are a few models to measurethe quality of supply and demand matching based on thesimilarities between SAD [10] ere are also models toestablish a double-sided matching theory to solve theproblem of public rental housing [11] At the same timesome scholars pointed out that SAD patterns considervarious housing attributes in the house matching selection

HindawiDiscrete Dynamics in Nature and SocietyVolume 2020 Article ID 4827503 21 pageshttpsdoiorg10115520204827503

process [12 13] and that these attributes affect ORH SADmatching [14] For example price floors play a central rolebetween SAD [15] while issues around house matching andcomfort transportation the surrounding environment andlandlord services are specific indicators of tenant concerns[16] Location is also a factor of housing mismatch [2] esize and location of a house are considered to be necessaryconditions for appropriate house matching [14] ereforehousing attributes play a very important role in balancingthe SAD of ORH

Although the aforementioned models proposed by ex-tant studies can reduce the cost of searching in the matchingprocessmdashconsidering that housing multiattribute indicatorsare factors in the SAD matching processmdashthey do notpromote the effective matching of ORH or the improvementof matching satisfaction between the SAD sides In factwhen a matching decision occurs in the actual process mostsubjects are in limited rationality [17] their expected valuesare limited by existing information and their own expec-tations [18 19] us the final matching pair may have ahigher or lower value than the expected value leading tobelow-optimal satisfaction with the matching results Inaddition perceived utility is a product of a demandersrsquoassessment of the services values and functions of the re-quired items compared to their own expectations how theyweigh the perceived benefits and costs and the value theyfinally put on the required items [20] In assessing profit andloss values the theory of disappointment reflects the samedifference between actual and expected results [21] Loomesand Sugden also believed that ldquodisappointmentrdquo and ldquoex-citementrdquo are key factors in making rational choices [22]erefore using disappointment theory to quantify theperceived utility of both SAD can reflect the psychologicalactivities of both sides

In recent years with the acceleration of urbanization thehousing problem of Chinarsquos floating population has becomeincreasingly prominent In 2018 the floating populationreached 241 million of which 210 million required rentalhousing covering an area of 673 billion square meters Inaddition large and medium-sized cities in China are re-quired to build a rental housing platform to promote thematching efficiency of rental housing However the housingrental market is undeveloped and has many problems suchas low supply efficiency lack of diverse supply systems andlow capability to meeting peoplersquos housing demand [6 23]Among them is Shanghai the central city of China with arelatively large annual flow of floating population and a greatdemand for rental housing erefore taking Shanghai asour case study may help understand and reflect the problemsof other cities is is of great significance for promoting thedevelopment of the rental housing market

In online rental housing transactions the real estatenetwork platform involved is a two-sided market thatconnects the SAD sides of rental housing through whichvarious agents interact with one another and the transac-tions cater to the needs of all the users (both SAD)erefore this study attempts to apply the two-sidedmatching theory to the housing rental market To improvethe satisfaction of both SAD sides this study uses

disappointment theory to construct quantitative perceivedutility value matrices First we start by quantifying the utilityof housing as perceived by both SAD sides based on themultiattribute matching characteristics of both sides Sec-ond we construct a multiattribute SAD matching decisionmodel for ORH platforms Finally we adopt online SADinformation from Shanghai China to ensure that themultiattribute information of rental housing has beenidentified and to empirically test the validity and rationalityof the model safeguarding the construction of an innovativemethod for ORH SAD matching

e contributions of this study are twofold First thestudy constructs an effective SADmatchingmodel for onlinerental housing platforms and enriches the application of thetwo-sided matching theory Currently research on two-sided matching is mostly applied in the marriage marketlabor market schools and hospitals but is rarely used in therental housing market especially for application in onlinerental housing service platforms erefore this study un-dertakes to verify the applicability and effectiveness of thetwo-sided matching theory in the rental housing marketis provides a reference and a theoretical method forcracking the SADmatching problem that has plagued onlinerental housing platforms with multisubject and multilevelsupply methods Second the attributes of ORH are deter-mined and measured ese can be easily extended to othercities and online platforms providing reference to thefeasibility of analyzing multiattribute decision-makingmatching problems is also helps to improve the overallsatisfaction and quality of SAD matching efforts by con-sidering the expectations and real values of both SAD sidesIn sum this study is valuable for improving the efficiency ofSAD matching for online platforms as well as the sus-tainable development of the rental housing market

e remainder of this article is arranged as followsSection 2 presents a detailed literature review Section 3introduces the research materials and methods e em-pirical results and discussion are presented in Section 4Finally Section 5 summarizes the conclusions and impli-cations of this study

2 Literature Review

21 Disappointment (eory e disappointment theoryproposed by Bell [21] and Loomes and Sugden [22] is basedon psychological reactions caused by the comparison ofactual results with expectations [24] Fundamentally thedisappointment theory suggests that when actual results arebetter than expected policymakers will be ecstatic whenactual results are worse than expected manufacturers will bedisappointed and that the greater the disparity between theoutcome and the expectation the greater the disappoint-ment [21] So far there are three main contemporary dis-appointment models [25 26] e first is the BellndashLoomesand Sugden disappointment model is model essentiallyquantifies the ldquomodified expected utilityrdquo of human satis-faction in the case of disappointment e second is Gulrsquosdisappointment aversion (DA)model which decomposes theparticipantsrsquo psychological cognition into disappointment

2 Discrete Dynamics in Nature and Society

and elation parts with respect to a new certainty equivalente third and the last model is Cillo and Delquiersquos disap-pointment without prior expectationmodel is model doesnot assume that the decision maker sets a single referencepoint of comparison prior to a certain experience Takingthis theory into account and the idea that actual utility is acombination of subjective utility functions and disap-pointment and exhilaration functions [21] this paper usesthe disappointment theory to calculate the perceived utilityvalues of both SAD sides

In recent years many scholars have quantified the sat-isfaction of matching objects based on the disappointmenttheory For example Quan et alrsquos study explored customerpsychological satisfaction based on customer disappoint-ment and pleasure behaviors and their method promotesretailer pricing and inventory decisions [27] Similarly Maet al established a SAD matching model for the electricityretail industry by considering the disappointment of sen-sitive customers and new electricity retail companies byconsidering the pleasant psychological perception andobtaining the perceived utility of both partiesis method isverified to be beneficial for themanagement of a high-qualityelectricity market Zhang et al built a matching optimizationmodel that maximizes satisfaction by calculating the dis-appointment and excitement associated with both SAD sidesbased on the disappointment theory [28] Zhao et al pro-posed a two-sided matching model to elaborate the pref-erence order of SAD by considering the participantsrsquopsychological perception Using the functions of disap-pointment and cheerfulness this model effectively improvesthe carpool matching problem [26] Another example is thatby Fan et al who proposed a two-waymatchingmethod thatconsiders the psychological behavior of the agents of bothparties and constructed a two-objective optimization modelto obtain satisfactory matching results [29] ese modelsmaximize the satisfaction of both SAD sides and by con-sidering the degree of their disappointment and elationthese models effectively reflect the perception activities ofboth sides which is conducive to promoting the improve-ment of the satisfaction of SAD

22 Two-Sided Matching e two-sided matching theoryoriginated from a study on marriage matching that focusedon satisfying both parties with matching results according tothe requirements of SAD sides [30] Gale and Shapley fromwhich Shapley became the 2012 Nobel laureate in eco-nomics first proposed the G-S algorithm for stable matchingbased on the strong preference information given by bothmen and women [31] Later Roth another Nobel laureate ineconomics applied the G-S algorithm to the hospital in-ternship market [30] Since then the two-sided matchingtheory has been developed and widely used in various fieldssuch as staff and job matching data trading marketmatching commodity trading issues and college admissionissues At the same time some scholars have proposed avariety of matching methods including the deferred algo-rithm [32] evolutionary algorithm [33 34] and multi-attribute preference decision-making methods [35]

Nonetheless the two-sided matching theory has proved tohave a wide range of practical applications

With the popularity of the Internet some scholars havebegun to talk about the application of the two-sidedmatching theory to the SAD matching problems of manyonline transactions For the second-hand housing markettaking the online rental-sale matching problem as an ex-ample Wang et al established a two-sided matching de-cision method based on heterogeneous information andassociation the feasibility of which was verified [36] In theelectronic market environment Gao et al provided a stablemultilateral automated negotiation system model andshowed that this model can promote effective matchingbetween the SAD sides For the power purchase market[37] Kong et al proposed a SAD matching model forpower retailers and buyers of cellular networks based on thetwo-sided matching theory which solves the energymanagement problem of microgrid-connected cellularnetworks for the small- and medium-sized market of thesharing economy [38] Xia et al constructed a two-sidedmatching model that promotes the maximization of theinterests of buyers sellers and agents and improves thematching efficiency thereof For the hospitalrsquos expert-outpatient matching appointment system [39] Yang et alconstructed a matching model based on the two-sidedmatching theory that improves the effectiveness of medicaltreatment [40] ese models built by scholars based on thetwo-sided theory have solved the problem of matching SADin different fields

Similarly in the existing literature the two-sidedmatching theory has been widely applied to online tradingplatforms and has improved thematching efficiency betweenSAD Nevertheless its application in ORH transactions islimited In addition existing two-sided matching decision-making methods rarely consider the psychological percep-tion of disappointment or elation when the subjective desiresof both parties match and when the psychological percep-tions are closely related to the satisfaction of both parties inthe final matching schemee satisfaction of the two partiesneeds to effectively characterize the psychological perceptionof both parties Moreover in the process of matching ORHSAD both sides will consider the multiattribute informationof housing [12] but there are very few studies covering themultiattribute two-sided matching model erefore thispaper proposes a multiattribute supply-demand matchingmethod for online rental listings based on the perceivedutility

On online house rental platforms tenants and landlordscan be regarded as two unconnected sets Each set willevaluate the actual value of the property according to its ownpsychological expectations e main goal of a matchingmethod in this case is to promote effective matching betweenSAD based on the tenantsrsquo and landlordsrsquo mental perceptionerefore this study aims to apply the two-sided matchingtheory to the SAD matching problem of online rentalhousing services to accurately characterize the SAD per-ceptions of both sides and to quantify the perceived utilitiesof both SAD based on the disappointment theory to promotesatisfaction over the matching results

Discrete Dynamics in Nature and Society 3

3 Materials and Methods

31 Framework and Schematic Diagram of the MultiattributeSAD Matching Decision Model of ORH

311 Description and Assumption On online rental plat-forms three parties are involved suppliers demanders andindependent intermediaries or brokers Suppliers on onlinerental platforms are usually landlords with vacant houses thedemanders are the potential tenants (those with housing needs)while independent intermediaries or brokers are service orga-nizations that assist in matching the SAD sides based on theinformation provided by the suppliers and demanders In thematching process the brokers satisfy the requirements of theSAD parties to the greatest extent according to the informationprovided by them In this study the interactions of the suppliersand demanders can be explained with a SAD matchingframework as done in the following All variable assumptionsand descriptions in the paper are shown in Table 1

is study describes the matching characteristics of SADsides If the tenant isT thenT T1 T2 Tm1113864 1113865 whereTi isthe i tenant and i isinM 1 2 m If a collection oflandlords is L then L L1 L2 Ln1113864 1113865 where Lj is the j

landlord and j isin N 1 2 n and mle n If a collectionof online rental house listings displayed by the landlords onthe online real estate platform is H then H H11113864

H2 Hn where Hj is the j online-listed rental houseIf a collection of housing attributes for evaluating ORH is

C then C C1 C2 Ck1113864 1113865 where Cl is the l attribute ofORH l isin K 1 2 k e factors for evaluating ORHare region rent transportation convenience units of housesdecoration house supporting facilities online ratings and soon ese attributes are divided into hard requirements andsoft requirements Hard requirements are equitation re-quirements while soft requirements are divided into benefit-orientated requirements and cost-orientated requirementse higher the attributes the better the benefit-orientatedrequirements the lower the attributes the better the cost-orientated requirements e tenants determine the ex-pected value and weights of the specific attributes while thelandlord determines the evaluation value and attributeweights of the specific attributes such as their actual needsAmong them E [eil]mtimesk is the expectation level matrix oftenant Ti regarding the ORH and eil is the expectation levelof tenant Ti regarding the attributes of ORH Cl R [rjl]ntimesk

is the real evaluation matrix of landlord Lj regarding theORH and rjl is the real evaluation value of landlord Lj

regarding the attributes of ORH Cl en tenants give theattribute weight vector wil w1l w2l wil1113864 1113865 where wil

represents the tenantrsquos Ti description of the importance ofthe attribute Cl 1113936

kl1 wil 1 0lewil le 1 where wjl is the

landlordrsquos Lj description of the importance of the attributeCl 1113936

kl1 wjl 1 0lewjl le 1 en according to the attribute

values given by tenants and landlords the weights of eachattribute are determined by the entropy weight method

Based on the above analysis and definition the multi-attribute SAD matching decision model for ORH can bedescribed in Figure 1 e first step is the landlords sub-mitting the real multiattribute evaluation value of the houses

to the broker and the broker displaying the multiattributeinformation of those houses on the online rental platforme second step is the tenants searching for the desiredrental house on the online rental housing platformaccording to the expected value of each attribute of the rentalhouses e third step involves the tenants measuring thereal attribute value of the house through the left expectedattribute value C1 C2 C3 Cp and the landlords mea-suring the expected attribute value of the tenants through theright expected attribute value C1 C2 C3 Ck

312 Multiattribute Supply-Demand Matching DecisionModel Development e schematic overview of the wholepaper as shown in Figure 2 presents processes and asso-ciated techniques used in this study for the construction ofthe multiattribute SAD matching decision model for ORHbased on the perceived utilityemajor steps of this processinclude (a) selecting and measuring housing multiattributeindicators for landlords and tenants to evaluate rentalhousing respectively (b) calculating the profit and lossmatrices for each attribute of the landlords and tenants (c)transforming the landlordsrsquo and tenantsrsquo profit and lossmatrices into normalized profit and loss matrices (d) cal-culating the perceived utility matrix for each attribute of thelandlords and tenants (e) determining the weight of eachattribute (f ) transforming the landlordsrsquo and tenantsrsquo per-ceived utility matrices of each attribute into a comprehensiveperceived utility matrix (g) establishing a multiattributeSAD matching decision model for ORH and (h) verifyingthe feasibility of the model based on the actual case

From Figure 2 the schematic overview of the multi-attributes based on the perceived utility is established forsupplier-demander interactions on online rental platformsrough the web crawler method the expected values andevaluation values of various housing attributes for both SADwere collected is was followed by selecting seven multi-attribute indicators of housing through word frequencyanalysis and semantic network analysisese include districttraffic convenience rent living room house supporting fa-cilities decoration and online ratings ese attributes werethenmeasured Moreover the profit and loss matrices of eachhousing attribute of the SAD were obtained based on theprofit and loss functionmethodemethod canmeasure thebenefits and costs of both SAD Next we transformed theprofit and loss matrices of the SAD into standardized profitand loss matrices by normalizing functions which can unifythe dimensions of each housing attribute Furthermore theperceived utility matrix of each housing attribute of the SADwas obtained based on the disappointment and elationfunction Considering the interaction between the housingattributes the entropy weight method was used to obtain theweight of each housing attribute and the perceived utilitymatrix of both the SAD was converted into a comprehensiveperceived utility matrix In addition based on a compre-hensive perceptual utility matrix the multiattribute SADmatching decision model for ORH was proposed e modelwas then converted into a single-objective optimizationmodel by a linear weighted method Finally to illustrate its


applicability and test its effectiveness the model was appliedto evidence from Shanghai

32 Multiattribute SAD Matching Decision Model for ORHPlatform Transactions Based on the Perceived Utility

321 Basis for the Construction of Profit and Loss MatricesFor both SAD sides benefits and losses occur during theprocess of matching the SAD of ORH ese benefits and

losses are subject to psychological perception andpsychological perception is closely related to the satis-faction of both SAD sides in the final matching schemeis study specifically describes the values of the profitsand losses of both suppliers and the demanders asfollows

When the expectation value of tenant Ti for an attributeof the rental house Cl is inferior to the real evaluation valueof landlord Lj in terms of this attribute profits occur

Table 1 Variable descriptions

NomenclatureT Collection of tenantsL Collection of landlordsH Collection of rental housingC Collection of rental housing attributesE e expectation level matrix of the tenanteil Level of expectations given by the i tenant for the l attribute of online rental housesR e real evaluation matrix of the landlordrjl Level of real evaluation given by the j landlord for the l attribute of online rental houseswil e weight given by the i tenant to the l attribute of ORHwjl e weight given by the j landlord to the l attribute of ORHDl Profit and loss matrix of the tenant under the l attributedijl Profit and loss value of the i tenant with respect to the j landlord under the l attributepij Transaction rentsFl Profit and loss matrix of the landlord under the l attributeaijl Profit and loss value of the j landlord with the i tenant under the l attributeDlprime Normative profit and loss matrix of the i tenant under the l attribute

dijlprime Normative profit and loss value of the i tenant with respect to the j landlord under the l attribute

Flprime Normative profit and loss matrix of the j landlord under the l attribute

aijlprime Normative profit and loss value of the j landlord with the i tenant under the l attribute

Vbl Tenantrsquos perceived utility matrix under attribute l

Vsl Landlordrsquos perceived utility matrix under attribute l

V Tenantrsquos comprehensive perceived utility matrixVprime Landlordrsquos comprehensive perceived utility matrixxij 0-1 variableZ e overall satisfaction valueGreek symbolsα e delight parameterβ e disappointment avoidance parameterAbbreviationsSAD Supply and demandORH Online-listed rental housing

T1

T2

T3

T4

TP

Expectedattributes

Searchfor

Show Provide Realattributes

B1

B2

B3

H1

H2

H3

Hn

TenantsRental website

platform

ORH Landlords

S1

S2

S3

Sn

C2

C3

Ck

C4

C1

Bm

Figure 1 Multiattribute SAD matching decision model for the ORH matching process


Web crawler method

Data processing

Word frequency analysis

Semantic network analysis

P amp L function method

Normalization matrixfunction method

Disappoinment and elationfunction method

Entropy weight method

Linear weighted method

Multiobjectiveoptimization method

Linear weighted method andmaximum method

Empirical study Verifying the validity andfeasibility of the model

Single-objectivemultiattribute decision model

for SAD

Multiattribute decisionmodel for SAD

Transforming thecomprehensive perceived

utility matrix of SAD

The weight of each housingattribute

Perceived utilitymatrix for each

attribute of SAD

Suppliersrsquo evaluations forhousing attributes

Demandersrsquo expectations forhousing attributes

Selecting and measuringhousing multiattribute

indicators

Profit and loss matrix foreach attribute of SAD

Normalized profit andloss matrix fro each

attribute of SAD

Figure 2 Schematic overview of the multiattribute SAD matching decision model for ORH based on the perceived utility


otherwise losses occur e above benefits and losses arequantified as follows

If Dl [dijl]mtimesn is the profit and loss matrix of tenant Ti

under attribute Cl then dijl is the profit or loss of landlord Lj

under attribute Cl Considering that tenant Ti will putforward different requirements according to their own ex-pectations dijl is calculated as follows

When attribute Cl is rent in order to ensure the fairnessof online transactions the transaction rent is set to themiddle value of the tenantsrsquo expected rent and the landlordsrsquoLj expected rent and the calculation equation of thetransaction rents pij and dijl are as follows

pij rjl + eil

2 i isinM j isin N l isin K (1)

When attribute Cl is rent dijl is calculated by the fol-lowing three cases [41]

Case 1 when eil rjl the tenantrsquos Ti performance tolandlord Lj is neither a gain nor a lossCase 2 when eil ltpij lt rjl the tenantrsquos Ti performanceto landlord Lj is a loss e loss would be 1 minus (pijeil)Case 3 when eil gt rjl the tenantrsquos Ti performance tolandlord Lj is gain e gain is 1

erefore the equation for calculating dijl is as follows

dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

i isinM j isin N l isin K

(2)

When attribute Cl is not rent there are three forms ofrequirements Wang et al gave everyonersquos gains and lossesbased on expectations and the equation is as follows [42]

(1) When tenant Ti has a hard requirement of attributeCl hard constraints refer to covenants that must besatisfied by bundle conditions When the value of eil

is equal to the value of rjl tenant i and landlord J canbe matched When the value of eil is not equal to thevalue of rjl tenant Ti and landlord Lj cannot bematched en the equation for calculating dijl is asfollows

dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)

(2) When tenant Ti has a benefit requirement of attri-bute Cl the larger the attribute value of the benefit-type attribute the better dijl is calculated by thefollowing three cases

Case 1 when eil rjl the tenantrsquos Ti performanceto landlord Lj is neither a gain nor a loss underattribute Cl

Case 2 when eil lt rjl the tenantrsquos Ti performance tolandlord Lj is a gain under attribute Cl e gain isrjl minus eilCase 3 when eil gt rjl the tenantrsquos Ti performance tolandlord Lj is a loss under attribute Cl e loss isrjl minus eil

erefore when attribute Cl is a benefit requirementthe equation for calculating dijl is as follows

dijl 0 rjl eil

rjl minus eil rjl ne eil

⎧⎨

⎩


(4)

(3) When tenant Ti has a cost-type requirement of at-tribute Cl the lower the value of the cost attributethe better dijl is calculated by the following threecases

Case 1 when eil rjl the tenantrsquos Ti performanceto landlord Lj is neither a gain nor a loss givenattribute ClCase 2 when eil lt rjl the tenantrsquos Ti performance tolandlord Lj is a loss given attribute Cl e loss iseil minus rjlCase 3 when eil gt rjl the tenantrsquos Ti performance tolandlord Lj is a gain given Cl e gain is eil minus rjl

erefore when attribute Cl is a cost-type requirementthe equation for calculating dijl is as follows

dijl 0 rjl eil

eil minus rjl rjl ne eil

⎧⎨

⎩


(5)

Similarly landlord Lj should consider whether thetenantrsquos Ti expected rent is within an acceptable range andmeets the requirements for the ORHrsquos area If Fl [aijl]mtimesn

is the profit and loss matrix of landlord Lj for attribute Cl

and aijl is the profit and loss value of landlord Lj with respectto tenant Ti for attribute Cl then the calculation equation ofaijl is as follows

aijl

0 rjl eil

pij

rjl

minus 1 eil ltpij lt rjl

1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)

e SAD sides concern about some attributes of onlinerental house As the dimensions of these attributes aredifferent Dl [dijl]mtimesn and Fl [aijl]mtimesn of the profit and


loss matrices of both parties in the transaction were con-verted into normative Dl

prime [dijlprime ]mtimesn and Fl

prime [aijlprime]mtimesn

among which the calculation equations of dijlprime and aijl

prime are asfollows [43]

dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868


322 Basis of the Construction of Perceptual Utility MatricesBased on the disappointment theory the normalized profitand loss matrices Dl


prime [aijlprime ]mtimesn are

transformed into the perceived utility matricesVbl [vb

ijl]mtimesn

and Vsl [vs

ijl]mtimesn and the perceived utility value of bothsupplier and the demander is determined by the disap-pointment and delight function φ(x) of Grant and Kajii [44]which can be expressed as [26]

φ(x) 1 minus αx xge 0

β(minus x) minus 1 xlt 01113896 (10)

α is the delight parameter satisfying 0lt αlt 1 while β isthe disappointment avoidance parameter satisfying 0lt βlt 1e larger α and β are the lower the subjectrsquos perceived valueof the matching results is compared to the expected value Inorder to facilitate calculation Laciana and Weber measuredthe beta value in accordance with most subject behavioralpreferences [45] 07le αle 09 07le βle 09 In this paper αand β take the same value erefore if α β 08 thenVb

l [vbijl]mtimesn and Vs

l [vsijl]mtimesn and the calculation

equations are as follows [26]

vbijl φ dijl

prime1113872 1113873 i isinM j isin N l isin K (11)

vsijl φ aijl


e tenantrsquos Ti comprehensive perceptual utility matrixV [vb

ij]mtimesn is constructed according to the tenantrsquos Ti

perceptual utility matrix Vbl [vb

ijl]mtimesn where the calcula-tion equation of vb

ij is as follows [46]

vbij 1113944

k

l1wilv

bijl i isinM j isin N l isin K (13)

Similarly a comprehensive perceived utility matrix Vprime [vs

ij]mtimesn of landlord Lj is constructed where the calculationequation of vs


vsij 1113944

k

l1wjlv

sijl i isinM j isin N l isin K (14)

In the constructed comprehensive perceived utilitymatrix the larger vb

ij and vsij the higher the satisfaction of

both suppliers and demanders

323 Construction of Supply-Demand Matching ModelBased on the Perceived Utility Set xij represents a 0-1variable where xij 0 represents that tenant Ti and land-lord Lj do not match while xij 1 represents that tenant Ti

and landlord Lj match According to the comprehensiveperceived utility matrices V and Vprime under the requirementof stable matching the following two-objective optimizationmodel can be established to maximize the comprehensiveperceived utility of suppliers and demanders

max Z1 1113936m

i11113936n

j1vb

ijxij i isinM j isin N (15a)

max Z2 1113936m

i11113936n

j1vs

ijxij i isinM j isin N (15b)

st 1113944m

i1xij le 1 j isin N (15c)

1113944

n

j1xij 1 i isinM (15d)

1113944

n

j1xijrij 1 i isinM (15e)

xij 0 or 1 i isinM j isin N (15f)

Equations (15a) and (15b) are the objective functionsrespectively maximizing the sums of the perceived utilitiesof suppliers and demanders in the final matching resultEquations (15c) and (15d) are the requirements of two-sided matching Equation (15c) is an inequality require-ment because mle n which means that each tenant Ti canmatch at most one landlord Lj Equation (15d) is anequality constraint meaning that each landlord Lj can onlymatch one tenant Ti while equation (15e) is a hardrequirement

In order to realize the multiobjective optimizationmodel and maximize the overall matching degree betweensuppliers and demanders the linear weighting method canbe used to weigh equations (15a) and (15b) w1 and w2 arethe weights of Z1 and Z2 respectively to satisfy0lew1 w2 le 1 and w1 + w2 1 Considering the fairness ofthe suppliers and demanders this paper provides thatw1 w2 05 and the two-objective model (15a)ndash(15f ) canbe transformed into a single-objective optimization model(16a)ndash(16e)

max Z 05Z1 + 05Z2 (16a)

st 1113944m

i1xij le 1 j isin N (16b)

1113944

n

j1xij 1 i isinM (16c)


1113944

n

j1xijrij 1 i isinM (16d)

xij 0 or 1 i isin N j isinM (16e)is single-objective optimization model will attempt to

apply the improved genetic algorithm given the large scale ofthis studyrsquos two-sided matching and requirements [47 48]

324 Solution Procedure According to the above analysisthe proposed methodrsquos solution procedure for the multi-attribute ORH SADmatching decisionmodel is summarizedas follows

Step 1 collection selection and measurement ofShanghairsquos housing property SAD information from itsonline rental platforms using a web crawlerStep 2 calculation of the profit and loss matrices ofSAD based on equations (1)ndash(7)Step 3 calculation of the normative profit and lossmatrices of SAD based on equations (8) and (9)Step 4 calculation of the perceived utility matrix ofSAD based on equations (11) and (12)Step 5 calculation of the comprehensive perceivedutility matrix of SAD based on equations (13) and (14)followed by the conversion of the multiobjective op-timization model to a single-objective optimizationmodel based on the comprehensive perceived utilitymatrix in equations (15a)ndash(15f) and (16a)ndash(16e)Step 6 solving the optimization model in equations(16a)ndash(16e) to obtain the optimal matching pairs ofonline rental platformsrsquo SAD sides using a geneticalgorithm

33 Data and Measurements is section includes threesections First we introduce the background of the Shanghairental housing market and explain why it is suitable fortesting our study Second we introduce the data set which isfrom Shanghairsquos current online rental platforms ird weintroduce the selection and measurement of multiattributeindicators

331 Background of Shanghairsquos Rental Housing MarketShanghai is one of Chinarsquos four municipalities It is locatedin the east of China at the mouth of the Yangtze River and isthe leading city in the Yangtze River Economic Belt In 2017Shanghai was organized by 16 districts and counties asshown in Figure 3 including Huangpu Xuhui ChangningJingan Hongkou Yangpu Minhang Baoshang Jiading andPudong By the end of 2018 the total population of Shanghaihad reached 2424 million of which 976 million was thefloating population ranking the highest in the country

Since 1980 Chinarsquos housing market has been dominatedby sales while the rental market developed slowly Howeverwith the acceleration of Chinarsquos urbanization processmdashapowerful means of regulating urban real estate retaining theworking population and attracting new talentsmdashthe rental

housing market has become an important part of deepeningthe reform of the housing system and an important way toachieve the goal of improving urban residentsrsquo quality of lifeShanghai as Chinarsquos largest economic center city attracts alarge floating population Since 2011 Shanghairsquos permanentmigrant population has remained above 96 million per yearwhich accounts for more than 40 of the total residentpopulation as shown in Figure 4 is huge population sizehas resulted in an increase in living demands erefore thedevelopment of Shanghairsquos rental housing market requiresurgent attention

In July 2017 Chinarsquos Ministry of Housing and Con-struction and nine other departments jointly issued theldquoNotice on Accelerating the Development of Housing RentalMarket in Large- and Medium-sized Cities with Net Pop-ulation Inflowrdquo requiring large- andmedium-sized cities witha net inflow of population to set up government-backed rentalhousing service platforms erefore Shanghai now has apublic house leasing service platform In addition to thisShanghai has many private online leasing platforms in-cluding Lianjiacom Anjuke and Fangtianxia Many peopleuse these platforms to find listings Online platforms candisplay a variety of information about the listed propertysuch as the number of rooms the size of the property thedegree of decoration and the housing facilitiese platformsalso include some rent-seeking information which helpsmatch the SAD sideserefore Shanghai is a suitable samplefor testing the model constructed in this study

332 Data Collection Using the Python web crawlertechnology on May 13th 2019 we performed a crawlingexercise on 21762 articles from the current mainstreamonline rental platforms like Shanghairsquos housing leasingpublic service platform Anjuke Lianjia and Fangcom Atthe same time we collected 1739 and 929 rent-seekingmessages from 58com and Weibo respectively and ob-tained 1226 effective massages after manually deletingunrelated data e keywords used for detecting unrelateddata included ldquoI am an ownerrdquo ldquoI am an intermediaryrdquoldquocommercialrdquo ldquoshoprdquo ldquorent outrdquo ldquoofficerdquo and ldquoofficebuildingsrdquo e origins of the final data are spread across 15of Shanghairsquos 16 districts e workflow used to crawl rent-seeking information on 58com is shown in Figure 5According to the crawled rent-seeking information shown inTable 2 there is a high degree of similarity between thehousing attribute indicators considered by the potentialtenants e frequencies of the feature words related tohousing area decoration rental price appliances trans-portation and so on are relatively high Given thatShanghairsquos floating population has a relatively high demandfor rental housing and that the consideration factors arerelatively complete in the transaction it appears that thecollected rent-seeking information is adequately represen-tative with a strong reference for other cities as well

333 Selection and Measurements of MultiattributeIndicators Word frequency can reflect the importance of aword in different contexts or expressions e higher the


word frequency the more important it is With the afore-mentioned Python crawled rent-seeking messages from theldquoPersonalized needsrdquo page of 58com and the commentsfrom Weiborsquos ldquoShanghai Rent-seekingrdquo page this paperemploys a word cloud to display the top 50 words related toproperty characteristics (shown in Figure 6) e top three

words are ldquonearrdquo ldquorentrdquo and ldquodecorationrdquo followed byldquosubwayrdquo ldquofurniturerdquo ldquohome appliancesrdquo and ldquosingle roomrdquoe search term ldquoNearrdquo reflects the requirements of thehousing location while ldquoSubwayrdquo indicates a requirement forproximity to public transportatione characteristic value ofldquorentrdquo reflects the demand for renting a house ldquoRoomrdquo

Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu

HuangpuXuhuiChangningJinganPutuoHongkou

Yangpu

MinhangBaoshangJiadingPudongJinshang

SongjiangQingpuFengxianChongming

0 4020Miles

EW

S

N

Figure 3 Administrative divisions of Shanghai in 2017

1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500

Household populationMigrant population

Figure 4 Population structure of Shanghairsquos permanent residents 2011ndash2018 (unit 10000)


indicates a requirement for a living room ldquoDecorationrdquoldquoFurniturerdquo and ldquoappliancesrdquo are requirements for the aes-thetics furniture and amenities of the house

Although a word frequency analysis can reflect thepersonalized needs of the tenant by extracting high-fre-quency words it cannot reflect the connections between

those words However a semantic network analysis canvisually display the relationship between elements by con-structing a semantic relationship network map [49]erefore for this study we performed a text analysis of thecrawled information using ROSTCM6 software First thecrawled rent-seeking information was processed throughword segmentation Second the high-frequency words wereextracted and the meaningless words were filtered then theline feature words were extracted to generate VNA files andwe then imported them into NetDraw software to constructa co-occurrence matrix Finally the semantic relationshipnetwork map (shown in Figure 7) of the rent-seeking in-formation was generated As seen in Figure 7 ldquonearrdquo ldquorentrdquoldquodecorationrdquo ldquoappliancesrdquo and ldquosubwayrdquo are the centralnodes of the entire network reflecting the similarity of dif-ferent tenants in selecting online rental houses Compre-hensively tenants conduct a systematic investigation ofoverall quality when searching rental houses On the onehand in terms of location and proximity to transportationtenants share similar requirements reflected by the ldquosubwayrdquoldquotrafficrdquo and ldquonearrdquo nodes On the other hand in terms of theoverall quality of the houses tenants require properties withfacilities as reflected by the ldquoappliancesrdquo ldquofurniturerdquo andldquokitchenrdquo nodes In fact these characteristic words reflect thereal needs of tenants when choosing a rental house onlineHowever both SAD sides of ORH include institutions andorindividuals thus the transaction takes place between unfa-miliar entities In such a case the authenticity of housing andthe construction of the social credit system are significant forthe smooth operation of platforms [50] erefore this studyanalyzed the word cloud maps and semantic network mapsand finally selected seven attributes district traffic conve-nience rent living room house supporting facilities deco-ration and online ratings ese seven indicators of thecrawled listing and rent-seeking information were thenquantified separately as shown in Table 3

e entropy weight method is effective for calculatingthe weight and objective orderings of multiattribute indi-cators by applying information entropy [51] e smaller theinformation entropy of the indicator the larger the amountof information provided Similarly the greater the entropyrsquosrole in the comprehensive evaluation the higher the weightus the paper uses the entropy weight method to calculateweight For the tenants it is necessary to pay attention to theseven attributes of area transportation convenience rentliving room housing matching decoration and onlineratings Regarding their types location is a hard require-ment living room house matching and decoration arebenefit requirements while rent and transportation con-venience are cost requirements eir weight values are w1

0302 w2 0137 w3 0193 w4 0074

w5 0162 w6 0038 and w7 0094 For the landlordsthe main focus is location and rent In this paper the weightvalues of both attributes are 05 for fairness

4 Results and Discussion

41 Results For the construction of the model first werandomly selected 50 of the 1226 tenants whose information

Table 2 Tenantrsquos rent-seeking information frequency of featurewords (top 30)

Feature words FrequencyNear 186House 137Decoration 124Clean 113Furniture 109Subway 106Rent 94One room 94Home appliances 93Traffic 80Hardcover 80Personal 78Subway station 67Price 63Cooking 63Tidy 60Within 60Share 57Two rooms 57Paperback 56Landlord 56Elevator 53Consider 52Budget 52Distance 52Facility 52Apartment 48Traffic 45Complete 41Health 41

Start

Initial URL

Check if thereis a next page

Fetch the list ofsublinks for the

current page

N

Loop crawlsublink

information

End

Figure 5 Workflow for crawling rent-seeking information on 58com


was crawled then according to their needs 50 landlordswere selected Second each attribute index was measurede landlordrsquos evaluation values of the housing attributes areshown in Table 4 while the tenantsrsquo expectation values ofhousing attributes are shown in Table 5ird the profit andloss matrices the standardized profit and loss matrices theperceived utility matrices and the comprehensive perceivedutility matrices of the SAD were calculated using Matlab2016 software e specific steps of the calculations are asfollows

Step 1 according to Table 3 the landlordsrsquo evaluationvalues of the housing attributes and the tenantsrsquo ex-pectation values of the housing attributes were mea-sured (as shown in Tables 4 and 5 respectively)

Step 2 by using equations (1)ndash(7) the landlordsrsquo profitand loss matrices Fl [aijl]50times50 and the tenantsrsquo profitand loss matrices Dl [dijl]50times50 for location andtransportation convenience were calculated (as shownin Tables 6 and 7 and Tables 8 and 9 respectively) eremaining tenantsrsquo profit and loss matrices are shownin AppendixStep 3 based on the landlordsrsquo and tenantsrsquo profit andloss matrices and by using equations (8) and (9) thelandlordsrsquo normative profit and loss matricesFlprime [aijlprime ]50times50 were calculated (as shown in Tables 10

and 11) and the tenantsrsquo profit and loss matrices Dlprime

[dijlprime ]50times50 for location and transportation convenience

were also calculated (as shown in Tables 12 and 13)e

Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen

Figure 7 Semantic relationship network map of rent-seeking information

Figure 6 Word cloud diagram of rent-seeking information results


Table 3 Measurement of multiattribute indicators

Variable name Original value of the variable Variable type Quantitative value ofthe variable

Location (C1)Huangpu Jingan Xuhui Pudong Changning Hongkou YangpuPutuo Minhang Baoshang Jiading Qingpu Fengxian Jinshan

Songjiang

Characterclassification

Assign 1 to 15respectively

Transportationconvenience (C2)

It is (1) within 500 meters from the subway (2) between 500 and1000 meters away (3) 1000ndash1500 meters away (4) 500ndash2000 meters

away and (5) 2000 meters and above away



Rent (C3) Rent value Numericalquantification mdash

Living room (C4) One room to four or more rooms Characterclassification


Appliances (C5)No simple furniture home appliances basic configuration

complete equipment full-fitCharacter

classificationAssign 1 to 5respectively

Decoration degree (C6)Blank simple decoration medium decoration fine decoration

luxury decorationCharacter


Online ratings (C7) Low average good excellent excellent Characterclassification


Table 4 Landlordsrsquo evaluation values of housing attributes

Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4

Table 5 Tenantsrsquo expectation values of housing attributes

Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5

Table 6 Profit and loss matrix F1 [aij1]50times50 for landlordsrsquohousing location

aij1 L1 L2 L3 middot middot middot L48 L49 L50

T1 1 1 0 middot middot middot 0 0 0T2 1 1 0 middot middot middot 0 0 0T3 1 1 0 middot middot middot 0 0 0⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 0 0 0 middot middot middot 0 0 1T49 0 0 0 middot middot middot 0 0 1T50 0 0 0 middot middot middot 0 0 1

Table 7 Profit and loss matrix F2 [aij2]50times50 for landlordsrsquohousing rent


T1 minus 00349 00000 00000 middot middot middot minus 01552 00000 minus 01923T2 minus 00581 minus 00250 00000 middot middot middot minus 01724 00000 minus 02077T3 00000 00000 00000 middot middot middot 00000 00000 00000⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 minus 02442 minus 02250 minus 01563 middot middot middot minus 03103 minus 01563 minus 03308T49 minus 00930 minus 00625 00000 middot middot middot minus 01983 00000 minus 02308T50 00000 00000 00000 middot middot middot 00000 00000 00000

Table 8 Profit and loss matrix D1 [dij1]50times50 for tenantsrsquo housinglocation

dij1 L1 L2 L3 middot middot middot L48 L49 L50


Table 9 Profit and loss matrix D2 [dij2]50times50 for tenantsrsquotransportation convenience


T1 minus 1 minus 1 minus 1 middot middot middot minus 1 minus 3 minus 3T2 0 0 0 middot middot middot 0 minus 2 minus 2T3 0 0 0 middot middot middot 0 minus 2 minus 2⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮T48 1 1 1 middot middot middot 1 minus 1 minus 1T49 1 1 1 middot middot middot 1 minus 1 minus 1T50 1 1 1 middot middot middot 1 minus 1 minus 1


remaining tenantsrsquo normative profit and loss matricesare given in AppendixStep 4 the perceived utility matricesVs

l [vsijl]50times50 and

Vbl [vb

ijl]50times50 of the landlords and tenants respec-tively were calculated using equations (11) and (12)e landlordsrsquo perceived utility matrices Vs

l [vsijl]50times50

are shown in Tables 14 and 15 while the tenantsrsquoperceived utility matrices Vs

l [vsijl]50times50 for house

location and transportation convenience are shown inTables 16 and 17 e remaining perceived utilitymatrices for the tenants are given in AppendixStep 5 the landlordsrsquo and tenantsrsquo comprehensiveperceived utility matrices Vprime [vs

ij]50times50 andV [vb

ij]50times50 receptively were calculated usingequations (13) and (14) as shown in Tables 18 and 19

Table 10 Normative profit and loss matrix F1prime [aij1prime]50times50 forlandlordsrsquo housing location

aij1prime L1 L2 L3 middot middot middot L48 L49 L50


Table 11 Normative profit and loss matrix F2prime [aij2prime]50times50 forlandlordsrsquo housing rent



Table 12 Normative profit and loss matrix D1prime [dij1prime]50times50 fortenantsrsquo housing location

dij1prime L1 L2 L3 middot middot middot L48 L49 L50


Table 13 Normative profit and loss matrix D2prime [dij2prime]50times50 fortenantsrsquo transportation convenience


T1 minus 025 minus 025 minus 025 middot middot middot minus 025 minus 075 minus 075T2 0 0 0 middot middot middot 0 minus 05 minus 05T3 0 0 0 middot middot middot 0 minus 05 minus 05⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 025 025 025 middot middot middot 025 minus 025 minus 025T49 025 025 025 middot middot middot 025 minus 025 minus 025T50 025 025 025 middot middot middot 025 minus 025 minus 025

Table 14 Perceived utility matrix Vs1 [vs

ij1]50times50 for landlordsrsquohousing location

vsij1 L1 L2 L3 middot middot middot L48 L49 L50



ij2]50times50 for landlordsrsquohousing rent



Table 16 Perceived utility matrix Vb1 [vb

ij1]50times50 for tenantsrsquohousing location

vbij1 L1 L2 L3 middot middot middot L48 L49 L50



ij2]50times50 for tenantsrsquotransportation convenience




According to the landlordsrsquo and tenantsrsquo comprehensiveperceived utility matrices the multiobjective optimizationmodel equation (17) was constructed as follows

max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)

Transforming the above multiobjective optimizationmodel to a single-objective optimization model(equation (18)) was done as follows

max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)

Step 6 the optimization model in equation (18) wassolved using a genetic algorithme derived matchingresults are shown in Table 20

As shown in Table 20 all tenants and landlords formedmatching pairs is not only shows matching results thatare satisfactory to both sidesmdashwith an overall satisfactionvalue of the matching results of Z 42374mdashbut also showsan improvement in matching efficiency at is the methodreduces matching costs and time for both SAD ereforethe SAD matching method for ORH proposed in this studycan provide reference to the multiattribute two-sidedmatching decision method and a basis for cracking the ORHSAD matching problem which is characterized by multi-agents and multilevel supply e rationality and effec-tiveness of this method given the multiple attributes ofhousing and both SAD sidesrsquo perceived utility have beenproved in matching the SAD of ORH

In this study a genetic algorithm is used to solve the finalmatching result of the model e population evolutioncurve of the genetic algorithm is shown in Figure 8 Asshown in the figure when the population evolves to 200generations the objective function value reaches the optimalvalue and overall stability In addition the total running timeof the algorithm is 878202 seconds which is very shortWhen the scale of the problem is large it is very feasible toapply genetic algorithms to solve the problem of matchingSAD of online rental housing

42 Discussion

421 Impact of the Weight of SAD During the transactionbetween the SAD sides the weights may not be fair whichmay cause the matching result to be inconsistent with theactual situation To further verify the rationality and com-prehensiveness of the algorithm we verified the weight ofthe SAD double from 0 to 1 respectively As shown inFigure 9 the overall satisfaction of the SAD sides increasedas the weight of the landlord increased but the opposite istrue for the tenants is may be because landlords havefewer housing attributes to consider during the transactionmatching process

422 Impact of the Number of SAD For online housingplatforms the number of SAD sides may be unequal and itmay be a situation where suppliers exceed demanderserefore to further verify the effectiveness of themodel andalgorithm we attempted to calculate a situation in which thesuppliers exceed demanders and added 5 pieces of rentalinformation for calculation It was found that when mle nthe overall satisfaction of both SAD sides became largerZ 43832 which was 01458 higher than the satisfactionvalue when m n is may be caused by some tenantsmatching with more suitable landlords making the satis-faction value higher e influence of the SAD quantities onthe overall satisfaction value Z is shown in Figure 10 Insummary this model is applicable in matching the supplyand demand of ORH

Table 18 Comprehensive perceived utility matrixVprime [vsij]50times50 of

landlords

vsij L1 L2 L3 middot middot middot L48 L49 L50

T1 00961 01000 00000 middot middot middot minus 00170 00000 minus 00210T2 00936 00972 00000 middot middot middot minus 00189 00000 minus 00226T3 01000 01000 00000 middot middot middot 00000 00000 00000⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 minus 00265 minus 00245 minus 00171 middot middot middot minus 00335 minus 00171 00644T49 minus 00103 minus 00069 00000 middot middot middot minus 00216 00000 00749T50 00000 00000 00000 middot middot middot 00000 00000 01000

Table 19 Comprehensive perceived utility matrix V [vbij]50times50 of

tenants

vbij L1 L2 L3 middot middot middot L48 L49 L50

T1 00514 00544 minus 00074 middot middot middot 00088 00045 minus 00017T2 00724 00750 00148 middot middot middot 00294 00260 00180T3 00616 00621 00012 middot middot middot 00291 00147 00209⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 00062 00094 00162 middot middot middot 00197 00275 00658T49 00024 00056 00073 middot middot middot 00211 00199 00694T50 minus 00264 minus 00250 minus 00264 middot middot middot minus 00003 minus 00151 00515


Overall from the analysis of the results the weightsoccupied by the SAD affected the overall satisfaction valuebut had no effect on the final matching result In additionthis model is applicable when the supply is equal to thedemand or the supply is greater than the demandis studyimproves the two-sided matching theory and extends it tothe online leasing market to provide matching efficiencybetween the SAD sides [1]

423 Comparison with Other Methods e method pro-posed in this study may have some differences comparedwith other methodsWith regard to model application someliterature studies have applied matching methods to fieldssuch as hospital diagnosis carpool matching job and per-sonnel matching electronic market matching electric powerretailer and buyer matching and technology marketmatching However application in the rental housingmarket is limited From the perspective of model quantifi-cation methods some scholars quantify the satisfactionvalues of the SAD based on fuzzy sets triangular intui-tionistic fuzzy numbers and gray correlation analysis butthese methods do not consider the psychological behavior ofparticipants erefore we quantify the perceived utilityvalue of the SAD sides based on the disappointment theorystarting from the perceptions of the SAD sides which are

Table 20 Matching results of the multiattribute SAD matchingdecision model of ORH

Number Results1 (T1 L2)

2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)

Best ndash423742 mean ndash159

ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation

Best fitnessMean fitness

(a)

0

05

1

15

2

25

3

35

4

45

Z

100 200 300 400 500 6000Number of iterations

(b)

Figure 8 Genetic algorithm evolution curve (a) Number of it-erations (b) Fitness function


36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant

Figure 9 Influence of the weight of the SAD on the overall sat-isfaction value Z

0

05

1

15

2

25

3

35

4

45

Z


m = nm le n

Figure 10 Influence of the number of the SAD on the overallsatisfaction value Z

Table 21 Profit and loss matrix D3 [dij3]50times50 for tenantsrsquohousing rent



Table 24 Profit and loss matrix D6 [dij6]50times50 for tenantsrsquohousing decoration degree



Table 22 Profit and loss matrix D4 [dij4]50times50 for tenantsrsquo livingroom


T1 0 0 0 middot middot middot 2 2 2T2 0 0 0 middot middot middot 2 2 2T3 minus 1 minus 1 minus 1 middot middot middot 1 1 1⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 0 0 0 middot middot middot 2 2 2T49 minus 1 minus 1 minus 1 middot middot middot 1 1 1T50 minus 2 minus 2 minus 2 middot middot middot 0 0 0

Table 23 Profit and loss matrix D5 [dij5]50times50 for tenantsrsquohousing matching



Table 26 Normative profit and loss matrix D3prime [dij3prime]50times50 fortenantsrsquo housing rent



Table 25 Profit and loss matrix D7 [dij7]50times50 for tenantsrsquohousing online ratings


T1 0 1 0 middot middot middot minus 1 minus 1 0T2 1 2 1 middot middot middot 0 0 1T3 2 3 2 middot middot middot 1 1 2⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 2 3 2 middot middot middot 1 1 2T49 1 2 1 middot middot middot 0 0 1T50 minus 1 0 minus 1 middot middot middot minus 2 minus 2 minus 1


highly significant for improving the overall matchingsatisfaction

ematching decision method for second-hand housingtransactions [41] and the two-sided matching decisionmethod for second-hand housing which considers theonline rentalsale matching attribute association [36] aretwo relatively close cases Regarding thematching algorithmHaaimin [41] designed an extended H-R algorithm thatconsiders that the stability of the matching scheme and thecomputational workload is large when obtaining matching

Table 27 Normative profit and loss matrix D4prime [dij4prime]50times50 fortenantsrsquo living room


T1 0 0 0 middot middot middot 1 1 1T2 0 0 0 middot middot middot 1 1 1T3 minus 05 minus 05 minus 05 middot middot middot 05 05 05⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮T48 0 0 0 middot middot middot 1 1 1T49 minus 05 minus 05 minus 05 middot middot middot 05 05 05T50 minus 1 minus 1 minus 1 middot middot middot 0 0 0

Table 28 Normative profit and loss matrix D4prime [dij4prime]50times50 fortenantsrsquo housing matching



Table 29 Normative profit and loss matrix D6prime [dij6prime]50times50 fortenantsrsquo housing decoration degree


T1 00000 minus 03333 00000 middot middot middot 00000 00000 00000T2 03333 00000 03333 middot middot middot 03333 03333 03333T3 03333 00000 03333 middot middot middot 03333 03333 03333⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮T48 03333 00000 03333 middot middot middot 03333 03333 03333T49 06667 03333 06667 middot middot middot 06667 06667 06667T50 03333 00000 03333 middot middot middot 03333 03333 03333


ij4]50times50 for tenantsrsquoliving room



Table 30 Normative profit and loss matrix D7prime [dij7prime]50times50 fortenantsrsquo housing online ratings




ij3]50times50 for tenantsrsquohousing rent




ij7]50times50 for tenantsrsquohousing online ratings




ij5]50times50 for tenantsrsquohousing matching




ij6]50times50 for tenantsrsquohousing decoration degree




results Wang et al [36] used the min-max method and usesLINGO software to solve the matching scheme Althoughthis method is simple and easy to operate it is not suitablefor large-scale two-sided matching problems For the sat-isfaction of both SAD Haaimin [41] ignored the psycho-logical characteristics of misfortunes to avoid losses andmaximize advantages However the current multiattributetwo-sided matching decision model can maximize the sat-isfaction of SAD Meanwhile not only does the geneticalgorithm applied in this study solve the large-scale two-sided matching problem but also has a short running timewhich can quickly and effectively promote effectivematching between SAD

5 Conclusions and Implication

In this study an ORHmultiattribute SADmatching decisionmodel based on the perceived utility is constructed ismodel determines the multiattribute indicators and pro-portions of housing that both SAD sides are interested in Byconsidering the psychological expectations of both SAD inmeasuring the perceived utility values this model maximizesthe overall satisfaction of both SAD Finally using Shang-hairsquos online rental and demand information a genetic al-gorithm is used to numerically analyze and solve the modelwhich not only obtains optimal matching results but alsoproves that the genetic algorithm can solve a large two-sidedmatching problem is model enriches the application ofdouble-sided matching theory and provides a referencemethod for online rental SAD matching At the same timethis model considers that the psychological perceptions ofthe SAD sides can maximize their overall satisfaction andpromote the matching accuracy of the model

In the context of ldquoInternet +rdquo and big data the effectivematching of online rental lists is of great implication forpromoting the effective operation of the rental housingmarket In a theoretical sense this study enriches the re-search on rental housing with particular application forrental platforms providing a new perspective for the de-velopment of rental platforms In addition it can be appliedto the rental housing markets of other cities Objectively themodel improves the effective docking of SAD and improvesthe supply sidersquos efficiency Subjectively the enthusiasm forSAD interaction is realized erefore this study has areference basis for promoting the effective matching ofonline SAD and the improvement of satisfaction of bothSAD

As with any study the article at hand suffers from severallimitations that are worth considering in further researchFirstly the method proposed in this study improves theoverall matching between the SAD but it needs to be furthercompared with other decision-making methods Such as inthe future we will further study to compare it with othermethods that actually produce results Second because theeconomic and social backgrounds of each SAD subject aredifferent the characteristic variables of the SAD matchingdecision model in different cities may be different In thefuture we will adjust the multiattribute equations andquantitative standards according to the characteristics of

different cities In addition the actual practice results shouldbe used to verify the SAD matching decision model indifferent cities to promote the sustainable development ofthe rental housing market

Furthermore in the transaction process of the ORHplatforms the multiattribute expectations of both partiesshould be considered Regardless of the tenants or landlordseach subject considers their own subjectrsquos interests based onmultiple values which will directly or indirectly reflect theexpected value of the property Moreover the supply side ofthe rental housing market should increase the informationsymmetry of SAD subjects to ensure that the information istransparent and open and that the transaction process isstandardized guaranteeing easy access to information forboth parties

Appendix

e remaining profit and loss matrices for tenants are givenin Tables 21ndash25 respectively

e remaining normative profit and loss matrices fortenants are given in Tables 26ndash30 respectively

e remaining perceived utility matrices for tenants aregiven in Tables 31ndash35 respectively

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is research was supported by the National Key RampDProgram of China (grant no 2018YFD1100202) the Min-istry of Education Humanistic and Social Science Programof China (grant no 19YJC630080) the General Project ofShaanxi Province Soft Science Research Program (grant no2019KRM197) the Philosophy and Social Science ResearchProgram of Education Department of Shaanxi Province(grant no12JK0070) and the Shaanxi Social Science FundGeneral Project (grant no 2015R006)

References

[1] A G Sharam ldquoDisruption and the matching market for newmultifamily housing in Melbourne Australiardquo Journal ofGeneral Management vol 44 no 3 pp 160ndash169 2019

[2] A F A Saleh T K Hwa and R Majid ldquoHousing mismatchmodel in suburban areasrdquo ProcediamdashSocial and BehavioralSciences vol 234 pp 442ndash451 2016

[3] G Boeing J Wegmann and J Jiao ldquoRental housing spotmarkets how online information exchanges can supplementtransacted-rents datardquo Journal of Planning Education andResearch 2020

[4] K A Kholodilin ldquoQuantifying a century of state interventionin rental housing in Germanyrdquo Urban Research amp Practicevol 10 no 3 pp 267ndash328 2017


[5] O O Makinde ldquoHousing delivery system need and demandrdquoEnvironment Development and Sustainability vol 16 no 1pp 49ndash69 2014

[6] Z Z Jin Lang ldquoProblems and development countermeasuresof Chinarsquos housing leasing marketrdquo Macroeconomic Man-agement vol 3 pp 80ndash85 2018

[7] L Li L Feng X Guo H Xie and W Shi ldquoComplex networkanalysis of transmission mechanism for sustainable incentivepoliciesrdquo Sustainability vol 12 no 2 p 745 2020

[8] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol E102D no 7 pp 1374ndash1383 2019

[9] A Manduchi A Petreski and A Stephan ldquoMarket forapartment swap and rental marketrdquo SSRN Electronic Journal2019

[10] S Zhou H Sun T Guan and T Li ldquoEquilibrium model ofhousing choice for heterogeneous households under publicrental housing policyrdquo Sustainability vol 10 no 12 p 45052018

[11] J Liu Y Zhan and X Ma Research on Demand of Replacingto Public Rental Housing Tenants in Chongqing SpringerBerlin Germany 2017

[12] X Sun and K P Tsang ldquoWhat drives the owner-occupied andrental housing markets Evidence from an estimated DSGEmodelrdquo Journal ofMoney Credit and Banking vol 49 no 2-3pp 443ndash468 2017

[13] H Fu M Wang P Li et al ldquoTracing knowledge developmenttrajectories of the Internet of things domain a main pathanalysisrdquo IEEE Transactions on Industrial Informatics vol 15no 12 pp 6531ndash6540 2019

[14] E Lopez and D Paredes ldquoTowards housing policies thatconsider householdrsquos preferences estimating the demand forhousing attributes in Chilerdquo International Journal of StrategicProperty Management vol 24 no 1 pp 24ndash36 2018

[15] W C Wheaton ldquoVacancy search and prices in a housingmarket matching modelrdquo Journal of Political Economyvol 98 no 6 pp 1270ndash1292 1990

[16] N Meng and X Xu ldquoResearch on customer attention ofonline short-term rental platformrdquo in Proceedings of the 2018IEEE 3rd Advanced Information Technology Electronic andAutomation Control Conference (IAEAC) pp 2455ndash2459IEEE Chongqing China October 2018

[17] A Tversky and D Kahneman ldquoLoss aversion in risklesschoice a reference-dependent modelrdquo (e Quarterly Journalof Economics vol 106 no 4 pp 1039ndash1061 1991

[18] D Kahneman ldquoA perspective on judgment and choicemapping bounded rationalityrdquo American Psychologist vol 58no 9 pp 697ndash720 2003

[19] G Gigerenzer ldquoMoral satisficing rethinking moral behavioras bounded rationalityrdquo Topics in Cognitive Science vol 2no 3 pp 528ndash554 2010

[20] J F de Medeiros J L D Ribeiro and M N CortimiglialdquoInfluence of perceived value on purchasing decisions ofgreen products in Brazilrdquo Journal of Cleaner Productionvol 110 pp 158ndash169 2016

[21] D E Bell ldquoDisappointment in decision making under un-certaintyrdquo Operations Research vol 33 no 1 pp 1ndash27 1985

[22] G Loomes and R Sugden ldquoDisappointment and dynamicconsistency in choice under uncertaintyrdquo (e Review ofEconomic Studies vol 53 no 2 pp 271ndash282 1986

[23] A B Makar K E McMartin M Palese and T R TephlyldquoFormate assay in body fluids application in methanol

poisoningrdquo Biochemical Medicine vol 13 no 2 pp 117ndash1261975

[24] P Delquie and A Cillo ldquoDisappointment without prior ex-pectation a unifying perspective on decision under riskrdquoJournal of Risk and Uncertainty vol 33 no 3 pp 197ndash2152006

[25] K C Cheung W F Chong and S C P Yam ldquoe optimalinsurance under disappointment theoriesrdquo InsuranceMathematics and Economics vol 64 pp 77ndash90 2015

[26] R Zhao M Jin P Ren and Q Zhang ldquoStable two-sidedsatisfied matching for ridesharing system based on preferenceordersrdquo (e Journal of Supercomputing vol 76 no 2pp 1063ndash1081 2020

[27] J Quan X Wang and Y Quan ldquoEffects of consumersrsquostrategic behavior and psychological satisfaction on the re-tailerrsquos pricing and inventory decisionsrdquo IEEE Access vol 7pp 178779ndash178787 2019

[28] Z Zhang X Kou I Palomares W Yu and J Gao ldquoStabletwo-sided matching decision making with incomplete fuzzypreference relations a disappointment theory based ap-proachrdquo Applied Soft Computing vol 84 Article ID 1057302019

[29] Z-P Fan M-Y Li and X Zhang ldquoSatisfied two-sidedmatching a method considering elation and disappointmentof agentsrdquo Soft Computing vol 22 no 21 pp 7227ndash72412018

[30] A E Roth ldquoCommon and conflicting interests in two-sidedmatching marketsrdquo European Economic Review vol 27 no 1pp 75ndash96 1985

[31] D Gale and L S Shapley ldquoCollege admissions and the sta-bility of marriagerdquo (e American Mathematical Monthlyvol 69 no 1 pp 9ndash15 1962

[32] F Kojima and P A Pathak ldquoIncentives and stability in largetwo-sided matching marketsrdquo American Economic Reviewvol 99 no 3 pp 608ndash627 2009

[33] L Tan W Su S Gao J Miao Y Cheng and P Cheng ldquoPath-flow matching two-sided matching and multiobjective evo-lutionary algorithm for traffic scheduling in cloud date centernetworkrdquo Transactions on Emerging TelecommunicationsTechnologies 2019

[34] C-H Chen ldquoA cell probe-based method for vehicle speedestimationrdquo IEICE Transactions on Fundamentals of Elec-tronics Communications and Computer Sciences vol E103Ano 1 pp 265ndash267 2020

[35] Y Lin Y-M Wang and K-S Chin ldquoAn enhanced approachfor two-sided matching with 2-tuple linguistic multi-attributepreferencerdquo Soft Computing vol 23 no 17 pp 7977ndash79902019

[36] R Wang D Li and G Yu ldquoResearch on bilateral matchingdecision method considering attribute association in het-erogeneous information environmentrdquo Journal of Intelligentamp Fuzzy Systems vol 38 no 4 pp 4779ndash4792 2020

[37] T Gao M Huang Q Wang et al ldquoA systematic model ofstable multilateral automated negotiation in e-market envi-ronmentrdquo Engineering Applications of Artificial Intelligencevol 74 pp 134ndash145 2018

[38] Y Kong W Huang and B Li ldquoe supply and demandmechanism of electric power retailers and cellular networksbased on matching theoryrdquo Information vol 9 no 8 p 1922018

[39] B Xia S Shakkottai and V Subramanian ldquoSmall-scalemarkets for a bilateral energy sharing economyrdquo IEEETransactions on Control of Network Systems vol 6 no 3pp 1026ndash1037 2019


[40] Y Yang S Luo J Fan X Zhou C Fu and G Tang ldquoStudy onspecialist outpatient matching appointment and the balancematching modelrdquo Journal of Combinatorial Optimizationvol 37 no 1 pp 20ndash39 2019

[41] H M Liang and Y P Jiang ldquoDecision-making method onsecond-hand house combination matchingrdquo Systems Engi-neeringmdash(eory amp Practice vol 37 no 2 pp 358ndash367 2015

[42] J Wang B Li W Li and S L Yang ldquoTwo-sided matchingmodel based on cumulative prospect theory for decisionmaking of two-way referral systemrdquo Journal of Interdisci-plinary Mathematics vol 21 no 5 pp 1097ndash1102 2018

[43] X Chen J Wang H Liang J Han and F Systems ldquoHesitantmulti-attribute two-sided matching a perspective based onprospect theoryrdquo Journal of Intelligent amp Fuzzy Systemsvol 36 no 6 pp 6343ndash6358 2019

[44] S Grant and A Kajii ldquoAUSI expected utility an anticipatedutility theory of relative disappointment aversionrdquo Journal ofEconomic Behavior amp Organization vol 37 no 3 pp 277ndash290 1998

[45] C E Laciana and E UWeber ldquoCorrecting expected utility forcomparisons between alternative outcomes a unified pa-rameterization of regret and disappointmentrdquo Journal of Riskand Uncertainty vol 36 no 1 pp 1ndash17 2008

[46] Y Liu and K W Li ldquoA two-sided matching decision methodfor supply and demand of technological knowledgerdquo Journalof Knowledge Management vol 21 no 3 pp 592ndash606 2017

[47] D G McVitie and L B Wilson ldquoStable marriage assignmentfor unequal setsrdquo Bit vol 10 no 3 pp 295ndash309 1970

[48] C-H Chen F Song F-J Hwang L Wu and I ApplicationsldquoA probability density function generator based on neuralnetworksrdquo Physica A Statistical Mechanics and Its Applica-tions vol 541 Article ID 123344 2020

[49] M L Doerfel ldquoWhat constitutes semantic network analysisA comparison of research and methodologiesrdquo Connectionsvol 21 no 2 pp 16ndash26 1998

[50] L Lalicic and C Weismayer ldquoe role of authenticity inairbnb experiencesrdquo in Information and CommunicationTechnologies in Tourism pp 781ndash794 Springer ChamSwitzerland 2017

[51] C Qiyue ldquoStructural entropy weight method for determiningindex weightsrdquo Systems Engineeringmdash(eory amp Practicevol 30 pp 1225ndash1228 2017


process [12 13] and that these attributes affect ORH SADmatching [14] For example price floors play a central rolebetween SAD [15] while issues around house matching andcomfort transportation the surrounding environment andlandlord services are specific indicators of tenant concerns[16] Location is also a factor of housing mismatch [2] esize and location of a house are considered to be necessaryconditions for appropriate house matching [14] ereforehousing attributes play a very important role in balancingthe SAD of ORH

Although the aforementioned models proposed by ex-tant studies can reduce the cost of searching in the matchingprocessmdashconsidering that housing multiattribute indicatorsare factors in the SAD matching processmdashthey do notpromote the effective matching of ORH or the improvementof matching satisfaction between the SAD sides In factwhen a matching decision occurs in the actual process mostsubjects are in limited rationality [17] their expected valuesare limited by existing information and their own expec-tations [18 19] us the final matching pair may have ahigher or lower value than the expected value leading tobelow-optimal satisfaction with the matching results Inaddition perceived utility is a product of a demandersrsquoassessment of the services values and functions of the re-quired items compared to their own expectations how theyweigh the perceived benefits and costs and the value theyfinally put on the required items [20] In assessing profit andloss values the theory of disappointment reflects the samedifference between actual and expected results [21] Loomesand Sugden also believed that ldquodisappointmentrdquo and ldquoex-citementrdquo are key factors in making rational choices [22]erefore using disappointment theory to quantify theperceived utility of both SAD can reflect the psychologicalactivities of both sides

In recent years with the acceleration of urbanization thehousing problem of Chinarsquos floating population has becomeincreasingly prominent In 2018 the floating populationreached 241 million of which 210 million required rentalhousing covering an area of 673 billion square meters Inaddition large and medium-sized cities in China are re-quired to build a rental housing platform to promote thematching efficiency of rental housing However the housingrental market is undeveloped and has many problems suchas low supply efficiency lack of diverse supply systems andlow capability to meeting peoplersquos housing demand [6 23]Among them is Shanghai the central city of China with arelatively large annual flow of floating population and a greatdemand for rental housing erefore taking Shanghai asour case study may help understand and reflect the problemsof other cities is is of great significance for promoting thedevelopment of the rental housing market

In online rental housing transactions the real estatenetwork platform involved is a two-sided market thatconnects the SAD sides of rental housing through whichvarious agents interact with one another and the transac-tions cater to the needs of all the users (both SAD)erefore this study attempts to apply the two-sidedmatching theory to the housing rental market To improvethe satisfaction of both SAD sides this study uses

disappointment theory to construct quantitative perceivedutility value matrices First we start by quantifying the utilityof housing as perceived by both SAD sides based on themultiattribute matching characteristics of both sides Sec-ond we construct a multiattribute SAD matching decisionmodel for ORH platforms Finally we adopt online SADinformation from Shanghai China to ensure that themultiattribute information of rental housing has beenidentified and to empirically test the validity and rationalityof the model safeguarding the construction of an innovativemethod for ORH SAD matching

e contributions of this study are twofold First thestudy constructs an effective SADmatchingmodel for onlinerental housing platforms and enriches the application of thetwo-sided matching theory Currently research on two-sided matching is mostly applied in the marriage marketlabor market schools and hospitals but is rarely used in therental housing market especially for application in onlinerental housing service platforms erefore this study un-dertakes to verify the applicability and effectiveness of thetwo-sided matching theory in the rental housing marketis provides a reference and a theoretical method forcracking the SADmatching problem that has plagued onlinerental housing platforms with multisubject and multilevelsupply methods Second the attributes of ORH are deter-mined and measured ese can be easily extended to othercities and online platforms providing reference to thefeasibility of analyzing multiattribute decision-makingmatching problems is also helps to improve the overallsatisfaction and quality of SAD matching efforts by con-sidering the expectations and real values of both SAD sidesIn sum this study is valuable for improving the efficiency ofSAD matching for online platforms as well as the sus-tainable development of the rental housing market

e remainder of this article is arranged as followsSection 2 presents a detailed literature review Section 3introduces the research materials and methods e em-pirical results and discussion are presented in Section 4Finally Section 5 summarizes the conclusions and impli-cations of this study

2 Literature Review

21 Disappointment (eory e disappointment theoryproposed by Bell [21] and Loomes and Sugden [22] is basedon psychological reactions caused by the comparison ofactual results with expectations [24] Fundamentally thedisappointment theory suggests that when actual results arebetter than expected policymakers will be ecstatic whenactual results are worse than expected manufacturers will bedisappointed and that the greater the disparity between theoutcome and the expectation the greater the disappoint-ment [21] So far there are three main contemporary dis-appointment models [25 26] e first is the BellndashLoomesand Sugden disappointment model is model essentiallyquantifies the ldquomodified expected utilityrdquo of human satis-faction in the case of disappointment e second is Gulrsquosdisappointment aversion (DA)model which decomposes theparticipantsrsquo psychological cognition into disappointment










































T1

T2

T3

T4

TP

Expectedattributes

Searchfor


B1

B2

B3

H1

H2

H3

Hn


platform

ORH Landlords

S1

S2

S3

Sn

C2

C3

Ck

C4

C1

Bm



Web crawler method

Data processing












for SAD






attribute of SAD




indicators



attribute of SAD








pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References
































































































T1

T2

T3

T4

TP

Expectedattributes

Searchfor


B1

B2

B3

H1

H2

H3

Hn


platform

ORH Landlords

S1

S2

S3

Sn

C2

C3

Ck

C4

C1

Bm



Web crawler method

Data processing












for SAD






attribute of SAD




indicators



attribute of SAD








pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References
























































































T1

T2

T3

T4

TP

Expectedattributes

Searchfor


B1

B2

B3

H1

H2

H3

Hn


platform

ORH Landlords

S1

S2

S3

Sn

C2

C3

Ck

C4

C1

Bm



Web crawler method

Data processing












for SAD






attribute of SAD




indicators



attribute of SAD








pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References





































































T1

T2

T3

T4

TP

Expectedattributes

Searchfor


B1

B2

B3

H1

H2

H3

Hn


platform

ORH Landlords

S1

S2

S3

Sn

C2

C3

Ck

C4

C1

Bm



Web crawler method

Data processing












for SAD






attribute of SAD




indicators



attribute of SAD








pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References
























































Web crawler method

Data processing












for SAD






attribute of SAD




indicators



attribute of SAD








pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References





























































pij rjl + eil





dijl

0 eil rjl

1 minuspij

eil

eil ltpij lt rjl

1 eil gtpij gt rjl

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(2)




dijl 1 rjl eil

0 rjl ne eil

⎧⎨

⎩


(3)





dijl 0 rjl eil


⎧⎨

⎩


(4)




dijl 0 rjl eil


⎧⎨

⎩


(5)




aijl

0 rjl eil

pij

rjl


1 rjl ltpij lt eil

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


(6)

aijl 1 eil ril

0 eil ne rjl1113896


(7)








dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References





























































dijlprime

dijl

max dijl

11138681113868111386811138681113868


aijlprime

aijl

max aijl

11138681113868111386811138681113868






ijl]mtimesn

and Vsl [vs








vbijl φ dijl


vsijl φ aijl







vbij 1113944

k

l1wilv





vsij 1113944

k

l1wjlv







max Z1 1113936m

i11113936n

j1vb


max Z2 1113936m

i11113936n

j1vs


st 1113944m


1113944

n


1113944

n





max Z 05Z1 + 05Z2 (16a)

st 1113944m


1113944

n



1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References
























































1113944

n
















Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References


























































Pudong

Chongming

Qingpu

Fengxian

Jinshang

Jiading

SongjiangMinxing

Baoshang Chongming

Putuo

Xuhui

YangpuJingan

Changning

HongkouHuangpu


Yangpu



0 4020Miles

EW

S

N


1419 1420 1425 1429 1434 1440 1446 1448

928 960 990 996 982 980 973 976

2011 2012 2013 2014 2015 2016 2017 20180

500

1000

1500

2000

2500








0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References




























































0302 w2 0137 w3 0193 w4 0074






Start

Initial URL



current page

N

Loop crawlsublink

information

End









Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References






























































Hardcover

MediumCommunity

Neat

Complete

Blanks

Simple

Tidy Walk

Convenient

TrafficContact

Minute Clean

Subway

Decoration

Rent

Near

House

Cooking

Room

Appliance

IndependentElevator

ContactFurniture

Floor

Kitchen







Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References



























































Songjiang




















Ln C1 C2 C3 C4 C5 C6 C7

L1 1 2 4300 1 4 4 4L2 1 2 4000 1 4 3 5L3 2 2 3200 1 4 4 4L4 2 2 3000 1 3 3 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮L47 10 1 6500 3 4 4 4L48 11 2 5800 3 4 4 3L49 14 4 3200 3 4 4 3L50 15 4 6500 3 4 4 4


Tm C1 C2 C3 C4 C5 C6 C7

T1 1 1 4000 1 4 4 4T2 1 2 3800 1 3 3 3T3 1 2 6500 2 4 3 2T4 2 2 3000 1 3 4 3⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮T47 14 5 1500 2 2 2 2T48 15 3 2200 1 4 3 2T49 15 3 3500 2 4 2 3T50 15 3 6500 3 4 3 5
















Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References


























































Vbl [vb


l [vsijl]50times50




































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References

























































max Z1 111394450

i11113944

50

j1v

bijxij i 123 50 j 123 50

max Z2 111394450

i11113944

50

j1v

sijxij i 123 50 j 123 50

st

1113944

50

i1xijle1 j 123 50

1113944

50

j1xij 1 i 123 50

1113944

50

j1xijrij 1 i 123 50

xij 0or1 i 123 50 j 123 50

(17)


max Z 05Z1 + 05Z2

st

1113944

50

i1xij le 1 j 1 2 3 50

1113944

50

j1xij 1 i 1 2 3 50

1113944

50

j1xijrij 1 i 1 2 3 50

xij 0 or 1 i 1 2 3 50 j 1 2 3 50

(18)




42 Discussion




landlords




tenants








2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References




























































2 (T2 L1)

3 (T3 L22)

4 (T4 L4)

5 (T5 L3)

6 (T6 L23)

7 (T7 L5)

8 (T8 L24)

9 (T9 L25)

10 (T10 L6)

11 (T11 L27)

12 (T12 L26)

13 (T13 L43)

14 (T14 L7)

15 (T15 L8)

16 (T16 L28)

17 (T17 L9)

18 (T18 L10)

19 (T19 L29)

20 (T20 L30)

21 (T21 L11)

22 (T22 L12)

23 (T23 L31)

24 (T24 L44)

25 (T25 L13)

26 (T26 L14)

27 (T37 L42)

28 (T28 L45)

29 (T29 L39)

30 (T30 L34)

31 (T31 L35)

32 (T32 L46)

33 (T33 L16)

34 (T34 L15)

35 (T35 L36)

36 (T36 L47)

37 (T37 L17)

38 (T38 L38)

39 (T9 L25)

40 (T40 L48)

41 (T41 L18)

42 (T42 L19)

43 (T43 L39)

44 (T44 L20)

45 (T45 L40)

46 (T46 L49)

47 (T47 L41)

48 (T48 L21)

49 (T9 L25)

50 (T50 L50)


ndash10

0

10

20

30

40

50

Fitn

ess v

alue

50 100 150 200 250 300 350 400 450 5000Generation


(a)

0

05

1

15

2

25

3

35

4

45

Z


(b)



36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References
























































36

38

4

42

44

46

48

5

Z

01 02 03 04 05 06 07 08 09 10Weight

LandlordTenant


0

05

1

15

2

25

3

35

4

45

Z


m = nm le n































































Appendix




Data Availability




Acknowledgments


References


































































































Appendix




Data Availability




Acknowledgments


References































































Appendix




Data Availability




Acknowledgments


References























































































































Documents

Multiattribute Supply and Demand Matching Decision Model