Commercial Optimal Layout Model of Stadium based on Utility Function Theory

Transcription

1 Commercal Optmal Layout Model of Stadum based on Utlty Functon Theory Ronghu Hu Physcal Educaton Insttute, Hunan Unversty of Technology, Zhuzhou , Chna Abstract Modern stadums undertake large sports events and meet people s demand for sprtual cvlzaton. However, to sustan ther development, these arenas should also conduct afflated busness actvtes and guarantee ther normal busness revenue. Therefore, the manner of settng up commercal outlets (.e., restaurants and supermarkets) n stadums s a topc that merts nvestgaton. Three studes conducted n dfferent tme perods analyzed the Bejng Natonal Stadum, popularly known as the Brd s Nest. In partcular, the stadum structure, people stream, characterstcs of sports events, parkng facltes, audence demands, and other factors were examned. The basc data were collected, and a mathematcal model of the commercal optmal layout was constructed based on the producton and utlty functon of the stadum. Ths model could be used n determnng the quantty of the best commercal outlets n dfferent areas, achevng the effect of mnmum cost and maxmum utlzaton, helpng mprove the operaton of the stadum, and provdng references for relevant nsttutons. Key words: ASYMMETRIC FINGERPRINTING, OBLIVIOUS TRANSFER, MULTICAST COMMUNICATION 1. Introducton Stadums play an mportant socetal role by holdng large events and enrchng the cultural lfe of people. However, to sustan ther normal operatons, stadums must establsh supportng commercal servces wthn ther premses to obtan suffcent proft and reflect a certan economc property [1]. Through these commercal outlets, stadums can ncrease ther operatng ncome and satsfy the demands of ther audence [2]. At present, relevant research s prmarly concentrated on as follows: Chen and L analyzed the nonoptmal layout of the regonal commercal combnaton and proposed the optmal countermeasures [3]. Ca and Chen dscussed the green land system layout method to acheve a wn wn stuaton between ecologcal envronment protecton and toursm development and constructon by mplementng ecologcal optmzaton n the green land system and desgnng a hot sprng resort n Chna [4]. Xao appled the nfluental relaton between the dynamc transfer of comparatve advantages and the ndustral structure upgradng of processng trade to analyze the optmal layout of the geographcal poston of processng trade n Shandong [5]. The majorty of the domestc stadums present the characterstcs of a comprehensve operaton. When they hold sports events, these stadums rapdly organze several temporary parkng areas, house utltes, and caterng servce outlets to meet the demand of ther Metallurgcal and Mnng Industry, 2015, No

2 growng audence; by contrast, durng daly operatons, stadums effectvely utlze ther spare spaces for sports accessores stores, supermarkets, and clubs [6]. The establshments that successfully admnster such a system nclude the Regal Shangha East Asa Hotel, Huanglong Sports Center Trust- Mart Supermarket, and Hongkou Gymnasum. In ths type of a setup, all of the premses of a stadum can be maxmzed. However, the commercal optmal layout cannot be stereotyped among all stadums because n actual operatons, the structures and audence demand of arenas generally vary. [7] Hence, the process of settng up busness outlets and determnng the reasonable number of such outlets that can be establshed n stadums should be nvestgated. The commercal layout and operatons of stadum can only be mproved when ther actual condtons are fully consdered. The sgnfcance and key ponts of the study are presented n ths paper. 2. Modelng bass 2.1 Modelng factors There are many factors nfluencng the commercal layout of the stadums, the dfferences n stadum capacty, number of audences, way of transportaton, consumpton ablty and consumpton habt etc. all can change the layout of busness outlets [8], characterzed by the dversty and complcaton of customer group. Durng the holdng of events, the man customers are players, judges, coaches, audences and journalsts etc.; durng the holdng of performance actvty, the man customers are performance companes, actors, audences and journalsts; n case of commercal actvtes the customer groups are transformed nto busnessmen and consumers etc., whle n the ordnary daly operatons, the publc are the man customers [9]. These customers have a large preference dfference, wth a sgnfcant nfluence on the commercal layout of the stadums. In addton, the capacty and postonng of the stadums themselves also drectly decde the sze and type of busness outlets. Therefore, durng research on the optmal commercal layout, t s requred to fully consder the factors of the stadum structure and audence demands. Meanwhle, t s requred to propose correspondng hypothess to ensure that the model s scentfc and feasble. 2.2 Modelng theory It can be known from the utlty theory that the audences consumpton desre value s related wth the utlty value of busness outlets. Dfferent szes of outlets play dfferent utlzatons [10]. At the same tme, wth the ncreasng of people stream n the busness dstrct, the utlty generated wll be even greater. Busness outlets should be amed at meetng the maxmum utlty of people group and t s requred to determne ther quantty and poston [11]. Therefore, durng the calculaton of layout, by ntroducng the thought of producton functon n economcs and wth the Cobb-Douglas producton functon theory, the producton functon can be obtaned: α β Q = f ( K, L) = AL K (1) Where Q s output, K s captal, L s labor, A α β are all constants, and α + β = 1, and there s a replaceable relaton between the producton elements L and K,.e., under the precondton of remanng the producton unchanged, ncreasng L can decrease K accordngly, and t can be obtaned that the utlty functon s: α β Q = f ( m, n) = Am n (2) s.t α + β = 1 (3) mu m + nu n = U Its equlbrum s: MPm MP (4) n = um un Accordng to ths model, t s possble to calculate the sze and quantty of optmal busness outlets n area,.e. the optmal layout model of the stadum, where Q : the utlty output of busness dstrct ( = 1, 2, 3 20 ); m : number of large busness outlets n busness dstrct ; n : number of small busness outlets n busness dstrct ; u m : utlty value that can be provded by a large busness outlet n busness dstrct ; u n : utlty value that can be provded by a small busness outlet n busness dstrct ; α : correspondence of coeffcent contrbuton of large MS n busness dstrct for Q to the necessty of large busness outlets to be set; β : correspondence of coeffcent contrbuton of small MS n busness dstrct for Q to the 214 Metallurgcal and Mnng Industry, 2015, No. 6

3 necessty of large busness outlets to be set; U : correspondence of total desre value of all people to the utlty output value provded by busness dstrct ; MP m : margnal output of utlty that can be provded by a large busness outlet n busness dstrct ; and MP n : margnal output of utlty that can be provded by a small busness outlet n busness dstrct 3 Modelng case analyss 3.1 Analyss on stadum base data Wth the Brd Nest as an example, the utlty functon theory s used to construct ts commercal optmal layout model, and the commercal layout structure most approprate for the Brd Nest s obtaned through calculaton. Brd Nest belongs to a stadum wth strong comprehensve functonalty and wth relatvely reasonable busness layout, so the valdty of ths model can be verfed n combnaton wth the actual condton of the Brd Nest. Frst, accordng to the stadum condton of the Brd Nest, the basc modelng hypothess s proposed. The Brd Nest s located n the south of central area of the Olympc Park, wth a total floor area of 21ha, and number of audence seats up to 91,000. Durng the Olympc Games, t undertook the openng and closng ceremones, football and track and feld events fnal of the Olympc Games and Paralympc Games. After the Olympc Games, t became a large venue for the Bejng ctzens to partcpate n sports and entertanment actvtes and a landmark buldng, as shown n Fgure 1. As shown n fgure 1, the Brd Nest has a large area, wth more seats, comprehensve functon, complcated personnel structure and hgh cost of constructon and operaton, and flexble fnancng and operaton mechansm were adopted n constructon and operaton. Durng operaton, n the form of 58% government fundng and 42% fundng by other companes, the problem of dffculty n fnancng was solved. Durng operaton, wth PDP model, CITIC consorta wth 42% shares operate the stadum for 30 years propretarly. Wth the operaton of professonal companes, the Brd Nest has successfully held a lot of sports events, art performances, natonal ftness entertanment and other projects, whether durng the game or n spare tme, the people stream s mantaned at a hgher level, and the requrements for the commercal layout are also relatvely hgh. Based on ths, a reasonable hypothess can be proposed to the audences of the Brd Nest. Assume that (1) each audence has meal after watchng the competton or playng n the stadum; (2) assume that the people stream n each grandstand area s smlar; (3) assume that the populaton proporton and personal preference n the stadum have the same structure. Second, observe the people stream n Brd Nest n a perod of tme, and ther actvty law and personal trend, and accumulate the basc data for modelng. In order to ensure the objectve and far modelng, three observaton perods are respectvely establshed: sports events, art performance and mass entertanment, and the contents manly nclude audence gender, way of travelng, consumpton habt and law of people stream n the stadum. The nvestgaton result s as shown n Table 1. Table 1. Number of male and female audences n the Brd Nest sports events Male Female art performance Male Female mass entertanment Male 8679 Female 7924 Fgure 1. Structural dagram of Brd Nest Stadum It can be known from Table 1 that although the tems are dfferent n settng, n the three nvestgatons, the proporton of male and female audences n the Brd Nest s bascally approxmate to 10:9, so the male and female proporton n the Brd Nest s set to be 10:9, and the age structure s set as 4 ntervals: Metallurgcal and Mnng Industry, 2015, No

4 below 20 years old, years old, years old and above 50 years old. Through the three nvestgatons, the populaton structure can be obtaned, as shown n Table 2. Table 2. Dstrbuton of populaton n the Brd Nest Male Female Age group 1 Age group 2 Age group 3 Age group 4 Age group 1 Age group 2 Age group 3 Age group On ths bass, the people groups of dfferent genders and age ntervals n the Brd Nest are analyzed n terms of dfference n way of travelng and consumpton habt accordngly, so as to reflect the basc structure of personal trend. Through the comprehensve analyss on the nvestgaton data n three tmes, t s found that such group has extremely smlar personal trend. In consderaton of dfferent total numbers of people n the three nvestgatons, the nvestgaton result s subject to weghted average processng, so as to mprove the relablty of data statstcs and the comparatve dagram of personal trend, as shown n Fgure 2. Fgure 2. Dstrbuton dagram of personal trend of populaton n the Brd Nest The data n the fgure show that n the populaton structure, the populaton at stage 2 has the hghest proporton, and the populatons of varous age groups are relatvely balanced n structure of way of travelng, presentng the characterstcs that most select metro and bus for travelng and few drve prvate cars, and ths mght be related wth the fact that the Brd Nest s far from the surroundng parkng spaces and that the publc transportaton s developed. In terms of det habt, the populatons of dfferent tenders and age groups all present the characterstcs of less Chnese food and more western food, ths mght be 216 Metallurgcal and Mnng Industry, 2015, No. 6

5 related wth the rapd and convenent characterstcs of western food and strong tmelness of events n the Brd Nest. In the age of the second stage, the proporton of male and female havng western food s about 41.2% and 39.5%. It s worth notng that the det structure of old men s relatvely balanced. In terms of consumpton habt, due to large base number of populaton n the second age group, such group s the man force of commercal consumpton. Accordng to the result of the three nvestgatons, whether n terms of age or age group, the consumpton quota n the stadum s manly concentrated on Grade 3,.e. RMB , and the number of people exceedng Grade 3 presents a decrease trend. Based on ths, t s possble to prelmnarly master the basc nformaton such as populaton structure and personal trend n the Brd Nest, so as to provde convenence for the follow-up analyss and modelng. 3.2 Analyss on law of people steam n the stadum In ths expermental study, AUS, average rankng score (RS) and precson are used to evaluate the effect of user-level personalzed recommendaton algorthm. These three evaluaton ndcators are very common and representatve n bpartte graph network recommendaton. The settng of busness outlets n the stadum s closely related wth the dstrbuton of stream of audences. Settng the correspondng outlets accordng to the change law of people stream can maxmally play ts commercal effect. Therefore, n combnaton wth the three hypotheses of audence property and stadum structure of the Brd Nest, the moblty law of audences n the Brd Nest can be obtaned. It can be known from the statstcal nvestgaton result that there are manly 10 exsts n the Brd Next n total, whch are correspondng to 10 grandstands. The consumpton proportons of the audences n the stadum are respectvely: 72.8% for det, ncludng about 53.6% for western food and about 19.2% for Chnese food and 27.2% for shoppng consumpton. Accordng to the prncple of shortest path, the travelng route of the audences durng consumpton s obtaned, as shown n Table 3. Table 3. Dstrbuton of travelng route of audences n the Brd Nest Grandstand Go out from ext B1 Go out from ext B6 B1 B1 B1 B2 B3 B4 B5 B6 B2 B1B2 B2 B3 B4 B5 B6 B3 B1 B2 B3 B3 B4 B5 B6 B4 B1 B2 B3 B4 B4 B5 B6 B5 B1 B2 B3 B4 B5 B5 B6 B6 B1 B2 B3 B4 B5 B6 B6 B7 B7 B8 B9 B10 B1 B7 B6 B8 B8 B9 B10 B1 B8 B7 B6 B9 B9 B10 B1 B9 B8 B7 B6 B10 B10 B1 B10 B9 B8 B7 B6 It can be known from the table above that take exsts B1 and B6 as an example, desgned based on the shortest path, durng the travelng of audences of varous grandstands, some areas are the nevtable road to take, and the proporton of people stream n these areas decde the layout scale of busness outlets. Therefore, they should be further calculated. Assume that the proporton stream proporton n B busness dstrcts s p, take Table 3 as an example, the followng can be obtaned: p = 6 = 1 αb + βb 1 6 ( αb + βb ) 1 6 (5) Where, Bj represents the tmes of people B stream comng out of area B j, α and β respectvely represent the proporton of people stream n dfferent exts. It can be seen from Table 3 and the consumpton proporton that the proportons of people comng out of exts B 1, B 6 are respectvely 27.2% and 72.8%; smlarly, the proporton of people stream n varous busness dstrcts of the Brd Nest can be obtaned, as shown n Table 4. Metallurgcal and Mnng Industry, 2015, No

6 Table 4. Proporton of people stream n varous busness dstrcts of the Brd Nest durng consumpton Busness dstrcts B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 Proporton Statstcs have shown that durng the consumpton perod, there s a dfference of people stream n varous busness dstrcts, wth the most people n area B1 and the fewest n area B9. In addton, after actvty n the stadum, the dstrbuton of people stream leavng the stadum also wll nfluence the busness proft. For example, generally some audences of the Brd Nest are used to purchasng relevant products when leavng the stadum. Therefore, accordng to formula (5) and the travelng structure, t can be known that the t s relatvely convenent for the audences takng bus and metro to select the ext opposte to exst B 6 ; and t s relatvely convenent for the audences takng prvate cars and taxes to select the ext opposte to B 1. In combnaton wth the nvestgaton data, the proporton of people stream n varous busness dstrcts durng the travelng perod can be obtaned, as shown n Table 5. Table 5. Proporton of people stream n varous busness dstrcts of the Brd Nest durng travelng Busness dstrcts B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 Proporton In consderaton that the actvty perods of audences of the Brd Nest n the stadum are between the ntervals of consumpton and travelng, so the overall dstrbuton of people stream on that day should be the average value of two stages, and the proporton of people stream n varous busness dstrcts of the Brd Nest on that day s obtaned, as shown n Table 6. Table 6. Proporton of people stream n varous busness dstrcts of the Brd Nest Busness dstrcts B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 Proporton It can be known from the table that n the Brd Nest, the people stream n area B1 s hgher than n other areas, whch meets the bass of establshng a large busness outlet. The busness potental n other areas s less than area B1, and t s consdered to establsh a small busness outlet. Masterng such law of people stream helps to prelmnarly determne whch place s most sutable to establsh a busness outlet, but for the specfc constructon quantty and whch sze of busness outlet s relatvely reasonable, t s requred to further construct an optmal layout model for soluton. 3.3 Analyss on optmal layout model The sze of people stream decdes the sze of busness potental, whle the purchase desre of the populaton decdes the sze of busness proft. Accordng to the utlty theory, the purchase desre value of the populaton s correspondng to the specfc utlty of the busness outlets, and dfferent szes of busness outlets provde dfferent utltes, and the utlty of busness outlet expands wth the ncreasng of people stream. In combnaton wth the producton (1), frst the necessary proporton of dfferent szes of busness outlets s proposed. β 0.05 α = (6) The sze of people stream of Ths reflects the necessty to construct the small busness outlet and large busness outlet. Then, accordng to the area proporton of the large and small outlets, the utlty rato s obtaned. (7) um = = u ( ) n 7 2 The area of large outlet s 60, and that 218 Metallurgcal and Mnng Industry, 2015, No. 6

7 of small one s Where, the utlty value of the small busness outlets s as follows: (8) ( q1+ 2q2 + 3 q3) un = p 6 Table 7. Utlty value of small busness outlets of Brd Nest Economy In combnaton wth formulas (1),(8), the utlty value of small outlets n varous busness dstrcts of the Brd Nest can be obtaned, as shown n Table 7. Busness dstrcts B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 Proporton The statstcs n the fgure show that when all areas n the Brd Nest are set as the small busness outlets, the utlty value n varous area s bascally consstent wth the sze of people stream, wth the hghest value stll n area B1; the utlty value of the large busness outlets s 12 tmes of that of the 7 small busness outlet, so the utlty value also presents the same relaton wth people stream, ndcatng that the people stream has an mportant nfluence on the settng of busness outlets. Based on the utlty functons (2)-(4) and utlty rato (7), the followng can be obtaned: Q β α 1 MPm = = α An m m Q β 1 α MPn = = β An m n MPm nα um n umβ = = = (9) MPn m β un m unα When =1, t can be obtaned that the total desre value of populaton passng through the frst busness dstrct s U1 = ; t can be known from (6) and β Table 6 that α =, and the followng can be obtaned from formulas (3) (7) and producton equlbrum condton: n1 um 1β = = = m1 un 1α mu 1 n mu 1 n1 = Namely 2.027mu 1 n1 = therefore, m = u = =5.899 n n 1= =1.847 After takng the nteger, t can be verfed from formula (7) that when m 1 = 3, n 1=2,.e. when the number of large busness outlets s 3 and that of the small ones s 2, the utlty value n area B 1 s the largest and the busness proft s the hghest. In a smlar fashon, the busness layout table of other areas can be obtaned, as shown n Table 8. Table 8. Layout table of varous busness outlets n the Brd Nest Busness dstrcts B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 (large, small) (3, 2) (3, 4) (2, 4) (2, 4) (3, 4) (3, 3) (2, 4) (2, 5) (2, 5) (2, 5) It can be seen from the table above that n areas B1 and B2 wth more populaton, t s possble to set more large busness outlets, and n areas B1 and B2 wth less populaton, t s possble to set more small busness outlets. These busness outlets have certan substtuton effect. When mantanng the total desre value of each busness dstrct unchanged, t s possble to use more small busness outlets to replace a large busness outlet. Because the small busness outlets are characterzed by low cost and flexble settng, they can provde hgher unt supply level. Through the comparson of layout of actual busness outlets n the Brd Nest, t s found that the modelng calculaton result s bascally consstent wth the settng of the actual area. In the areas wth more people stream, there are ndeed large supermarkets and restaurants, and lcensed merchandse retalng stores and wax work museum are also ntroduced, whch fully meet the dfferent demands of audences. In the areas wth less populaton, only scattered fast food and retalng pavlons are set, whch Metallurgcal and Mnng Industry, 2015, No

8 reflect the flexblty of operaton. 4. Conclusons Through the nvestgaton of the statstcs of the audence populaton n the Brd s Nest, the populaton structure and people stream law n ths stadum are analyzed n terms of travel mode, consumpton behavor, detary habt, and audence structure. Research has ndcated that people of dfferent ages and genders have sgnfcantly dverse consumpton behavors, but the populaton of the same age has relatvely smlar behavor and psychology. Therefore, a certan law n the populaton acton exsts. Masterng the moblty law of the populaton of dfferent perods s benefcal for establshng a reasonable busness layout of stadums. Large supermarkets must be set up n areas wth a large stream of people, whereas small supermarkets should be constructed n areas wth a small stream of people. However, the number of these supermarkets should be controlled because ther overabundance could strengthen competton, waste resources, and engender populaton congeston; by contrast, the scarcty of supermarkets could fal to satsfy the demands of the populaton. In combnaton wth the optmal layout model, the optmal number and type of busness outlets n dfferent areas are obtaned. Upon actual nspecton, the results are generally consstent. Ths model may be appled n creatng a reasonable busness layout that consders the actual condtons of the stadum, and thus ncrease busness proft and comprehensvely beneft the stadum. References 1. Chase, J., Healey, M. (1995) The spatal externalty effects of football matches and rock concerts: The case of Portman Road Stadum, Ipswch, Suffolk. Appled Geography, 15(1), p.p Sapotchne, J. (2012) Rhetorcal strategy n stadum development poltcs. Cty, Culture and Socety, 3(3), p.p Chen, Q.B., L, C.Z. (2010) Non-optmal Analyss on and Countermeasures for Regonal Busness Combnaton. Journal of Suzhou College of Educaton, 13(5), p.p Ca, S.H., Chen, J.H. (2007) The Investgaton on Optmzaton Space Layout Method of Tourst Resort Eco- Green Space System. Guangdong Garden, 29(4), p.p Xao, D.D. (2011) Optmal Industry Layout of Processng Trade n Shandong Provnce Base on Dynamc Comparatve Advantage. East Chna Economc Management, 25(11), p.p Wang, X.H. (2015) Research and Dscusson on Operaton and Management Model of Unversty Stadum. Inner Mongola Sports Scence and Technology, 28(2), p.p Zha, N.T. (2015) Dscusson on Contradcton between Idleness of School Stadum and Demand of the Mass for Ftness Plate. Journal of Dalan College of Educaton, 31(1), p.p Copenheaver, C.A., Seler, J.R., Peterson, J.A., Evans, A.M., McVay, J.L., Whte, J.H. (2014) Stadum Woods: A dendroecologcal analyss of an oldgrowth forest fragment on a unversty campus. Dendrochronologa, 32(1), p.p Fang, Z.X., L, Q.Q., L, Q.P., Han, L.D., Wang, D. (2011) A proposed pedestran watng-tme model for mprovng space tme use effcency n stadum evacuaton scenaros. Buldng and Envronment, 46(9), p.p Dham, S., Al al-nowah, A. (2013) An extenson of the Becker proposton to non-expected utlty theory. Mathematcal Socal Scences, 65(1), p.p Fredrk, W. (2009) Andersson Consumpton theory wth reference dependent utlty. The Journal of Soco- Economcs, 38(3), p.p Metallurgcal and Mnng Industry, 2015, No. 6