Mathematical methods on management problems(2)(End)

ZHANG　Shengkai,　LIU　Chao,　LIU　Yan,　ZHANG　Fengrong

(School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China )

?

Mathematical methods on management problems(2)(End)

ZHANGShengkai,LIUChao,LIUYan,ZHANGFengrong

(School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China )

One-timemanagementsequencingproblemisstudied,thatisserviced-elementsservedbyservice-elementswillbecompletedintheonetime.Thismethodisappliedfortheactualsituationtosolvetheundergroundparkingservicemodeltodealwiththeparkingproblem.Asuggestionisputforwardthatthroughtheentranceoftheconversionorreservedvariablelanelifting,theutilizationefficiencyofundergroundparkingwillbeenhanced.

serviced-elements; underground parking; utilization efficiency

4 Underground parking lot of canonical correlation analysis of a moving vehicle

In many practical problems, the correlation between the two sets of random variables is need to study[1-2]. Although the correlation coefficient is necessary to understand the correlation between variables, it can not fully reflect the overall correlations. Therefore, the appropriate linear combination structure of groups of variables are considered.

4.1Canonical correlation analysis

To study the relationship between the two variables X and Y, linear combinations between two sets of variables are given:

Where a=(a1,a2,…,ap)\%T\%, b=(b1,b2,…,bq)\%T\%areanynonzeroconstantvector,toseethecovariancematrixofthevectorU,V can be expressed as

Var(U)=Var(a\%T\%X)=a\%T\%Var(X)a=a\%T\%Σ11a

Var(V)=Var(b\%T\%Y)=b\%T\%Var(Y)b=b\%T\%Σ22b

(1)

CovariancematrixofvectorU,V can be expressed as

Cov(U,V)=a\%T\%Σ12b

(2)

SothecorrelationcoefficientofU and V is

(3)

Because of ρ(k1U,k2V)=ρ(U,V),therefore,defineU,V as the standardized variables:

Var(U)=1, Var(V)=1

(4)

That is

a\%T\%Σ11a=1, b\%T\%Σ22b=1

(5)

If and only if

ρ(U,V)=a\%T\%Σ12breachedthemaximumvalue,thenwehave

U1=a\%T\%1X, V1=b\%T\%1Y

(6)

whichisthefirstpairofcanonicalcorrelationvariables,λ1isthefirstcanonicalcorrelationcoefficient.

ThefirstpairofcanonicalcorrelationvariablesU1and V1extracts the main part correlation between original variables X and Y, if this part is not enough, we can find out second pairs of canonical correlation variables in the residual correlation, which satisfy the constraints(4) and does not include the first pair containing the information of U2, V2. The method was ibid.

4.2Application analysis

The underground parking is the rational development and utilization of underground space, so underground parking is an important part of the development of underground space. Therefore, the data of Dalian city underground daily parking lot of vehicles are selected. The following variables are selected to study the relationship between the number of entering and leaving vehicles.

x1(x2,x3) and y1(y2,y3) are indicated the maximum(minimum, average) number of entering or leaving vehicles at each unit of time(hours), respectively. Fourteen samples are selected, and the correlation between the fourteen sets of data are analyzed.

Let X=(x1,x2,x3)\%T\%andY=(y1,y2,y3)\%T\%betwogroupsofrandomvariables,calculatingthecorrelationcoefficientR of matrix(X\%T\%,Y\%T\%)\%T\%,thatis

λ1=ρ^21=0.9875,λ2=ρ^22=0.7378,λ3=ρ^23=0.0878

Thusfirst,secondandthirdcanonicalcorrelationcoefficientsare

wecangetthefirstpairsofcanonicalvariablescoefficient

Finally,thecalculationofformula(6)is

U^1=-0.4721x1+0.0276x2+1.4423x3V^1=-0.0230y1+0.2372y2+0.8234y3

Empathycouldbeobtainedbythesecondtypicalvariablecoefficientsa2,b2.Fromformula(6),wecangetsecondpairsofcanonicalvariables.

U^2=-4.1028x1-0.3469x2+3.7909x3V^2=-1.5194y1+1.0745y2+0.4630y3

Generallyspeaking,typicalvariablemeaningwasmainlydeterminedbythosecoefficientswithlargerabsolutevaluesofvariables.

5 Quantity analysis on the personnel safety flow in Dalian Victory Shopping Plaza

ThepersonnelflowdistributionofDalianVictoryShoppingPlazaisveryimportanttomall’ssecurityproblem.Thediscussionwasfollowedaccordingtotheabstractmodelofthegeneral,tomaketheapplicationscopeoftheresultsmorewidely[3-4].

(7)

(8)

(9)

Sothetotalpassengerflowinthemallis

Theaverageflowdensityofthemallpersonnelshouldbe

(10)

Andthemeansquarevalueofλis

(11)

Passengerflowdistributionisnotstatic,andthemalltrafficdensityindifferenttimesofeachdayisnotthesame.Ifthetimeintervalofadaydividedissetto

Theflowofitseachtimealsotaggedsuperscript,thereis

(12)

(13)

(14)

(15)

(16)

(17)

Sothenumberofpersonnelflowthroughoutadayis

(18)

Afterpreciseanalysisofmall’scustomerflow,ensuringthesafetyofmallrunningsmoothlycanpromotegreateconomicbenefits[7]fromtheperspectiveofbusinessoperators.

6Conclusion

In this paper, the model applied to the practical problems of the underground parking lot is studied, using the method of canonical correlation. The results show that the serviced-elements served by service-elements model is suitable for the actual situation, which has the certain instruction significance and practical significance.

References:

[1] 張鳳榮.關(guān)于\%n\%人合作對策與集對策若干問題的研究[D].沈陽：東北大學(xué)，2006.

[2] 劉德明.對策論在中國[J].經(jīng)濟數(shù)學(xué),2009,26(4):1-5.[3] 張盛開.P-J型最優(yōu)服務(wù)排序問題的推廣[J].科學(xué)通報,1981,26(22):1349-1352.

[4] ZHANG S K. Generalization of sequencing problems of the optimum service for model P-J[J]. A Monthly Journal of Science, 1982, 27(6): 594-597.

[5] ZHANG S K, YE T X. The values of denumerable persons games on the equivalent spaces[J]. Science Bulletin, 1987, 32(21): 1452-1456.

[6] ZHANG S K, GONG X L. ZS-value for random coalition games[J]. Chinese Science Bulletin, 1989, 34(15): 1236-1242.

[7] ZHANG S K. Convex linear generalization of random coalition games[J]. Chinese Science Bulletin, 1998, 43(9): 713-716.

1674-1404(2016)04-0304-04

管理問題的數(shù)學(xué)方法應(yīng)用(2)(續(xù)完)

張 盛 開,劉 超,劉 燕,張 鳳 榮

(大連工業(yè)大學(xué) 信息科學(xué)與工程學(xué)院， 遼寧 大連116034 )

研究了一個時間管理排序問題，即每一個服務(wù)單位在單位時間內(nèi)只能服務(wù)一個被服務(wù)單位，同時被服務(wù)單位在單位時間內(nèi)，只能被一個服務(wù)單位所服務(wù)，并且一經(jīng)服務(wù)又必須一次服務(wù)完畢。將此方法應(yīng)用到實際情況中，用以解決地下停車服務(wù)模型處理停車問題。最后，提出了通過入口的轉(zhuǎn)換或預(yù)留可變車道的建議，用以提高地下停車場的利用效率。

服務(wù)單位；地下停車場；利用效率

TB114.1

A

ZHANG Shengkai, LIU Chao, LIU Yan, ZHANG Fengrong. Mathematical methods on management problems(2)(End)[J]. Journal of Dalian Polytechnic University, 2016, 35(4): 304-307.

by: 2015-12-22.

ZHANG Shengkai, Male, Professor.