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Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations

Publicado en línea: 15 Jul 2022
Volumen & Edición: AHEAD OF PRINT
Páginas: -
Recibido: 10 Jan 2022
Aceptado: 22 Mar 2022
Detalles de la revista
License
Formato
Revista
eISSN
2444-8656
Primera edición
01 Jan 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Abstract

The article applies mathematical statistics to the dynamic analysis of the demand for talents in large companies. Prediction of the overall demand for talents through the use of deep learning models. We use the theory of diminishing marginal utility to solve the degree of enterprise human resource investment under each index. Based on the analysis of traditional human resource management methods, this paper uses the three-dimensional fuzzy model to construct a new three-dimensional fuzzy model of human resource management model. The research found that the algorithm proposed in this paper can improve the quality of data training and improve the matching of people and posts.

Keywords

MSC 2010

Introduction

The competition of the market is the competition of talents. Talent forecasting is an important prerequisite for the implementation of the talent resource development strategy. The use of modern scientific methods to do a good job of talent forecasting highlights its importance. One of our group’s talent needs in 2020 has made a macro forecast [1]. This article only introduces the quick process of using mathematical models to make macro forecasts. At the same time, the article focuses on giving statistical analysis methods and satisfactory prediction results.

Data collection and processing

The talent management department provides the historical data we collect. The planned value of the original value of fixed assets is plotted on a scatter plot based on twenty years of statistical data [2]. The estimated value is calculated using time-series simulation extrapolation and random time series forecasting based on the changing trend presented. Finally, we solicit the opinions of relevant experts from the group company and make appropriate amendments (Table 1).

Statistics of main indicators of group companies from 2000 to 2020

Years Conversion turnover Total number of professional and technical personnel (ten thousand) Total number of employees (ten thousand)
Transportation production department Non-transportation production sector
2000 44303.2 0.7826 10.108 2.1199
2001 46466.6 0.8602 10.2225 2.2537
2002 50624.2 1.089 10.0275 2.9387
2003 56962.1 1.1465 IO.5152 3.0979
2004 68242.9 1.2613 11.5404 2.382
2005 75376.5 1.3288 11.8932 2.4988
2006 84037.1 1.4543 12.139 2.8373
2007 91678.6 1.8422 13.1091 2.806
2008 96612 1.9312 12.8916 2.9591
2009 98949 1. 9061 13. 1643 2.8623
2010 108965.8 2.0025 13.3669 2.8981
2011 120063.3 2.2908 13.362 2.8719
2012 131010.8 2.4121 12.9326 3.3311
2013 139288.4 2.4982 16.2635 2.9982
2014 140999.5 2.5156 13.2385 3.0245
2015 133743.6 2.6669 13.039 3.5383
2016 135593.8 2.7206 12. 3611 4.3116
2017 132645.1 2.6023 10.4685 5.6665
2018 130739.8 2.7532 11.521 4.6589
2019 150521.7 2.7604 11.1572 4.9899
2020 223010
Modeling method

The choice of methods when making talent predictions should be multifaceted. One method can only reveal the development trend of talents from a certain side. In the forecast of the total demand for talents in 2020, we use various methods to combine and select reasonable mathematical models to calculate to improve the prediction accuracy.

Time series extrapolation forecasting model

It is difficult to determine the various factors that affect the demand for talents. Instead of considering multiple factors, it is better to consider only the relationship with a single time. We take the time factor as a combination of various influencing factors [3]. The time-series extrapolation model predicts the total demand for talents and focuses on analyzing the development trend of talents themselves.

Power function prediction model

There are many types of time series extrapolation models. After screening, we use the following model to predict the total number of talents: r(t)=atb r(t) = a{t^b}

r(t) is the number of talents in a year t. a, t is the model parameter. The value of a, t is determined by the historical data of talents. We use the nonlinear least-squares method to fit the power function curve program to calculate it.

Logistic prediction model

Make a scatter plot based on the historical data of the total number of employees of the group company. According to its changing trend, it is considered that it conforms to the characteristics of the Logistic growth curve, so we use this model to predict the total number of employees. The Logistic prediction model is: 1G(t)=k+abt {1 \over {G(t)}} = k + a{b^t}

Where G(t) is the total number of employees in a year t. k, a, b is the model parameter. The value of k, a, b is calculated using the logic growth curve program.

Growth curve prediction model

The historical data of talent density conforms to the characteristics of the growth curve, so this model is used to predict talent density. The growth curve prediction model is: P(t)=1Aat(0<a<1) P(t) = 1 - A{a^t}(0 < a < 1)

P(t) is the talent density in a year t. A, a is the model parameter. We take the logarithm of the above formula to get: ln(1p)=(lna)t+lnA \ln (1 - p) = (\ln \,a)t + \ln \,A

Suppose y = ln(1 − p), k = ln a, b = ln A, has y = kt + b. According to the historical data of talent density, we use a linear regression program to calculate the sum. So we can get A, a.

Production function model

The production function is a mathematical model describing the relationship between input and output. The transportation industry uses conversion turnover as output and the original value of fixed assets as a capital investment [4]. The labor volume uses the annual average number of employees. We establish a production function model of the total labor force in the transportation production sector. The production function model is: Q(t)=a0ertk(t)aG1(t)β(a+β=1) \matrix{{Q(t) = {a_0}{e^{rt}}k{{(t)}^a}{G_1}{{(t)}^\beta}} & {(a + \beta = 1)} \cr}

Q(t) is the converted turnover in a year t. K(t) is the original value of fixed assets in a year t (unit: ten thousand yuan). G(t) is the total labor force in a year t. a is the capital elasticity coefficient. β is the labor elasticity coefficient. γ is the technological progress factor. α, β, γ is determined by Q, K, G1 historical data and calculated using multiple linear regression procedures.

Grey prediction model GM(1,3)

Grey system theory is an original theory created by Professor Deng Julong of Huazhong University of Science and Technology in 1982. The starting point of the theory is to study the system from its internal characteristics. It can make full use of the known information in the system [5]. As a marginal subject, this method has been widely used in many fields. The talent system is a half-dark gray system. Among them, there are many uncertain and invisible factors. Therefore, we regard the gray forecasting model as one of the forecasting models for the total talent demand.

Model GM (1,3) is a first-order three-variable differential equation model. This method is suitable for establishing the dynamic correlation analysis model of each variable. We use GM (1,3) to predict the total demand for talent [6]. The article focuses on analyzing the relationship between talents, conversion turnover, and the total number of employees. Key points of model GM (1,3) : We accumulate the historical data column (Xi(0)(1), Xi(0)(2),∧, Xi(0)(n)(i = 1, 2,3) of the three variables Xi(t) (i = 123) in the model to get the generated number sequence (Xi(0)(1), Xi(0)(2),∧, Xi(0)(n)(i = 1, 2,3). We will express it in a differential equation: dx1(1)(t)dt+ax1(1)(t)=b1x2(1)(t)+b2x3(1)(t) {{dx_1^{(1)}(t)} \over {dt}} + ax_1^{(1)}(t) = {b_1}x_2^{(1)}(t) + {b_2}x_3^{(1)}(t)

We use the above formula to predict the future value (t > n) of the generated number x1(1) (t). a, b1, b2 is the parameter determined by historical data x1(0)(t)(i = 1, 2,3). Calculated as follows: A=[a,b1,b2]T=(BTB)1BTY A = {[a,{b_1},{b_2}]^T} = {({B^T}B)^{- 1}}{B^T}Y B=[12[x1(1)(1)+x1(1)(2)]x2(1)(2)x3(1)(2)12[x1(1)(2)+x1(1)(3)]x2(1)(3)x3(1)(3)MMM12[x1(1)(n1)+x1(1)(n)]x2(1)(n)x3(1)(n)],Y=[x1(0)(2)x1(0)(3)Mx1(0)(n)] B = \left[ {\matrix{{- {1 \over 2}[x_1^{(1)}(1) + x_1^{(1)}(2)]} & {x_2^{(1)}(2)} & {x_3^{(1)}(2)} \cr {- {1 \over 2}[x_1^{(1)}(2) + x_1^{(1)}(3)]} & {x_2^{(1)}(3)} & {x_3^{(1)}(3)} \cr M & M & M \cr {- {1 \over 2}[x_1^{(1)}(n - 1) + x_1^{(1)}(n)]} & {x_2^{(1)}(n)} & {x_3^{(1)}(n)} \cr}} \right],Y = \left[ {\matrix{{x_1^{(0)}(2)} \cr {x_1^{(0)}(3)} \cr M \cr {x_1^{(0)}(n)} \cr}} \right]

The solution of this differential equation x1(t+1)=[x1(1)(t)b1x2(1)(t)+b2x3(1)(t)a]eat+1a[b1x2(1)(t)+b2x3(1)(t)] {x_1}(t + 1) = [x_1^{(1)}(t) - {{{b_1}x_2^{(1)}(t) + {b_2}x_3^{(1)}(t)} \over a}]{e^{- at}} + {1 \over a}[{b_1}x_2^{(1)}(t) + {b_2}x_3^{(1)}(t)]

The above formula represents the predicted value of the number generated in the t + 1 year. We restore ẋ1(1) (t) to obtain the required predicted value x1 (t), where t is the predicted year.

Mathematical model and statistical analysis

The following forecasting models are established using the relevant procedures in the “Economic Forecasting Methods, Procedures and Examples.” Data processed by the computer. Prediction I: Time series model of total talent r(t)=0.4564t0.611 r(t) = 0.4564{t^{0.611}}

The correlation coefficient is 0.9847, and the standard deviation is 0.1175. The result proved that the inspection passed.

The predicted value (I) of total talent demand in 2020 is 37.215 million, according to the relationship (*): the predicted value of real talent = predicted value of talent secret x predicted value of the total number of employees (*).

Talent density forecast

The predictive model of talent density is P(t)=10.9473×(0.9930)t P(t) = 1 - 0.9473 \times {(0.9930)^t}

The correlation coefficient is 0.9894, and the standard deviation is 0.053. The result proved that the inspection passed [7]. The predicted value of talent density in 2020 is 0.2376.

Forecast of the total number of employees

Prediction 1: Time series model of the total number of employees: 1G(t)=k+abt(t=1,2,,30) \matrix{{{1 \over {G(t)}} = k + a{b^t}} & {(t = 1,2, \cdots,30)} \cr}

Among them: k = 0.0592, a = 0.0346, b = 0.8251.

The correlation coefficient is 0.9847, and the standard deviation is 0.2809. This result indicates that various tests passed. The predicted value of the total number of employees in 2020 (I) is 268,665.

Forecast 2: Sub-sector forecasting method

We divide the various departments of the group company into two major categories: transportation production department and non-transportation production department. This way, we can choose different forecasting methods.

Forecast of the total labor force in the transportation production sector

Production Letter Model of Total Labor Force in Transportation Production Department Q˙(t)=a0ertk(t)aG1(t)β(α+β=1) \matrix{{\dot Q(t) = {a_0}{e^{rt}}k{{(t)}^a}{G_1}{{(t)}^\beta}} & {(\alpha + \beta = 1)} \cr}

Q(t) is the converted turnover in a year t. K(t) is the original value of fixed assets in a year t. G(t) is the total labor force in a year t. α is the capital elasticity coefficient. β is the labor elasticity coefficient. γ is the technological progress factor.

Let us suppose: Y=lnQ(t)G1(t),X=lnK(t)G1(t),c=lna0 Y = \ln {{Q(t)} \over {{G_1}(t)}},X = \ln {{K(t)} \over {{G_1}(t)}},c = \ln {a_0}

Then we have a linear model of the deformed production function: Y=c+aX+γt Y = c + aX + \gamma t

We calculate c, a and γ based on historical data and using a binary linear regression program. In this way, we get the regression equation Y = −0.8447 − 0.0757 X + 0.0669t.

1) The value of several statistics

The mean value of the explained variable is −0.3191. The multiple correlation coefficient is 0.9885. The remaining sum of squares is 0.0440. The statistic F value is 341.8480. Regression Sum of squares: 1.8819D. The W check value is 2.4054. The remaining standard deviation is 0.0525.

2) F test and goodness of fit test

For a given significance level a = 0.05, F0.05(2.17) = 3.59. Because the overall F-test value is F = 341.848 >> 3.59, the overall test is highly significant. Therefore, the linear relationship of the deformed production function is highly significant. From the multiple correlation coefficient R=0.9885 equivalents to the F test, it can also be seen that the goodness of fit is very good.

3) D-W inspection

At the significance level a = 0.05 dl = 1.10, du = 1.55 dl < dw < 4 − du, the model has no autocorrelation. The model can be used for prediction. Therefore, the production function regression (model) equation is Q˙(t)=0.4297×(1.0692)tK˙(t)0.0757G1(1)1.0757 \dot Q(t) = 0.4297 \times {(1.0692)^t}\dot K{(t)^{- 0.0757}}{G_1}{(1)^{1.0757}}

The predicted value of the total labor force in the transportation and production sector in 020 is 91,481 people

Forecast of the total labor force in the non-transportation production sector

The forecast of the total labor force in the non-transportation production sector is based on the relevant regulations of the organization and personnel department. They use the fixed post and fixed number estimation method [8]. The forecast value of the total labor force in the non-transportation production sector in 2020 is 65,899 million. Comprehensively (1) and (2) can be obtained: the forecast value of the total number of employees in 2020 (2) is 1573.8 million. We take the average of the two forecast results of the total number of employees, and the forecast value of the total number of employees in 2020 is 163,230. According to the relationship (*), the forecast value of the total demand for talents in 2020 can be obtained. The forecast value (II) of the total demand for talents in 2020 is 38,734.

Prediction 3: The gray prediction model GM (1,3) of the total talents is dr(1)(t)dt+0.8044r(1)(t)=0.0180x1(1)(t)+0.00133x2(1)(t) {{d{r^{(1)}}(t)} \over {dt}} + 0.8044{r^{(1)}}(t) = 0.0180x_1^{(1)}(t) + 0.00133x_2^{(1)}(t)

r(t) is the total annual talents. x1 (t) is the total number of employees in a year t. x2(t) is the converted turnover in a year t. Posterior error test: (1) the original generated value mean x¯=1.7921 \bar x = 1.7921 . (2) the original generated variance S12=120t=120[x(0)(t)x¯]2=8.5363 S_1^2 = {1 \over {20}}\sum\limits_{t = 1}^{20} {{{[{x^{(0)}}(t) - \bar x]}^2}} = 8.5363 . (3) the residual mean ε¯=120t=220[x(0)(t)x˙(0)(t)]2=0.0253 \bar \varepsilon = {1 \over {20}}\sum\limits_{t = 2}^{20} {{{[{x^{(0)}}(t) - {{\dot x}^{(0)}}(t)]}^2} = 0.0253} . (4) the residual variance S22=120t=220[εtε¯]2=0.5323 S_2^2 = {1 \over {20}}\sum\limits_{t = 2}^{20} {{{[{\varepsilon _t} - \bar \varepsilon ]}^2}} = 0.5323 . (5) the posterior difference ratio C=S2S1=0.2497 C = {{{S_2}} \over {{S_1}}} = 0.2497 . (6) Probability of small error P=P{|εtε¯|<0.6745S1}=0.947 P = P\{|{\varepsilon _t} - \bar \varepsilon | < 0.6745{S_1}\} = 0.947 .

If P > 0.95, C < 0.35, the model is level one. Therefore, the accuracy of the above model is level two (close to level one) and can be used for prediction. After accumulative reduction, the forecast value (1) of the total demand for talents in 2020 is 38.056 million. Combining the above three forecasting methods, the forecast value of the total demand for talents in 2020 is obtained by simple arithmetic, as shown in Table 2.

Forecast results of total talent demand unit: 10,000

Method of prediction Forecast I Forecast II Forecast III Average predicted
Predictive value 3.7215 3.8734 3.8056 3.8002

The above three methods are used to forecast the total talent demand of the group company. Although the workload increases, it can be calculated from different angles, and the results can be evaluated [9]. This is conducive to improving prediction accuracy. The final result is as follows: In 2020, the company's total talent demand is 38,002 million.

Analysis and evaluation of forecast results
Analysis of talent demand

The total number of talents in the group company in 2019 is 27,604. The total demand for talents in 2020 is 38,002. This is 1.37 times of 2019. The average annual talent demand from 2021 to 2020 is 1040.

Analysis of the growth rate of talent demand

In 2020, the converted turnover of the group company was 150521.7 million ton-kilometers. It is planned that the converted turnover volume in 2020 will be 223,010 million ton-kilometers. The average annual growth rate is 4.01%. According to the forecast results of talent demand in 2020, the demand for talents of the group company will increase by 3.25% every year on average, and the growth rate of employees will be 0.096%. Therefore, the annual average increase rate of output value>the average annual increase rate of talents>the average annual increase rate of the total number of employees, the forecast result is reasonable in terms of economic benefits. This also reflects the needs of the group company to accelerate the training and improvement of the quality of the care team.

Analysis of talent content in output value

In 2020, the number of employees of the group company per million converted ton-kilometers was 0.1834, and the number of employees per million converted ton-kilometers was 1.027. It is predicted that in 2021, the number of talents per million converted ton-kilometers will be 0.17, and the number of employees per million converted ton-kilometers will be 0.73. While the content of talents has been reduced, the content of employees has been greatly reduced. This improves economic efficiency and is also a requirement for streamlining and streamlining the ranks of cadres.

Conclusion

In 2020, the talents of the group company accounted for 23.31%, which is a larger increase than the current ratio of 17.10%. This indicates that the task of personnel training in the future will be very arduous. The group company must adopt strong policies and measures to encourage existing cadres to improve their academic qualifications and technical titles and speed up personnel training. At the same time, the talent introduction policy should be tilted towards high-level talents to meet the group company's development needs.

Statistics of main indicators of group companies from 2000 to 2020

Years Conversion turnover Total number of professional and technical personnel (ten thousand) Total number of employees (ten thousand)
Transportation production department Non-transportation production sector
2000 44303.2 0.7826 10.108 2.1199
2001 46466.6 0.8602 10.2225 2.2537
2002 50624.2 1.089 10.0275 2.9387
2003 56962.1 1.1465 IO.5152 3.0979
2004 68242.9 1.2613 11.5404 2.382
2005 75376.5 1.3288 11.8932 2.4988
2006 84037.1 1.4543 12.139 2.8373
2007 91678.6 1.8422 13.1091 2.806
2008 96612 1.9312 12.8916 2.9591
2009 98949 1. 9061 13. 1643 2.8623
2010 108965.8 2.0025 13.3669 2.8981
2011 120063.3 2.2908 13.362 2.8719
2012 131010.8 2.4121 12.9326 3.3311
2013 139288.4 2.4982 16.2635 2.9982
2014 140999.5 2.5156 13.2385 3.0245
2015 133743.6 2.6669 13.039 3.5383
2016 135593.8 2.7206 12. 3611 4.3116
2017 132645.1 2.6023 10.4685 5.6665
2018 130739.8 2.7532 11.521 4.6589
2019 150521.7 2.7604 11.1572 4.9899
2020 223010

Forecast results of total talent demand unit: 10,000

Method of prediction Forecast I Forecast II Forecast III Average predicted
Predictive value 3.7215 3.8734 3.8056 3.8002

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