This paper presents a modeling method for analyzing a small transportation company’s startup and growth during a global economic crisis which had an impact on China which is designed to help the owners make better investment and operating decisions with limited data. Since there is limited data, simple regression model and binary regression model failed to generate satisfactory results, so an additive periodic time series model was built to forecast business orders and income. Since the transportation market is segmented by business type and transportation distance, a polynomial model and logistic curve model were constructed to forecast the growth trend of each segmented transportation market, and the seasonal influence function was fitted by seasonal ratio method. Although both of the models produced satisfactory results and showed very nearly the same of goodnessoffit in the sample, the logistic model presented better forecasting performance out of the sample therefore closer to the reality. Additionally, by checking the development trajectory of the case company’s business and the financial crisis in 2008, the modeling and analysis suggest that the sample company is affected by national macroeconomic factors such as GDP and import & export, and this effect comes with a time lag of one to two years.
Transport infrastructure is critical to economic development of a country and can provide competitive advantage. Within China there is a diversity of transport companies which could be split between with largescale transport enterprises (LTEs) and small and mediumsized transportation enterprises (SMTEs). There are many distinct differences between the two types of enterprises. Generally, LTEs, more geographically spread, attract larger enterprises and resource management is not as critical. SMTEs especially in their startup period need to be more agile in the use of their financial resources to ensure survival. This is particularly true during a period of economic change. This paper focuses on SMTEs since they are the main suppliers of road transportation services in China. They necessarily play the role of firstand/orlast kilometer carriers for doortodoor logistics services. Some 225 259 enterprises and 4 595 600 individually owned businesses were engaged in transportation, storage, and postal services in 2008 [
Demand forecasting is so significant for SMTEs that it can help to improve equipment utilization and establish smarter operational and investment strategies. Realistically, business owners estimate the service demand from their past experiences which can be wrong or misleading. Almost all freight demand analysis usually accounts for a whole country, a region, or a corridor between cities by integration or by mode and is usually to do with public transportation planning [
The objective of this study is to model the startup and growth of a newly established truck transportation company during the economic recession whose main business is seaport containers and bulk inland transportation. It ultimately aims to help SMTEs to look for ways of improving equipment utilization in the short to medium term by forecasting the orders and the trucks required, as well as the impact of financial crisis. The main feature of our work is its use of limited data to analyze and forecast a small transportation company’s business as it starts up in a rapidly changing environment.
The context of the model has two distinct elements: enterprise startup and the short time series. Obviously, most enterprises in their startup period need to grow their business to an economic scale. If they fail to do so the long time survival of the enterprise may be under question. Hence, the model selected will have to accommodate such growth. The second element reflects the need for quick appraisal of likely demand, so that appropriate economic strategy can be developed by the enterprise. This differentiates startup SMTEs from LTEs where there is possibly longer times series and higher correlation of performance with macroeconomic factors. The modeling proposed attempts to cope with these two elements.
The data covers all the business orders of a small truck transportation company during a 40month period (January 2008 to April 2011). Registered at the end of 2007, the small truck transportation company currently has a fleet of 30 trucks and 30 drivers. Some trucks are container trucks suitable for container transportation and others are bulk trucks designed for heavy longdistance bulk transportation services. This company mainly provides services for pier container transportation and inland bulk transportation. The container transportation service is mainly provided for container customers who have exporting and importing businesses at three ports located in Shenzhen, namely, Yantian, Shekou, and Mawan. In order to make use of the empty containers at these ports, a small part of the bulk is transported for the container customers in container trucks at the same price as bulk transportation. Most of the rest is carried by bulk trucks for different customers.
All the business orders from this company are classified according to the categories of the customer industry (see Table
Business data by industry.
Industry  No. of customers  No. of orders  Money  

Absolute 
Percentage 
Absolute 
Percentage 
Absolute 
Percentage  
Food  1  3.125  24  0.2221  91900  0.4495 
Toy  1  3.125  154  1.4253  430492  2.1054 
Chinaware  1  3.125  358  3.3133  949029  4.6414 
Material  2  6.250  151  1.3975  363945  1.7799 
Machine  3  9.375  4423  40.9348  4474611  21.8837 
Craft  4  12.500  1001  9.2642  2867729  14.0250 
Electronics  5  15.625  1999  18.5007  2541727  12.4307 
Logistics  15  46.875  2695  24.9422  8727782  42.6845 
 
Total  32  100  10805  100  20447215  100 
Further analysis shows that there are two patterns as regards gaps in orders, regular and irregular. Regular orders are made either continuously on weekdays and broken at weekends and vacations (shown in Figure
Regular and irregular customers.
Regular: 12 customers, 
Irregular: 20 customers,  

HYu/craft  YLM/toy  OWY/craft  QS/logistics 
GL/craft  HM/machine  HS/craft  XQ/logistics 
XG/electronics  HYa/electronics  YLX/logistics  
GD/electronics  WLi/electronics  CH/logistics  
WLin/electronics  ZH/food  GY/logistics  
GH/logistics  LH/logistics  JFX/logistics  
HF/logistics  LR/logistics  FY/logistics  
KLD/logistics  QFT/logistics  XQ/chinaware  
KZ/logistics  JY/logistics  SH/machine  
HL/material  AD/material  HLD/machine 
Gaps between regular orders in days.
Continuous, only broken at weekends and vacations
Discrete and regular
Gaps between irregular orders in days.
Occasional orders
Relatively longer span and irregular
In order to find out whether the economic recession of 2008 had an effect on the company’s business, further analysis of the orders and money per month was conducted for both regular and irregular businesses. It should be noted that the Chinese New Year usually falls in February when almost all businesses are at their lowest level of production. A threeyear period is considered and the cycle starts from February of the first year to January of the last year. Therefore, “1” in Figure
Irregular orders and money per month in total.
The plots of the irregular orders and money per month shown in Figure
Originating in the developed countries, the economic crisis soon spread to China, as shown by the decreasing number of orders. Those companies involved in overseas markets were affected first, in the third quarter of 2008. Pure OEM (original equipment manufacturing) and excessive reliance on overseas market were the two major factors which made these companies fail in the recession rapidly. Those companies relying on the home market were affected by a time lag, because of reduced business with the exportoriented companies and the declining purchasing power of workers laid off by those companies.
The regular orders and money per month in total are given in Figure
There is obvious periodicity by year both for orders and for income.
There is an increase in trend, but the slope is gradually decreasing.
Orders and money surprisingly increase after the arrival of the recession.
Regular orders and money per month in total.
Some weak companies ceased trading almost immediately, but the robust ones survived. Businesses concentrated on those surviving companies.
Every coin has two sides. The recession had both negative and positive impacts on the company’s business. Whereas the business trade was slowing down, the quality of the company’s customers was better after the recession and a large number of irregular businesses disappeared. Graphs of the orders and income have similar shapes, so the regular group is the focus of the following work.
Most modeling and forecasting approaches with limited data are about rapidly changing industries like motion pictures, telecommunications, or new products with a short history [
A significant improvement in nonlinear time series analysis (NTSA) has been seen since the 1990s [
No single model or combination model has been proved to outperform the rest. In order to model and forecast the small truck transportation company’s startup and growth after the economic recession from the limited data described in Section
Simple linear regression and binary linear regression are two basic versions of the generalized linear model (GLM) proposed by [
Linear regression was employed to search for the relation between orders and import & export in months or orders and import & export and GDP in quarters for GDP only available in quarters. The general form of a linear regression model is
In statistics, signal processing, econometrics, and mathematical finance, a time series is a sequence of data points, measured typically at successive times at uniform time intervals. Time series forecasting is the use of a model to predict future values based on previously observed values. Methods for time series analyses may be divided into two classes: frequencydomain methods and timedomain methods. The former include spectral analysis and, recently, wavelet analysis; the latter include autocorrelation and crosscorrelation analysis.
Our time series analysis began by regrouping the data, splitting the distance into five sections and business into two kinds. The first model was the polynomial, as in the following:
Then for an alternative of the logistic curve regression
Therefore, the turnover forecast is as the following for both trend forecast models:
Any time series is made up of systematic components, such as a trend, cycle, and seasonal and random elements, which are by definition unpredictable. Therefore, a set of time series data can be decomposed into trend, cycle, and seasonal and random components. The four elements can be combined in either an additive or a multiplicative model [
Moving averages are often used to isolate the trend. We propose, however, to extract the trend directly from the original data with both the polynomial and logistic curve models and then to decompose the combination of the cycle and seasonality by the additive model in (
We take the additive model, (
Let
First, simple linear regression analysis is taken to model the relationship between the national export & import and the orders. The result is given in Figure
Simple linear regression of the regular orders and national import & export.
The predicted regular orders per month
Then the binary linear regression of the orders and imports & exports and GDP per quarter is presented in Figure
Binary linear regression: regular orders and import & export and GDP.
The predicted regular orders per quarter
As the relative analysis cannot give satisfactory results even intuitively, we turn to the time series analysis. The whole regular business is separated by distance and truck type when the time series analysis is chosen. Distance is separated into five categories according to the rates and transport time, and container and bulk are the two types of services. Variable
Segmentation of the distance.

1  2  3  4  5 

distance  <90 km  90–179 km  180–350 km  351–800 km  >801 km 
The result shows that almost all the container transport orders are included in distance groups 1, 2, and 3, with just one out of 7755 regular container orders from February 2008 to January 2011 in container group 4. Most bulk transport orders are included in distance groups 1, 3, and 5. As the data of bulk groups 2 and 3 are insufficient for modeling, we merge bulk groups 1, 2, and 3 into a new bulk group 1 and bulk groups 4 and 5 into a new bulk group 2.
Thus,
The seasonal ratios in the polynomial model.
Group  Cycle  

1  2  3  4  5  6  7  8  9  10  11  12  
11  −0.4104  −0.3695  −0.1292  −0.0093  −0.1897  −0.1207  0.2280  0.3509  0.5158  0.0453  0.0209  −0.1597 
21  −0.4775  −0.3617  −0.2347  0.1407  0.2389  0.3525  0.3019  0.2410  0.0508  −0.1913  0.0472  0.2199 
31  −0.4325  −0.1774  0.5607  −0.1737  −0.1317  0.3161  0.2004  0.3484  −0.1109  −0.5404  −0.2736  0.3707 
12  0.5909  −0.8788  0.1113  −0.0745  0.4005  0.3488  −0.3943  −0.1522  −0.0579  −0.1450  0.2265  0.2134 
22  −0.6800  0.6150  0.3167  −0.1666  −0.4749  −0.0283  −0.4198  −0.3530  −0.1552  −0.0745  −0.4022  −0.2205 
The orders of container transportation predicted by the polynomial model.
The orders of bulk transportation predicted by the polynomial model.
Forecast orders of all groups are presented in Figures
Putting (
Therefore, an alternative logistic model is needed. Equation (
The orderprediction models are given in (
Results of calculation of seasonal ratios are presented in Table
Calculation of seasonal ratios by the logistic model.
Group  Cycle  

1  2  3  4  5  6  7  8  9  10  11  12  
11  −0.1069  −0.0242  0.4384  0.6197  0.2914  0.4368  0.4109  0.6343  0.7970  0.2457  0.1089  −0.0297 
21  −0.5951  −0.5055  −0.0923  0.3730  0.4713  0.6163  0.2290  0.1802  0.0183  −0.2400  −0.0248  0.1769 
31  −0.1282  0.2625  1.5265  0.2267  0.2936  0.9351  0.4475  0.5893  0.0670  −0.4422  −0.1267  0.6150 
12  0.3373  1.1651  0.6528  −0.0700  0.1107  0.0369  0.2534  −0.1151  0.4275  −0.1993  0.0686  −0.1443 
22  −0.6800  0.6150  0.3167  −0.1666  −0.4749  −0.0283  −0.4198  −0.3530  −0.1552  −0.0745  −0.4022  −0.2205 
The results of the logistic model are shown in Figures
The container orders predicted by the logistic model.
The bulk orders predicted by the logistic model.
The results of the polynomial and logistic models are compared in Figure
Comparison of the results of the two forecasting models: orders.
In conclusion, the initial modeling of the orders cannot immediately account for the demand in terms of exports & imports or GDP. The polynomial trend does not give a sound prediction in the sample, and the logistic modeling of the orders seems appropriate. The forecasted total money is presented in Figure
Comparison of the results of the two forecasting models: income.
Model selection depends primarily on two aspects. One is the forecast in the sample. The second is the prediction out of the sample. The forecasts of the polynomial model decrease abruptly out of the sample and the logistic has a better performance in this aspect. Therefore the logistic model outperforms the polynomial model out of the sample.
Now let us turn to the analysis in the sample. There are some specific criteria, such as the coefficient of determination
Measure of goodnessoffit of polynomial and logistic trend models.
Model  Difference  Polynomial trend seasonal adjustment  Logistic trend seasonal adjustment 


0.0066  0.7826  0.7760 

−0.0453  0.8569  0.9022 
From Table
This paper introduces a small truck transportation company’s startup whose main business is pier containers and whose minority business is longdistance bulk transportation. We have attempted to elucidate how our analysis led to useful information for SMTE owners. Modeling the forecasting of order numbers of both kinds of businesses and the total turnover contributes to establishing the company’s strategy for investment and operations.
Initial modeling of orders by simple regression and binary regression models cannot immediately account for demand in terms of exports or GDP. The results show that the company’s business is certainly affected by the national macroeconomic factors such as GDP and import & export, and this effect comes with a time lag of one to two years since transportation service demand is derived demand. The seasonal fluctuation of orders, however, is much more dramatic than that of the national GDP and total import & export. It may be the main reason why the regression models did not perform well in forecasting. Competitive environment factors such as customers and competitors affect performance directly for SMTEs.
There are insufficient data about customers and competitors to support the simple regression model. Therefore, the time series analysis is the inevitable choice. We segmented the data by business and transportation distance to get a set of time series data. The polynomial and the logistic trend models combined with additional seasonal components were employed to fit the data of different segments. Both fitted the sample data very well, but the polynomial trend does not give sound forecasting for the fast decreasing trend out of the sample. From the perspective of goodnessoffit, the polynomial trend model is still acceptable.
We have to say that forecasting in future is obviously at variance with reality. On the one hand, small transportation companies are not necessarily bound to continue to grow into large ones because of indifferent marketing and the lack of economies of scale. On the other hand, most small transportation companies can survive for a relatively long period thanks to their flexible operation mode. Usually a polynomial trend model does not work well for unlimited increasing or decreasing trends while higherorder coefficients are positive or negative, respectively. One of the reasons why the logistic modeling of the orders seems appropriate is that it has given the upper limit of business. Acceptable goodnessoffit and forecasting performance can only be provided by the logistic model, even though the performance of the two models in the sample is nearly the same to solve the question in this paper.
Unexpectedly, the analysis presented the process of the financial crisis’s effect on SMTEs. First, irregular business disappears immediately the crisis emerges; at the same time, the regular business increases rather than decreases and then slows down with a time lag of one to two years, which is established by the logistic model. Within the effective distance of the truck transportation, the total transportation demand is relatively stable and the market is competitive or contestable. The growth rate of most small and medium transportation enterprises will become slower after their quick growth period and have an upper limit scale of business.
Our approach can cope with the different impetus of SMTEs’ growth and a period of financial stress. One would expect that in less periods of financial stress then growth might be more rapid for SMTEs but not that they necessarily will continue to grow rapidly. With further data one could explore how later SMTEs might develop in more benign economic contexts. We believe, however, that the proposed model would still achieve a reasonable fit.
This work was supported by the National Natural Science Foundation of China (NSFC) under Grant no. 61203162. It was also supported in part by the Science Progress and Innovation Program of Hunan DOT under Grant no. 201244.