Regional Logistics Demand Forecast Based on Least Square and Radial Basis Function

WEI LeqinZHANG Anguo

1 School of Humanities and Teachers’ Education，Wuyi University，Wuyishan 354300，China 2 College of Physics and Information Engineering，F(xiàn)uzhou University，F(xiàn)uzhou 350108，China

Abstract：Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies. It has the characteristics of a small amount of data and being nonlinear，so the traditional prediction method can not guarantee the accuracy of prediction. Taking Xiamen City as an example，this paper selects the primary industry，the secondary industry，the tertiary industry，the total amount of investment in fixed assets，total import and export volume，per capita consumption expenditure，and the total retail sales of social consumer goods as the influencing factors，and uses a combining model least square and radial basis function (LS-RBF) neural network to analyze the related data from years 2000 to 2019，so as to predict the logistics demand from years 2020 to 2024. The model can well fit the training data，and the experimental results obtained from the comparison between the predicted value and the actual value in 2019 show that the error rate is very small. Therefore，the prediction results are reasonable and reliable. This method has high prediction accuracy，and it is suitable for irregular regional logistics demand forecast.

Key words:regional logistics；demand forecast；least square and radial basis function(LS-RBF)

Introduction

The study of logistics demand prediction mainly includes two aspects：one is the study of logistics demand related indicators；the other is the research of logistics demand forecast methods.In terms of the selection of influencing indicators related to logistics demand，Reza[1]selected the traffic flow and economic indices of Indonesia from years 1988 to 2010 as the data basis，studied the relationship between logistics volume and economic indices，and further analyzed the relationship between the growth of logistics volume and economic development.He took the freight volume of shipping，aviation and railway as logistics demand indices，and built a series of models with GDP and other related impact indicators.The results showed that logistics played an important role in promoting economic growth，and it was suggested to strengthen the construction of logistics infrastructure to ensure the sustainable and healthy development of economy.Liimatainenetal.[2]selected Finland’s road cargo transport volume as the logistics demand index，and selected seven economic development indices as the relevant impact indices of logistics demand.He used the Delphi method to analyze the impact of logistics demand related indices on the highway freight volume，and drew the conclusion that different economic development will produce different transport demand.Zeng and Zhu[3]used radial basis function (RBF) neural network and random forest algorithm to predict regional logistics demand with total regional foreign trade，per capita consumption level，total regional retail sales and three industrial production values as influencing factors.Through the calculation and analysis of Pearson’s correlation coefficient，Zhang[4]found that the main influencing factors of logistics demand forecast in Jiangsu Province were GDP，the primary industry，the secondary industry，the tertiary industry and truck ownership.Then he predicted the future logistics needs of Jiangsu Province.Researchers[5-6]also introduced a variety of economic factors such as GDP，total import and export volume，investment in fixed assets，and output value of the tertiary industry to predict logistics demand，in an attempt to reduce the prediction error of logistics demand.Based on the data related to logistics demand of Fujian Province from years 1981 to 2017，such as investment in fixed assets，gross industrial product，total retail sales of social consumer goods，total import and export volume，output value of the primary industry，the secondary industry and the tertiary industry.Huangetal.[7]constructed a logistics demand portfolio prediction model based on auto-regressive integrated moving average(ARIMA) model and principal component regression(PCR)，and the logistics demand for Fujian Province from years 2018 to 2022 was forecasted.Wangetal.[8]took freight volume as the scale of logistics demand in Nanping City，and built a prediction model with GDP，industrial and agricultural output values，total retail sales of social consumer goods，total investment in fixed assets，household consumption，total import and export volume，total population，and highway mileage as influencing indicators from years 2001 to 2017.Combined with principal component regression and GM(1，1) prediction model，the region’s logistics demand from years 2018 to 2022 was predicted through mathematical calculation.

As a tool to reveal the internal relationship between logistics demand indicators and the influencing indicators related to logistics demand，the logistics demand forecast method is the core research content of logistics demand forecast and has been widely concerned by scholars for a long time.Huetal.[9]selected relevant logistics data of the whole country from years 1993 to 2014，and used the multiple linear regression method，the exponential smoothing method，the polynomial fitting method and the nonlinear forecasting method to predict logistics demand，and the prediction results were highly accurate.Yuetal.[10]used the exponential smoothing method to process the data from years 2009 to 2017 and predicted the logistics demand of Yunnan Province.The results showed that the exponential smoothing method was a more practical short-term prediction method than the multiple linear regression model，the grey prediction method and the weighted arithmetic mean method.Gao[11]analyzed the major influencing factors of logistics demand in Hainan Province，and used a back propagation(BP) neural network model to predict logistics demand from years 2017 to 2022 based on relevant statistical data from years 2003 to 2016.Caoetal.[12]used genetic algorithm to optimize support vector machines(GA-SVMs)，an auto-regressive integrated moving average (ARIMA) model and a grey prediction method，and selected data of Guangxi Province’s freight volume from years 1990 to 2015 to establish a logistics demand prediction model.The results showed that GA-SVM method had good predictive effect.Samvedi and Jain[13]used the data of the four-stage beer distribution game simulation model established on the MATLAB platform，and selected the moving average method，the weighted moving average method，the exponential smoothing method and the grey prediction method to establish the prediction model.The results showed that the grey prediction model had the best prediction effect and still had good prediction effect in the case of supplying chain disruption.Lauetal.[14]improved the artificial neural network with a minimum description length (MDL) method，determined the optimal hidden layer of the artificial neural network，and obtained good prediction effect，which was proved to have wide applicability.Xiaoetal.[15]took air passenger volume as a logistics demand index，established an air passenger volume prediction model based on the adaptive network fuzzy reasoning system，and used improved particle swarm optimization algorithm to predict short-term air passenger volume，so as to solve the problem of air transport demand prediction.In order to reduce inventory cost，Jaipuria and Mahapatra[16]collected logistics data of three different manufacturing enterprises，and used a discrete wavelet transform analysis and artificial neural network (DWT-ANN) model and an ARIMA model to predict regional logistics demand respectively.The research showed that the DWT-ANN model had comparatively good prediction accuracy.

The establishment of a regional logistics demand forecast index system is the basis of accurate and reliable forecast，and the selection of a reasonable and scientific regional logistics demand forecast index system is the premise of building a perfect logistics demand forecast index system.The rationality of index selection and the scientific reliability of index system construction are the keys to improve the prediction accuracy.In order to ensure the scientific nature of the regional logistics demand forecast index system and the accuracy and reliability of the forecast results，the selection of a regional logistics demand forecast index system should follow the principles：comprehensive，systematic，relevant and accessible[17].

1 Index System Construction：Data and Methodology

1.1 Data collection

Considering the data availability and statistical consistency[18]，this paper considers that it is feasible to use freight volumeYas the research object.Seven other indices，including output value in the primary industryX1，output value in the secondary industryX2，output value in the tertiary industryX3，investment in fixed assetsX4，total import and export volumeX5，per capita consumption expenditureX6，and total retail sales of social consumer goodsX7，are selected as the influencing factors of Xiamen’s freight volume.The specific index system is shown in Table 1.

1.2 Correlation analysis

In order to test whether the selected indices are reasonable，the Pearson correlation coefficient method[19-20]is used to test the correlation degree and significance level among variables，and the correlation coefficientPX，Ybetween variables is calculated by Eq.(1).

(1)

Generally，it can be divided into three levels：|P|<0.4 refers to low linear correlation，0.4≤|P|<0.7 refers to significant correlation and 0.7≤|P|<1 refers to high linear correlation.According to Eq.(1)，we calculate the Pearson correlation value between the seven external indices and the total freight volume，as shown in Table 2.It can be seen that each index is highly related to the total freight volume，although the primary industry is relatively low.

Table 1 Statistical data of economic indicators related to logistics demand volume of Xiamen City from years 2000 to 2019

Table 2 Correlation value between indicators and total freight volume

1.3 Methodology

The seven indices were modeled independently.The least square (LS) method was used to fit the parameters，and the fitting variance was recorded.After establishing an accurate mathematical model，the change of each index in the next five years was predicted.Then，according to the incremental changes of seven indices year by year，the artificial RBF neural network was constructed by the MATLAB2020a software to study the incremental changes，so as to obtain the development trend of freight volume in the next five years，as shown in Fig.1.

Fig.1 Five-year prediction method in this paper

2 Data Analysis and Prediction

2.1 Related indices of mathematical modeling

Some special indices are needed to evaluate the fitting effect in the numerical fitting of each index.In this paper，we mainly selectR-square and adjustedR-square for evaluation，as explained below[21].

(1)R-squareRS：multiple measurement coefficient.The value is between 0 and 1，which indicates that the closer you get to 1，the better your equation will be at interpretingy.

(2)

(3)

whereFis the characteristic number.

2.2 Mathematical modeling of seven external indices

2.2.1Modelforprimaryindustry

As shown in Fig.2,the fitting result of the output value of the primary industry is (95% confidence interval)，fp(x)=54.24 sin (0.118 7x-0.445 1)+34.44×sin (0.215 3x+1.469)+8.042 sin (0.420 4x+2.208)，wherefpis the fitting value for primary industry，andx=1，2，…，nwhich represents the serial number of the special year from 2000，with 1 as the initial value and increasing year by year，the same to that in Figs.3-8 below.

Fig.2 Model fitting of 20-year data of output value of primary industry with abscissa representing years starting from 2000

2.2.2Modelforsecondaryindustry

As shown in Fig.3,the fitting result of the output value of the secondary industry is (95% confidence interval)，fs(x)=0.157 6x3-1.824x2+80.03x+143.6，wherefsis the fitting value for the secondary industry.

Fig.3 Model fitting of 20-year data of output value of secondary industry with abscissa representing years starting from 2000

2.2.3Modelfortertiaryindustry

As shown in Fig.4,the fitting result of the output value of the tertiary industry is (95% confidence interval)，ft(x)=9.144x2-37.38x+298.1，whereftis the fitting value for the tertiary industry.

Fig.4 Model fitting of 20-year data of output value of tertiary industry with abscissa representing years starting from 2000

2.2.4Modelforinvestmentinfixedassets

As shwon in Fig.5,the fitting result of investment in fixed assets is (95% confidence interval)，ff(x)=0.286 4x3-3.408x2+100.6x-44.59，whereffis the fitting value for investment in fixed asserts.

THERE was, once upon a time, a man and his wife fagot-makers2 by trade, who had several children, all boys. The eldest1 was but ten years old, and the youngest only seven.3

Fig.5 Model fitting of 20-year data of investment in fixed assets with abscissa representing years starting from 2000

2.2.5Modelfortotalimportandexportvolume

As shown in Fig.6,the fitting result of total import and export volume is (95% confidence interval)，fi(x)=36 560 sin (0.118 1x+0.447 6)+36 070 sin(0.119x+3.595)+40.16 sin(0.649 7x-0.557 9)，wherefiis the fitting value for total import and export volume.

Fig.6 Model fitting of 20-year data of total import and export volume with abscissa representing years starting from 2000

2.2.6Modelforpercapitaconsumptionexpenditure

As shown in Fig.7,the fitting result of per capita consumption expenditure is (95% confidence interval)，fc(x)=31.48x2+954.3x+5 926，wherefcis the fitting value for per capita consumption expenditure.

Fig.7 Model fitting of 20-year data of per capita consumption expenditure with abscissa representing years starting from 2000

As shown in Fig.8,the fitting result of total retail sales of social consumer goods is (95% confidence interval)，fr(x)=3.859x2+2.498x+144.8，wherefris the fitting value for total retail sales of social consumer goods.

Fig.8 Model fitting of 20-year data of total retail sales of social consumer goods with abscissa representing years starting from 2000

2.3 Multivariate forecasting based on external indices

Based on the mathematical modeling of the seven external indicators in section 2.2，we can independently predict the values of these seven indicators in the next five years，as shown in Table 3.

Table 3 Predictive values of seven indices in next five years

As shown in Table 3，the total import and export volume in 2020 and 2021 is increasing year by year，but then begins to decline year by year.The main reasons are as follows.Firstly，the historical data show a certain pattern of wave rise，as shown in Fig.9.After several years of rising，there will be a short slow decline process，and then it continues to rise.Secondly，it can be seen from Table 4 that since 2006，the proportion of China’s import and export volume in GDP has been declining year by year，which also shows that the focus of China’s economic development has shifted from import and export volume trade to domestic consumption and investment.

Fig.9 Trend of total import and export volume in Xiamen City from years 2000 to 2019

Table 4 Proportion of total import and export volume in GDP in China from years 1999 to 2019

3 RBF Prediction of Total Freight Volume

In this paper，we use the RBF neural network to forecast the total freight volume in the next five years.The structure of RBF is shown in Fig.10.The left is the input node，and each node inputs one characteristic datum.The activation function (kernel function) of the intermediate hidden layer node is the radial basis function，and the activation value of the hidden layer node is weighted and added by the output node as the final output of the network[22].

Fig.10 Structure of RBF neural network

The kernel function of hidden nodes is Gaussian function.

(4)

where，xis the input eigenvector，ciis the center point of the nodei，andσis the center width of the node.

In order to verify the rationality of the method based on the RBF neural network to predict the total freight volume in the future，we first conduct a preliminary verification on the existing data.After the nonlinear functions of variables in Figs.2-8 are obtained to fit the parameters，we use these functions to predict the external variables in 2019.The predicted values are shown in Table 5.

Based on the data from years 2000 to 2018，the RBF neural network was trained，and the network and the external index prediction data in Table 5 were used to predict the total freight volume in 2019.The predicted value is 353 million tons，which is very close to the actual value of 356 million tons so that the effectiveness of the method is proved.

Then，the annual change of seven external indices (i.e.the difference between the current year and the previous year) in the 18 years from years 2001 to 2019 is used to take the normalized value as the network input.The annual change of total freight volume was normalized into the expected output of the network，and the RBF neural network was trained.

Table 5 Forecast of related variables in 2019

Figure 11 shows the prediction results of the RBF neural network after training from years 2000 to 2024.We can see that in the period from years 2000 to 2019，the network can well fit the training data，i.e.，the network has been well trained，so the prediction results of the next five years are basically reliable.Based on the training error of RBF from years 2000 to 2019，we can predict the total freight volume data in the next five years.It can also be seen from Fig.11 that the network can well fit the annual increase in freight volume over the past 20 years.Therefore，the predictive values of total freight volume from the years 2020 to 2024 can be respectively predicted as shown in Table 6.

Fig.11 Fitting error effect of RBF neural network after training

Table 6 Predictive values of total freight volume in Xiamen City

4 Practical Implications and Theoretical Contributions

Accurate and reliable prediction of regional logistics demand can not only truly measure the development status and scale of regional logistics，but also provide important technical support for the government scientific decision-making and ensure the reasonable allocation of regional resources.The accurate prediction of logistics demand can provide reliable quantitative support and important decision-making basis for the planning of logistics system development，the calculation of logistics related infrastructure construction scale and the formulation of regional logistics system management scheme.Accurate prediction of regional logistics demand helps government departments solve the contradiction between supply and demand in the logistics market，reasonably adjust and control the development scale and speed of logistics industry，and has practical guiding significance for avoiding resource waste and promoting sustainable and healthy development of regional economy[23-25].

Xiamen City is located in the southeast of Fujian Province.It is one of the first four state special economic zones.At present，Xiamen City is also a national pilot zone for comprehensive reform，a national logistics hub，an international shipping center in southeast China and a pilot free trade zone.The accurate prediction of regional logistics demand in Xiamen City provides support for the rational allocation of regional logistics resources and the construction of scientific and efficient regional logistics system，and provides guarantee for the improvement of government governance capacity and the construction and development of Xiamen Special Economic Zone.At present，there are few researches on the prediction of regional logistics demand for Xiamen City.The establishment of regional logistics demand forecast index system and the related research contents enrich theoretical and practical analyses of regional logistics demand.

5 Conclusions

Based on the theory of regional logistics demand prediction and combined with the actual development of regional logistics in Xiamen City，this paper uses the correlate analysis method to select the relevant indicators of regional logistics，and establishes the index system of regional logistics prediction.Then，LS-RBF is applied to analyze the relevant indices of regional logistics demand in Xiamen City from years 2000 to 2019 and forecast the regional logistics demand from years 2020 to 2024.The results show that the logistics demand in Xiamen City will maintain a sustained growth trend in the next five years，and the contribution of logistics industry to the economy will increase year by year.On this basis，the departments in Xiamen Municipal Government can scientifically plan the logistics system according to the logistics demand in the next five years，accelerate the investment in logistics nodes and transportation lines，strengthen the connection of various transportation modes，and further promote the efficient operation of the logistics industry.Logistics enterprises should improve the service level，change the mode of economic development，and enhance the ability of coordination and linkage with manufacturing enterprises.This paper mainly focuses on the selection of indicators from the perspective of economics.In the future research，comprehensive selection of indicators can be carried out from more levels，such as increasing the quantitative analysis and the selection of relevant qualitative impact indicators，so as to make the logistics demand forecasting index system more comprehensive and objective.