Research Article Modeling of a Small Transportation ...downloads.hindawi.com/journals/ddns/2013/802528.pdflisted the following as the ve most promising directions: the interface between

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2013 Article ID 802528 10 pageshttpdxdoiorg1011552013802528

Research ArticleModeling of a Small Transportation Companyrsquos Start-Up withLimited Data during Economic Recession

Xiaoping Fang1 Jake Ansell2 and Weiya Chen1

1 School of Traffic and Transportation Engineering Central South University Changsha 410075 China2 Business School University of Edinburgh Edinburgh EH8 9JS UK

Correspondence should be addressed to Weiya Chen wychencsueducn

Received 9 October 2013 Revised 11 November 2013 Accepted 25 November 2013

Academic Editor Wuhong Wang

Copyright copy 2013 Xiaoping Fang et al This 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

This paper presents a modeling method for analyzing a small transportation companyrsquos start-up and growth during a globaleconomic crisis which had an impact onChinawhich is designed to help the ownersmake better investment and operating decisionswith limited data Since there is limited data simple regression model and binary regression model failed to generate satisfactoryresults so an additive periodic time seriesmodel was built to forecast business orders and income Since the transportationmarket issegmented by business type and transportation distance a polynomial model and logistic curve model were constructed to forecastthe growth trend of each segmented transportationmarket and the seasonal influence function was fitted by seasonal ratiomethodAlthough both of the models produced satisfactory results and showed very nearly the same of goodness-of-fit in the sample thelogistic model presented better forecasting performance out of the sample therefore closer to the reality Additionally by checkingthe development trajectory of the case companyrsquos business and the financial crisis in 2008 the modeling and analysis suggest thatthe sample company is affected by national macroeconomic factors such as GDP and import amp export and this effect comes witha time lag of one to two years

1 Introduction

Transport infrastructure is critical to economic developmentof a country and can provide competitive advantage WithinChina there is a diversity of transport companies whichcould be split between with large-scale transport enter-prises (LTEs) and small- and medium-sized transportationenterprises (SMTEs) There are many distinct differencesbetween the two types of enterprises Generally LTEs moregeographically spread attract larger enterprises and resourcemanagement is not as critical SMTEs especially in theirstart-up period need to be more agile in the use of theirfinancial resources to ensure survival This is particularlytrue during a period of economic change This paper focuseson SMTEs since they are the main suppliers of road trans-portation services in China They necessarily play the role offirst-andor-last kilometer carriers for door-to-door logisticsservices Some 225 259 enterprises and 4 595 600 individuallyowned businesses were engaged in transportation storage

and postal services in 2008 [1] The total value of the top50 logistics enterprises about 4756 billion Yuan is only053 of the national added value of the logistics industry[2] Compared with LTEs SMTEs face much greater riskespecially during an economic downturn The survival of abusiness entity depends heavily on its ability to anticipate andprepare for change rather than wait for it and then react to it[3]

Demand forecasting is so significant for SMTEs thatit can help to improve equipment utilization and establishsmarter operational and investment strategies Realisticallybusiness owners estimate the service demand from theirpast experiences which can be wrong or misleading Almostall freight demand analysis usually accounts for a wholecountry a region or a corridor between cities by integrationor by mode and is usually to do with public transportationplanning [4ndash6] Two previous research articles which exam-ined SMTEsrsquo demand forecasting tackled less than truckload(LTL) for both short-term and long-term forecasting In [7]

2 Discrete Dynamics in Nature and Society

Table 1 Business data by industry

Industry No of customers No of orders MoneyAbsolute value Percentage Absolute value Percentage Absolute value Percentage

Food 1 3125 24 02221 91900 04495Toy 1 3125 154 14253 430492 21054Chinaware 1 3125 358 33133 949029 46414Material 2 6250 151 13975 363945 17799Machine 3 9375 4423 409348 4474611 218837Craft 4 12500 1001 92642 2867729 140250Electronics 5 15625 1999 185007 2541727 124307Logistics 15 46875 2695 249422 8727782 426845Total 32 100 10805 100 20447215 100

it is believed that the combination of neural networks andtraditional time series analysis is good for forecasting short-term logistic demand for an LTL carrier A small-to-medium-sized road transport servicewhich offered a limited collectionand delivery service for small and large consignments in anumber of geographical zones of equal area is reported in [8]

The objective of this study is to model the start-up andgrowth of a newly established truck transportation companyduring the economic recession whose main business is sea-port containers and bulk inland transportation It ultimatelyaims to help SMTEs to look for ways of improving equipmentutilization in the short to medium term by forecasting theorders and the trucks required as well as the impact offinancial crisis The main feature of our work is its use oflimited data to analyze and forecast a small transportationcompanyrsquos business as it starts up in a rapidly changingenvironment

The context of the model has two distinct elementsenterprise start-up and the short time series Obviouslymost enterprises in their start-up period need to grow theirbusiness to an economic scale If they fail to do so the longtime survival of the enterprisemay be under question Hencethe model selected will have to accommodate such growthThe second element reflects the need for quick appraisal oflikely demand so that appropriate economic strategy canbe developed by the enterprise This differentiates start-upSMTEs from LTEs where there is possibly longer times seriesand higher correlation of performance with macroeconomicfactors The modeling proposed attempts to cope with thesetwo elements

2 Data

The data covers all the business orders of a small trucktransportation company during a 40-month period (January2008 to April 2011) Registered at the end of 2007 the smalltruck transportation company currently has a fleet of 30trucks and 30 drivers Some trucks are container truckssuitable for container transportation and others are bulktrucks designed for heavy long-distance bulk transportationservices This company mainly provides services for piercontainer transportation and inland bulk transportationThe container transportation service is mainly provided

for container customers who have exporting and import-ing businesses at three ports located in Shenzhen namelyYantian Shekou and Mawan In order to make use of theempty containers at these ports a small part of the bulk istransported for the container customers in container trucksat the same price as bulk transportation Most of the rest iscarried by bulk trucks for different customers

All the business orders from this company are classifiedaccording to the categories of the customer industry (seeTable 1) ldquoMoneyrdquo in this paper represents the gross incomewhich equals the orders multiplying the unit price Thecustomers come from eight industries and 15 logistics cus-tomers contribute 427 of the total money three machinecustomers account for 409 of the orders and 219 of thegross income and the remaining 14 customers from the foodtoy chinaware material craft and electronics industriesaccount for 34123 of the orders and 35432 of the totalgross income

Further analysis shows that there are two patterns asregards gaps in orders regular and irregular Regular ordersare made either continuously on weekdays and broken atweekends and vacations (shown in Figure 1(a)) or discretelyand regularly (shown in Figure 1(b)) Irregular orders aremade randomly as shown in Figures 2(a) and 2(b) Thecustomers who make regular and irregular orders are listedin Table 2

In order to find out whether the economic recession of2008 had an effect on the companyrsquos business further analysisof the orders and money per month was conducted for bothregular and irregular businesses It should be noted that theChinese New Year usually falls in February when almost allbusinesses are at their lowest level of production A three-yearperiod is considered and the cycle starts from February of thefirst year to January of the last year Therefore ldquo1rdquo in Figure 3represents February 2008 and ldquo36rdquo means January 2011

The plots of the irregular orders and money per monthshown in Figure 3 describe two factors (1) The irregularbusiness was affected by the economic recession which hitChina between the third and fourth quarters of 2008 Thedownturn began inOctober 2008 (2)Orders declined rapidlyfrom October 2008 and eventually disappeared

Originating in the developed countries the economic cri-sis soon spread to China as shown by the decreasing number

Discrete Dynamics in Nature and Society 3

012345

Date

Gap

bet

wee

n or

ders

HM-machine

04

-10

04

-17

04

-24

05

-01

05

-08

05

-15

05

-22

05

-29

06

-05

06

-12

06

-19

06

-26

07

-03

07

-10

07

-17

07

-24

07

-31

08

-07

08

-14

(a) Continuous only broken at weekends and vacations

Date

Gap

bet

wee

n or

ders

05

10152025

XG-electronics

01

-17

01

-31

02

-14

02

-28

03

-13

03

-27

04

-10

04

-24

05

-08

05

-22

06

-05

06

-19

07

-03

07

-17

07

-31

08

-14

08

-28

09

-11

09

-25

10

-09

10

-23

11

-06

11

-20

(b) Discrete and regular

Figure 1 Gaps between regular orders in days

Date

Gap

bet

wee

n or

ders

0100200300400500

XQYP-chinaware

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19

09

-19

10

-19

11

-19

12

-19

01

-19

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19

(a) Occasional orders

Date

Gap

bet

wee

n or

ders

0

5

10

15

20

JY-logistics01

-05

01

-19

02

-02

02

-16

03

-02

03

-16

03

-30

04

-13

04

-27

05

-11

05

-25

06

-08

06

-22

07

-06

07

-20

08

-03

08

-17

08

-31

09

-14

09

-28

(b) Relatively longer span and irregular

Figure 2 Gaps between irregular orders in days

Table 2 Regular and irregular customers

Regular 12 customers9147 orders

Nameindustry

Irregular 20 customers1658 orders

NameindustryHYucraft YLMtoy OWYcraft QSlogisticsGLcraft HMmachine HScraft XQlogisticsXGelectronics HYaelectronics YLXlogistics

GDelectronics WLielectronics CHlogistics

WLinelectronics ZHfood GYlogistics

GHlogistics LHlogistics JFXlogistics

HFlogistics LRlogistics FYlogistics

KLDlogistics QFTlogistics XQchinaware

KZlogistics JYlogistics SHmachine

HLmaterial ADmaterial HLDmachine

of ordersThose companies involved in overseasmarketswereaffected first in the third quarter of 2008 PureOEM (originalequipment manufacturing) and excessive reliance on over-seas market were the two major factors which made thesecompanies fail in the recession rapidlyThose companies rely-ing on the home market were affected by a time lag becauseof reduced business with the export-oriented companies andthe declining purchasing power of workers laid off by thosecompanies

The regular orders and money per month in total aregiven in Figure 4 from which conclusions can be drawn asfollows

(1) There is obvious periodicity by year both for ordersand for income

(2) There is an increase in trend but the slope is graduallydecreasing

(3) Orders and money surprisingly increase after thearrival of the recession

Some weak companies ceased trading almost immedi-ately but the robust ones survived Businesses concentratedon those surviving companies

Every coin has two sidesThe recession had both negativeand positive impacts on the companyrsquos businessWhereas thebusiness tradewas slowing down the quality of the companyrsquoscustomers was better after the recession and a large numberof irregular businesses disappeared Graphs of the orders andincome have similar shapes so the regular group is the focusof the following work

3 Modeling and Forecasting

Most modeling and forecasting approaches with limited dataare about rapidly changing industries like motion picturestelecommunications or new products with a short history[9ndash13] They suggest that combining ARIMA and diffusionmodels can improve one-year-ahead predictions especiallyin the high technology market The drawback however


050

100150200250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Orders

0100200300400500600700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY

1000

Money

Time (month) Time (month)

Figure 3 Irregular orders and money per month in total


Ord

ers

Orders

0100200300400500600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Money

0100200300400500600700800900

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35CH

Y 10

00

Figure 4 Regular orders and money per month in total

is the need for enough historical data points to create atime series The necessity of judgment in forecasting withinsufficient data for statistical methodology was discussed in[14] The key is to impose a structure with methods suchas surveys of intentions or expectations judgmental boot-strapping structured analogies and simulated interaction Acase study about fashion products generally characterizedby high demand uncertainty high stock out costs and ahigh risk of obsolescence proposes that preorder data andjudgments can be used to overcome the lack of data indemand forecasting Advance order data can be obtainedby allowing a selected group of customers to preorder ata discount from a preview catalogue Judgments can beobtained from purchase managers or other company experts[15]

A significant improvement in nonlinear time seriesanalysis (NTSA) has been seen since the 1990s [16] Tonglisted the following as the five most promising directionsthe interface between NTSA and chaos the nonparamet-ricsemiparametric approach nonlinear state space model-ing financial time series (in both discrete time and contin-uous time) and nonlinear modeling of panels (eg spatiallydistributed) in time series A polynomial spline approxi-mation was employed to estimate the functional coefficientregression models for nonlinear time series [17] A time-varying coefficient time series model with a time trendfunction and serially correlated errors to characterize thenonlinearity nonstationarity and trending phenomena wasdiscussed in [18] A time series can be decomposed intotrend cycle and seasonal and random components [19]Thatis moving averages isolating seasonal factors and seasonal

adjustments are common methodology for treating seasonaladjustment of time series

No single model or combination model has been provedto outperform the rest In order to model and forecast thesmall truck transportation companyrsquos start-up and growthafter the economic recession from the limited data describedin Section 2 relative variable analysis and time series analysiswere used to predict the orders and turnover Meanwhilecorrelation analysis and polynomial and logistic curve mod-els were also employed to find the trend by combiningseasonality adjustment to predict order number and turnover

Simple linear regression and binary linear regression aretwo basic versions of the generalized linear model (GLM)proposed by [20] as a way of unifying various other statisticalmodels including linear regression logistic regression andPoisson regression

Linear regression was employed to search for the relationbetween orders and import amp export inmonths or orders andimport amp export and GDP in quarters for GDP only availablein quarters The general form of a linear regression model is

119910 = 119886 + 119887119894119909119894+ 119890 119894 = 1 2 119899 (1)

where 119910 is the dependent variable denoting the orders119909119894(119894 = 1 2 119899) is the predictor variable with a subscript

119894 and 119899 is the number of variables 119890 is noiseIn statistics signal processing econometrics and math-

ematical finance a time series is a sequence of data pointsmeasured typically at successive times at uniform time inter-vals Time series forecasting is the use of a model to predictfuture values based on previously observed values Methods


for time series analyses may be divided into two classesfrequency-domain methods and time-domain methods Theformer include spectral analysis and recently wavelet anal-ysis the latter include autocorrelation and cross-correlationanalysis

Our time series analysis began by regrouping the datasplitting the distance into five sections and business into twokindsThe firstmodel was the polynomial as in the following

119874119889119904

= 120583 + 1205731119905119910+ 12057321199052

119910+ 12057331199053

119910+ 119904119894 (2)

Then for an alternative of the logistic curve regression

119874119889119904

= 120572119889119904

sdot (119890120573119889119904119905119898

1 + 119890120573119889119904119905119898) (3)

Therefore the turnover forecast is as the following forboth trend forecast models

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119889119904 (4)

where 119881119889119904

is average price or value of distant 119889 and type 119904119874119889119904the orders of distant 119889 and type 119904 119878

119894the noise 119905

119910is the

time by year and 1 = the starting year 2008 in this case 120572119889119904

and 120573119889119904are coefficients of the logistic model in subgroups of a

distance119889 (= 1 2 3 4 5) and a type 119904 (= 1 2) 119905119898(= 1 2 36)

represents the time by monthAny time series is made up of systematic components

such as a trend cycle and seasonal and random elementswhich are by definition unpredictable Therefore a set oftime series data can be decomposed into trend cycle andseasonal and random components The four elements can becombined in either an additive or a multiplicative model [19]

119883119905119898

= 119879 + 119862 + 119878 + 119877 (5)

119883119905119898

= 119879 times 119862 times 119878 times 119877 (6)

where119883119905119898represents the dependent variable of orders 119879 the

trend component 119862 the seasonal factor and 119877 the randomelement

Moving averages are often used to isolate the trend Wepropose however to extract the trend directly from theoriginal data with both the polynomial and logistic curvemodels and then to decompose the combination of the cycleand seasonality by the additive model in (5) Considering theclose relationship between transportation and economics wecan ignore the cyclical component by taking the seasonalityas a cycle of 12 months The cycle was previously defined asrunning from February to January of the next year as thelowest demand usually falls in February

We take the additive model (5) and rewrite it as

119883119905119898

minus 119879 = 119878 + 119877 (7)

Let 119878119877 (= 119878 + 119877) be the combination of the seasonal andrandom components and then divide 119878119877 by the trend 119879 toget the seasonal ratio 119878

119888(including the random) Hence the

seasonal factor can be obtained by averaging the three ratio

Table 3 Segmentation of the distance

119889 1 2 3 4 5distance lt90 km 90ndash179 km 180ndash350 km 351ndash800 km gt801 km

components (February 2008 to January 2009 February 2009to January 2010 and February 2010 to January 2011) for eachmonth 119878

119888 119888 = 1 2 12 For example for February the

average seasonal ratio 119878119888is as follows

1198781=

1

3(

119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=1

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=13

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=25

)

(8)

where 119905119898(=12 36) represents months from the beginning

in the series Now the forecasting value of119883119905119898can be obtained

by

119883119905119898

= 119879 + 119878 + 119877 = 119879 (1 + 119878119888)

119905119898

= 1 2 36 119888 = 1 2 12

(9)

Then the total orders in (10) and (4) should be changed to

orders =5

sum

119889=1

2

sum

119904=1

119874119905119903

119889119904(1 + 119878

119888) (10)

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119905119903

119889119904(1 + 119878

119888) (11)

119874119905119903

119889119904is the trends forecast by the polynomial or logistic model

4 Application

First simple linear regression analysis is taken to model therelationship between the national export amp import and theorders The result is given in Figure 5

The predicted regular orders per month = minus148296 +

0330 lowast national import amp exportThen the binary linear regression of the orders and

imports amp exports and GDP per quarter is presented inFigure 6

The predicted regular orders per quarter = minus560432 +

1076 lowast GDP + 0158 lowast import amp exportAs the relative analysis cannot give satisfactory results

even intuitively we turn to the time series analysisThewholeregular business is separated by distance and truck type whenthe time series analysis is chosen Distance is separated intofive categories according to the rates and transport time andcontainer and bulk are the two types of services Variable 119889

represents the different segmentation of the distance shownin Table 3 Type variable 119904 = 1 represents container and 119904 = 2

the bulkThe result shows that almost all the container transport

orders are included in distance groups 1 2 and 3 with just oneout of 7755 regular container orders from February 2008 toJanuary 2011 in container group 4Most bulk transport ordersare included in distance groups 1 3 and 5 As the data of bulk


Table 4 The seasonal ratios in the polynomial model

Group Cycle1 2 3 4 5 6 7 8 9 10 11 12

11 minus04104 minus03695 minus01292 minus00093 minus01897 minus01207 02280 03509 05158 00453 00209 minus0159721 minus04775 minus03617 minus02347 01407 02389 03525 03019 02410 00508 minus01913 00472 0219931 minus04325 minus01774 05607 minus01737 minus01317 03161 02004 03484 minus01109 minus05404 minus02736 0370712 05909 minus08788 01113 minus00745 04005 03488 minus03943 minus01522 minus00579 minus01450 02265 0213422 minus06800 06150 03167 minus01666 minus04749 minus00283 minus04198 minus03530 minus01552 minus00745 minus04022 minus02205

0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers

Order regularPredicted order

Time (month)

Figure 5 Simple linear regression of the regular orders and nationalimport amp export

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers

Predicted ordersOrder regular

Time (season)

Figure 6 Binary linear regression regular orders and import ampexport and GDP

groups 2 and 3 are insufficient for modeling we merge bulkgroups 1 2 and 3 into a new bulk group 1 and bulk groups 4and 5 into a new bulk group 2

Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452

= 0 and only theremaining five subgroups need to be estimatedThe results ofthe polynomial trend models and seasonal ratios in Table 4

are listed in the following calculations and shown in Figures7 and 8

11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)

Forecast orders of all groups are presented in Figures 7and 8

Putting (12) into (11) we can calculate the money(turnover) The results show that (1) the container and thebulk have linear and quadratic trends respectively and (2) theresults are acceptable until March 2011 but the linear trendjust increases and the quadratic trend abruptly decreases afterApril 2011 which is not in line with the actual situation

Therefore an alternative logistic model is needed Equa-tion (3) is the assumed trend function of orders Let (10) and(11) be the total orders and money prediction formulation

The order-prediction models are given in (13) with thesecond bulk group showing a polynomial trend

11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Predicted 011Observed 011

Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070

Time (month)Time (month)

Time (month)

Figure 7 The orders of container transportation predicted by the polynomial model

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50


Figure 8 The orders of bulk transportation predicted by the polynomial model

Results of calculation of seasonal ratios are presented inTable 5

The results of the logistic model are shown in Figures 9and 10 Only the group 119874

22could not be fitted by the logistic

modelThe results of the polynomial and logistic models are

compared in Figure 11 The predictions given by the twomodels are not very different at present but the logistic trendwill be more significant in the future

In conclusion the initial modeling of the orders cannotimmediately account for the demand in terms of exportsamp imports or GDP The polynomial trend does not give asound prediction in the sample and the logistic modeling of

the orders seems appropriate The forecasted total money ispresented in Figure 12

Model selection depends primarily on two aspects Oneis the forecast in the sample The second is the predictionout of the sample The forecasts of the polynomial modeldecrease abruptly out of the sample and the logistic hasa better performance in this aspect Therefore the logisticmodel outperforms the polynomial model out of the sample

Now let us turn to the analysis in the sample There aresome specific criteria such as the coefficient of determination1198772 and 119865-test which measure the goodness-of-fit to discrim-

inate which model is better than the others with regard tolinear regression models This is not the case with nonlinear


0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)

Figure 9 The container orders predicted by the logistic model

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045


Figure 10 The bulk orders predicted by the logistic model

Table 5 Calculation of seasonal ratios by the logistic model

Group Cycle1 2 3 4 5 6 7 8 9 10 11 12

11 minus01069 minus00242 04384 06197 02914 04368 04109 06343 07970 02457 01089 minus0029721 minus05951 minus05055 minus00923 03730 04713 06163 02290 01802 00183 minus02400 minus00248 0176931 minus01282 02625 15265 02267 02936 09351 04475 05893 00670 minus04422 minus01267 0615012 03373 11651 06528 minus00700 01107 00369 02534 minus01151 04275 minus01993 00686 minus0144322 minus06800 06150 03167 minus01666 minus04749 minus00283 minus04198 minus03530 minus01552 minus00745 minus04022 minus02205


0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Order observedOrder polynomialOrder logistic

Time (month)

Figure 11 Comparison of the results of the two forecasting modelsorders

0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY

PolynomialLogisticObserved

Time (month)

Figure 12 Comparison of the results of the two forecasting modelsincome

regression models (NLRMs) however According to [20] wecannot use the 119905-test (to test the significance of an individualcoefficient) or the 119865-test (to test the overall significance of theestimated regression) because we cannot obtain an unbiasedestimate of the error variance1205902 from the estimated residualsFurthermore the residuals (the difference between the actual119910 values and the estimated 119910 values from the NLRM) donot necessarily sum to zero ESS and RSS do not necessarilyadd up to the TSS and therefore 119877

2= ESSTSS may not

be a meaningful descriptive statistic for such models Analternative of pseudo 119877 square to 119877

2 is proposed by [21] asfollows

1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)

where 119899 is the observation number 119910 = regress and 119894=

119910119894minus 119910119894 where 119910

119894are the estimated 119910 values from the (fitted)

NLRM Results are shown in Table 6From Table 6 the values of 1198772 of orders prediction by

the two models are nearly the same When it comes to theincome prediction the value of 1198772 of the logistic model has

Table 6 Measure of goodness-of-fit of polynomial and logistictrend models

Model DifferencePolynomial

trend seasonaladjustment

Logistic trendseasonal

adjustment1198772orders prediction 00066 07826 07760

1198772money prediction minus00453 08569 09022

a slight advantage over the polynomial model As previouslydescribed the logistic model is better than the polynomialone in predicting performance out of the sample The com-parison in the sample shows however that performances ofthe two models are very similar On balance however thelogistic model is better than the polynomial

5 Conclusions and Discussion

This paper introduces a small truck transportation companyrsquosstart-up whose main business is pier containers and whoseminority business is long-distance bulk transportation Wehave attempted to elucidate how our analysis led to usefulinformation for SMTE owners Modeling the forecasting oforder numbers of both kinds of businesses and the totalturnover contributes to establishing the companyrsquos strategyfor investment and operations

Initial modeling of orders by simple regression andbinary regression models cannot immediately account fordemand in terms of exports or GDP The results show thatthe companyrsquos business is certainly affected by the nationalmacroeconomic factors such as GDP and import amp exportand this effect comes with a time lag of one to two yearssince transportation service demand is derived demandThe seasonal fluctuation of orders however is much moredramatic than that of the national GDP and total importamp export It may be the main reason why the regressionmodels did not perform well in forecasting Competitiveenvironment factors such as customers and competitors affectperformance directly for SMTEs

There are insufficient data about customers and competi-tors to support the simple regression model Therefore thetime series analysis is the inevitable choice We segmentedthe data by business and transportation distance to get a setof time series data The polynomial and the logistic trendmodels combined with additional seasonal components wereemployed to fit the data of different segments Both fittedthe sample data very well but the polynomial trend doesnot give sound forecasting for the fast decreasing trend outof the sample From the perspective of goodness-of-fit thepolynomial trend model is still acceptable

We have to say that forecasting in future is obviously atvariance with reality On the one hand small transportationcompanies are not necessarily bound to continue to grow intolarge ones because of indifferent marketing and the lack ofeconomies of scale On the other hand most small trans-portation companies can survive for a relatively long periodthanks to their flexible operationmode Usually a polynomialtrend model does not work well for unlimited increasing or


decreasing trends while higher-order coefficients are positiveor negative respectively One of the reasons why the logisticmodeling of the orders seems appropriate is that it has giventhe upper limit of business Acceptable goodness-of-fit andforecasting performance can only be provided by the logisticmodel even though the performance of the twomodels in thesample is nearly the same to solve the question in this paper

Unexpectedly the analysis presented the process of thefinancial crisisrsquos effect on SMTEs First irregular businessdisappears immediately the crisis emerges at the same timethe regular business increases rather than decreases and thenslows down with a time lag of one to two years whichis established by the logistic model Within the effectivedistance of the truck transportation the total transportationdemand is relatively stable and the market is competitive orcontestableThegrowth rate ofmost small andmedium trans-portation enterprises will become slower after their quickgrowth period and have an upper limit scale of business

Our approach can cope with the different impetus ofSMTEsrsquo growth and a period of financial stress One wouldexpect that in less periods of financial stress then growthmight be more rapid for SMTEs but not that they necessarilywill continue to grow rapidly With further data one couldexplore how later SMTEs might develop in more benigneconomic contexts We believe however that the proposedmodel would still achieve a reasonable fit

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) under Grant no 61203162It was also supported in part by the Science Progress andInnovation ProgramofHunanDOTunderGrant no 201244

References

[1] National Bureau of Statistics of China ldquoThe second economiccensus data bulletin (no1)rdquo 2009 httpwwwstatsgovcntjsjpcsjjjpc2jpindexchhtm

[2] National Development and Reform Commission NationalBureau of Statistics of China and China Federation of Logisticsamp Purchasing ldquo2008 National Logistics operation SituationBulletinrdquo 2009 httpwwwsdpcgovcnjjyxxdwlt20090306264999htm

[3] X Chen X Wang and D D Wu ldquoCredit risk measurementand early warning of SMEs an empirical study of listed SMEsin Chinardquo Decision Support Systems vol 49 no 3 pp 301ndash3102010

[4] J Ansell and J Banasik ldquoForecasting white goods in a recesionrdquoIMA Journal of Management Mathematics vol 6 no 3 pp 315ndash331 1995

[5] T J Fite G D Taylor J S Usher J R English and J N RobertsldquoForecasting freight demand using economic indicesrdquo Interna-tional Journal of Physical Distribution amp Logistics Managementvol 32 no 4 pp 299ndash308 2002

[6] S Shen T Fowkes T Whiteing and D Johnson ldquoEconometricmodelling and forecasting of freight transport demand inGreat Britainrdquo in Proceedings of European Transport Conferencehttpabstractsaetransportorg

[7] L Zhou B Heimann and U Clausen ldquoForecasting a logisticservice demand based on neural networkrdquo in Proceedings ofthe International Conference on Service Systems and ServiceManagement (ICSSSM rsquo06) vol 1 pp 530ndash534 October 2006

[8] J Harris Fuzzy Logic Applications in Engineering Science Intelli-gent Systems Control and Automation Science and EngineeringSpringer Dordrecht The Netherlands 2006

[9] B G S Hardie P S Fader and M Wisniewski ldquoAn empiricalcomparison of new product trial forecasting modelsrdquo Journal ofForecasting vol 17 no 3-4 pp 209ndash229 1998

[10] P McBurney S Parsons and J Green ldquoForecasting marketdemand for new telecommunications services an introduc-tionrdquo Telematics and Informatics vol 19 no 3 pp 225ndash2492002

[11] A Mukherjee and V Kadiyali ldquoForecasting in rapidly changingenvironments an application to the US motion picture indus-tryrdquo Cornell University Johnson School Research Paper Series10-07

[12] G Madden R Cooper and R Fildes ldquoTheoretically-motivatedlong-term forecasting with limited datardquo Working Paper 240The MIT Center for Digital Business 2008

[13] C Christodoulos C Michalakelis and D Varoutas ldquoFore-casting with limited data combining ARIMA and diffusionmodelsrdquo Technological Forecasting amp Social Change vol 77 no4 pp 558ndash565 2010

[14] K C Green and J S Armstrong ldquoDemand forecastingevidence-based methodsrdquo Working Paper University of Penn-sylvania Department of Marketing 2005

[15] J Mostard R Teunter and R De Koster ldquoForecasting demandfor single-period products a case study in the apparel industryrdquoEuropean Journal of Operational Research vol 211 no 1 pp 139ndash147 2011

[16] H Tong ldquoNonlinear time series analysis since 1990 somepersonal reflectionsrdquo Acta Mathematicae Applicatae Sinica vol18 no 2 pp 177ndash184 2002

[17] J Z Huang and H Shen ldquoFunctional coefficient regres-sion models for non-linear time series a polynomial splineapproachrdquo Scandinavian Journal of Statistics vol 31 no 4 pp515ndash534 2004

[18] Z Cai ldquoTrending time-varying coefficient time series modelswith serially correlated errorsrdquo Journal of Econometrics vol 136no 1 pp 163ndash188 2007

[19] M Barrow Statistics for Economics Accounting and BusinessStudies Pearson Education London UK 5th edition 2009

[20] J A Nelder and R W M Wedderburn ldquoGeneralized linearmodelsrdquo Journal of the Royal Statistical Society Series A vol 135no 3 pp 370ndash384 1972

[21] D N Gujarati Basic Econometrics McGraw-Hill New YorkNY USA 4th edition 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Table 1 Business data by industry

Industry No of customers No of orders MoneyAbsolute value Percentage Absolute value Percentage Absolute value Percentage

Food 1 3125 24 02221 91900 04495Toy 1 3125 154 14253 430492 21054Chinaware 1 3125 358 33133 949029 46414Material 2 6250 151 13975 363945 17799Machine 3 9375 4423 409348 4474611 218837Craft 4 12500 1001 92642 2867729 140250Electronics 5 15625 1999 185007 2541727 124307Logistics 15 46875 2695 249422 8727782 426845Total 32 100 10805 100 20447215 100

it is believed that the combination of neural networks andtraditional time series analysis is good for forecasting short-term logistic demand for an LTL carrier A small-to-medium-sized road transport servicewhich offered a limited collectionand delivery service for small and large consignments in anumber of geographical zones of equal area is reported in [8]

The objective of this study is to model the start-up andgrowth of a newly established truck transportation companyduring the economic recession whose main business is sea-port containers and bulk inland transportation It ultimatelyaims to help SMTEs to look for ways of improving equipmentutilization in the short to medium term by forecasting theorders and the trucks required as well as the impact offinancial crisis The main feature of our work is its use oflimited data to analyze and forecast a small transportationcompanyrsquos business as it starts up in a rapidly changingenvironment

The context of the model has two distinct elementsenterprise start-up and the short time series Obviouslymost enterprises in their start-up period need to grow theirbusiness to an economic scale If they fail to do so the longtime survival of the enterprisemay be under question Hencethe model selected will have to accommodate such growthThe second element reflects the need for quick appraisal oflikely demand so that appropriate economic strategy canbe developed by the enterprise This differentiates start-upSMTEs from LTEs where there is possibly longer times seriesand higher correlation of performance with macroeconomicfactors The modeling proposed attempts to cope with thesetwo elements

2 Data

The data covers all the business orders of a small trucktransportation company during a 40-month period (January2008 to April 2011) Registered at the end of 2007 the smalltruck transportation company currently has a fleet of 30trucks and 30 drivers Some trucks are container truckssuitable for container transportation and others are bulktrucks designed for heavy long-distance bulk transportationservices This company mainly provides services for piercontainer transportation and inland bulk transportationThe container transportation service is mainly provided

for container customers who have exporting and import-ing businesses at three ports located in Shenzhen namelyYantian Shekou and Mawan In order to make use of theempty containers at these ports a small part of the bulk istransported for the container customers in container trucksat the same price as bulk transportation Most of the rest iscarried by bulk trucks for different customers

All the business orders from this company are classifiedaccording to the categories of the customer industry (seeTable 1) ldquoMoneyrdquo in this paper represents the gross incomewhich equals the orders multiplying the unit price Thecustomers come from eight industries and 15 logistics cus-tomers contribute 427 of the total money three machinecustomers account for 409 of the orders and 219 of thegross income and the remaining 14 customers from the foodtoy chinaware material craft and electronics industriesaccount for 34123 of the orders and 35432 of the totalgross income

Further analysis shows that there are two patterns asregards gaps in orders regular and irregular Regular ordersare made either continuously on weekdays and broken atweekends and vacations (shown in Figure 1(a)) or discretelyand regularly (shown in Figure 1(b)) Irregular orders aremade randomly as shown in Figures 2(a) and 2(b) Thecustomers who make regular and irregular orders are listedin Table 2

In order to find out whether the economic recession of2008 had an effect on the companyrsquos business further analysisof the orders and money per month was conducted for bothregular and irregular businesses It should be noted that theChinese New Year usually falls in February when almost allbusinesses are at their lowest level of production A three-yearperiod is considered and the cycle starts from February of thefirst year to January of the last year Therefore ldquo1rdquo in Figure 3represents February 2008 and ldquo36rdquo means January 2011

The plots of the irregular orders and money per monthshown in Figure 3 describe two factors (1) The irregularbusiness was affected by the economic recession which hitChina between the third and fourth quarters of 2008 Thedownturn began inOctober 2008 (2)Orders declined rapidlyfrom October 2008 and eventually disappeared

Originating in the developed countries the economic cri-sis soon spread to China as shown by the decreasing number


012345

Date

Gap

bet

wee

n or

ders

HM-machine

04

-10

04

-17

04

-24

05

-01

05

-08

05

-15

05

-22

05

-29

06

-05

06

-12

06

-19

06

-26

07

-03

07

-10

07

-17

07

-24

07

-31

08

-07

08

-14


Date

Gap

bet

wee

n or

ders

05

10152025

XG-electronics

01

-17

01

-31

02

-14

02

-28

03

-13

03

-27

04

-10

04

-24

05

-08

05

-22

06

-05

06

-19

07

-03

07

-17

07

-31

08

-14

08

-28

09

-11

09

-25

10

-09

10

-23

11

-06

11

-20



Date

Gap

bet

wee

n or

ders

0100200300400500

XQYP-chinaware

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19

09

-19

10

-19

11

-19

12

-19

01

-19

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19


Date

Gap

bet

wee

n or

ders

0

5

10

15

20

JY-logistics01

-05

01

-19

02

-02

02

-16

03

-02

03

-16

03

-30

04

-13

04

-27

05

-11

05

-25

06

-08

06

-22

07

-06

07

-20

08

-03

08

-17

08

-31

09

-14

09

-28





Nameindustry




















050

100150200250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Orders

0100200300400500600700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY

1000

Money




Ord

ers

Orders

0100200300400500600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Money

0100200300400500600700800900

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35CH

Y 10

00








119910 = 119886 + 119887119894119909119894+ 119890 119894 = 1 2 119899 (1)







119874119889119904

= 120583 + 1205731119905119910+ 12057321199052

119910+ 12057331199053

119910+ 119904119894 (2)


119874119889119904

= 120572119889119904

sdot (119890120573119889119904119905119898

1 + 119890120573119889119904119905119898) (3)


money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119889119904 (4)

where 119881119889119904


119894the noise 119905

119910is the






119883119905119898

= 119879 + 119862 + 119878 + 119877 (5)

119883119905119898






119883119905119898

minus 119879 = 119878 + 119877 (7)









1198781=

1

3(

119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=1

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=13

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=25

)

(8)



by

119883119905119898

= 119879 + 119878 + 119877 = 119879 (1 + 119878119888)

119905119898

= 1 2 36 119888 = 1 2 12

(9)


orders =5

sum

119889=1

2

sum

119904=1

119874119905119903

119889119904(1 + 119878

119888) (10)

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119905119903

119889119904(1 + 119878

119888) (11)

119874119905119903


4 Application













Group Cycle1 2 3 4 5 6 7 8 9 10 11 12


0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers


Time (month)


0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers


Time (season)



Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452



11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)





11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










012345

Date

Gap

bet

wee

n or

ders

HM-machine

04

-10

04

-17

04

-24

05

-01

05

-08

05

-15

05

-22

05

-29

06

-05

06

-12

06

-19

06

-26

07

-03

07

-10

07

-17

07

-24

07

-31

08

-07

08

-14


Date

Gap

bet

wee

n or

ders

05

10152025

XG-electronics

01

-17

01

-31

02

-14

02

-28

03

-13

03

-27

04

-10

04

-24

05

-08

05

-22

06

-05

06

-19

07

-03

07

-17

07

-31

08

-14

08

-28

09

-11

09

-25

10

-09

10

-23

11

-06

11

-20



Date

Gap

bet

wee

n or

ders

0100200300400500

XQYP-chinaware

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19

09

-19

10

-19

11

-19

12

-19

01

-19

02

-19

03

-19

04

-19

05

-19

06

-19

07

-19

08

-19


Date

Gap

bet

wee

n or

ders

0

5

10

15

20

JY-logistics01

-05

01

-19

02

-02

02

-16

03

-02

03

-16

03

-30

04

-13

04

-27

05

-11

05

-25

06

-08

06

-22

07

-06

07

-20

08

-03

08

-17

08

-31

09

-14

09

-28





Nameindustry




















050

100150200250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Orders

0100200300400500600700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY

1000

Money




Ord

ers

Orders

0100200300400500600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Money

0100200300400500600700800900

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35CH

Y 10

00








119910 = 119886 + 119887119894119909119894+ 119890 119894 = 1 2 119899 (1)







119874119889119904

= 120583 + 1205731119905119910+ 12057321199052

119910+ 12057331199053

119910+ 119904119894 (2)


119874119889119904

= 120572119889119904

sdot (119890120573119889119904119905119898

1 + 119890120573119889119904119905119898) (3)


money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119889119904 (4)

where 119881119889119904


119894the noise 119905

119910is the






119883119905119898

= 119879 + 119862 + 119878 + 119877 (5)

119883119905119898






119883119905119898

minus 119879 = 119878 + 119877 (7)









1198781=

1

3(

119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=1

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=13

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=25

)

(8)



by

119883119905119898

= 119879 + 119878 + 119877 = 119879 (1 + 119878119888)

119905119898

= 1 2 36 119888 = 1 2 12

(9)


orders =5

sum

119889=1

2

sum

119904=1

119874119905119903

119889119904(1 + 119878

119888) (10)

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119905119903

119889119904(1 + 119878

119888) (11)

119874119905119903


4 Application













Group Cycle1 2 3 4 5 6 7 8 9 10 11 12


0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers


Time (month)


0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers


Time (season)



Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452



11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)





11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










050

100150200250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers

Orders

0100200300400500600700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY

1000

Money




Ord

ers

Orders

0100200300400500600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Money

0100200300400500600700800900

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35CH

Y 10

00








119910 = 119886 + 119887119894119909119894+ 119890 119894 = 1 2 119899 (1)







119874119889119904

= 120583 + 1205731119905119910+ 12057321199052

119910+ 12057331199053

119910+ 119904119894 (2)


119874119889119904

= 120572119889119904

sdot (119890120573119889119904119905119898

1 + 119890120573119889119904119905119898) (3)


money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119889119904 (4)

where 119881119889119904


119894the noise 119905

119910is the






119883119905119898

= 119879 + 119862 + 119878 + 119877 (5)

119883119905119898






119883119905119898

minus 119879 = 119878 + 119877 (7)









1198781=

1

3(

119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=1

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=13

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=25

)

(8)



by

119883119905119898

= 119879 + 119878 + 119877 = 119879 (1 + 119878119888)

119905119898

= 1 2 36 119888 = 1 2 12

(9)


orders =5

sum

119889=1

2

sum

119904=1

119874119905119903

119889119904(1 + 119878

119888) (10)

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119905119903

119889119904(1 + 119878

119888) (11)

119874119905119903


4 Application













Group Cycle1 2 3 4 5 6 7 8 9 10 11 12


0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers


Time (month)


0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers


Time (season)



Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452



11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)





11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119874119889119904

= 120583 + 1205731119905119910+ 12057321199052

119910+ 12057331199053

119910+ 119904119894 (2)


119874119889119904

= 120572119889119904

sdot (119890120573119889119904119905119898

1 + 119890120573119889119904119905119898) (3)


money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119889119904 (4)

where 119881119889119904


119894the noise 119905

119910is the






119883119905119898

= 119879 + 119862 + 119878 + 119877 (5)

119883119905119898






119883119905119898

minus 119879 = 119878 + 119877 (7)









1198781=

1

3(

119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=1

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=13

+119883119905119898

minus 119879

119879

100381610038161003816100381610038161003816100381610038161003816119905119898=25

)

(8)



by

119883119905119898

= 119879 + 119878 + 119877 = 119879 (1 + 119878119888)

119905119898

= 1 2 36 119888 = 1 2 12

(9)


orders =5

sum

119889=1

2

sum

119904=1

119874119905119903

119889119904(1 + 119878

119888) (10)

money =

5

sum

119889=1

2

sum

119904=1

119881119889119904

sdot 119874119905119903

119889119904(1 + 119878

119888) (11)

119874119905119903


4 Application













Group Cycle1 2 3 4 5 6 7 8 9 10 11 12


0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers


Time (month)


0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers


Time (season)



Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452



11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)





11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Group Cycle1 2 3 4 5 6 7 8 9 10 11 12


0100200300400500600700800

1 4 7 10 13 16 19 22 25 28 31 34 37

Ord

ers


Time (month)


0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

Ord

ers


Time (season)



Thus 11987441

= 11987451

= 11987432

= 11987442

= 11987452



11987411

= (minus557778 + 9158333119905119910) sdot (1 + 119878

11

119888)

11987421

= (10 + 2745833119905119910) sdot (1 + 119877

21

119888)

11987431

= (49444 + 908333119905119910) sdot (1 + 119877

31

119888)

11987412

= (minus198967 + 29610881199052

119910minus 038809119905

3

119910)

sdot (1 + 11987712

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(12)





11987411

= 10638 times119890095+0104119894

1 + 00519119890095+0104119894sdot (1 + 119877

11

119888)

11987421

= 151 times119890095+0104119894

1 + 00169119890095+0104119894sdot (1 + 119877

21

119888)

11987431

= 396 times119890095+0104119894

1 + 0145119890095+0104119894sdot (1 + 119877

31

119888)

11987412

= 12823 times119890minus1605+01643119894

1 + 0164119890095+0104119894sdot (1 + 119877

12

119888)

11987422

= (minus436667 + 580833119905119910minus 135833119905

2

119910)

sdot (1 + 11987722

119888)

(13)


050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










050

100150200250300350400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Ord

ers

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


010203040506070


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50














0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

50

100

150

200

250

300

350

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


020406080

100120140160

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

10

20

30

40

50

60

70


Time (month)


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


05

1015202530354045




Group Cycle1 2 3 4 5 6 7 8 9 10 11 12



0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0100200300400500600700800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Ord

ers


Time (month)


0100000200000300000400000500000600000700000800000900000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CHY


Time (month)



2= ESSTSS may not



1198772

= 1 minussum119899

119894=12

119894

sum119899

119894=1(119910119894minus 119910)2 (14)


119910119894minus 119910119894 where 119910




















Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Modeling of a Small Transportation ...downloads.hindawi.com/journals/ddns/2013/802528.pdflisted the following as the ve most promising directions: the interface between