Intelligent selection of strategic alliance partners in automobile manufacturing industry based on DEA and grey system theory

Abstract

Since the 1980s, the number of international strategic alliances has been on the rise and the alliance has become a novel mode of corporate growth. Therefore, the selection of strategic partners has always been relevant to the fulfillment of strategic objectives of a corporation. Since the conflicts among partners’ motivations can easily lead to the breakup of a strategic alliance, the pursuit of an appropriate strategic partner has become essential to the success of an enterprise. This paper mainly conducts a case study on the French auto-manufacturer Renault with the grey system theory and DEA analysis. Relevant data from Bloomberg BusinessWeek of 2015 have been studied, and the data concerns 19 auto-manufacturers including Group Renault in four consecutive fiscal years from 2012 to 2015. After the data analysis, an intelligent method of selecting appropriate strategic partners has been proposed. According to the intelligent method, among the 19 decision-making units on the list, Nissan Motor Company (DMU8) and Daimler AG (DMU3) are the most suitable strategic partners to form an alliance with Renault (DMU13).

Keywords

Strategic alliance DEA grey prediction model automobile manufacturing

1 Introduction

Automobile manufacturing industry is one of the global pillar industries and the main driving force of macro-economic development and innovative development. The business cycle of automobile manufacturing industry mingles with that of other industries. Therefore, automobile manufacturing industry is greatly influenced by economic situations.

Established in 1898, Renault S.A. is the second largest vehicle manufacturer in France with cars, official business vehicles and sports cars as its main products. Besides selling its products to domestic customers, the affiliated overseas branches distributed in Europe, Africa, North America and Oceania sell its products to more than 150 countries taking up 1/2 of its business volume. As reported on Les Échos, during 2015, the number of Renault cars sold to Europe reached to 1.613 million, registering a 10.2% growth from the previous year. Among them, the sales volume of the cars sold in Spain witnessed a 22.3% growth, a 17.7% growth to the British, an 18% growth in Italy and 5.1% growth in France. In 2015, Carlos Ghosn, CEO of France Renault S.A., claimed: “According to the statistics and analysis in recent years, the market share of Renault in China is predicted to be 6% next year. And we will increase our investment in China.”

As shown in Fig. 1, from 2008 to 2015, the global sales volume of Renault S.A. generally increased year by year. Due to the impact of global economy and finance crisis in 2008, the sales volume of cars in 2009 dropped to 2.3092 million from 2.382 million in 2009, a decrease of 4.2%. The main reason lies in that European automobile market shrunk rapidly in the latter half of 2008. That is to say, in European automobile market, the sales volume dropped 11.8% year-on-year. Dragged by the 18% decrease of the sales volume in European automobile market, in 2012, the global sales volume of Renault S.A. dropped to 2.55 million and the relevant market share dropped to 9.1%. The main reason was that the company wanted to guarantee its profit margin instead of maintaining the sales volume in this terrible price war.

Fig.1

Global sales volume and market shares of Renault S.A.

Additionally, Renault S.A. also faced some negative effects during its development process such as automobile recall events.

The clamp nut of steering shaft on steering engine might loosen, causing that the gear is likely to be separated from the rack when the driver turns the steering wheel at a wide angle but low speed. Thus, the automobile might fail to steer, influencing driving safety. From Dec. 25th, 2009, Renault Company decided to recall the imported 2009 Koleos cars produced from Mar. 5th, 2008 to Aug. 21st, 2009. Among those recalled cars, the number of cars involved in Mainland China was 2,136.

The pretentioner strings at the lower part of some of the chairs might make the strings break off under extreme conditions, making the seat belt’s restricting function invalid. From June 15th, 2010, France Renault Company decided to recall the 2008 and 2009 imported Renault LAGUNA III cars. The number of cars involved in Mainland China was 124 that were produced during the period from Nov. 8th, 2006 to Aug. 24th, 2009.

In 2012, during assembly process at the factory, the connection block of brake fluid reservoir fractured making the gradual release of brake fluid and seal failure. Renault Company decided to recall all of the Twizy electric automobiles produced from Jan. 27th, 2012 to Mar. 1st. Among those recalled cars, the number of cars recalled in France was 1,736 and the number of the recalled cars all over the Europe was 8,000.

In 2016, Renault, a French automobile manufacturer, recalled 15,000 cars to adjust the car engines to make the remitted gas meet the emission standard.

Faced with a series of negative influences above, besides expanding production scale, satisfying customer’s demand, saving cost, producing high quality cars and protecting the environment, what could this company do to maintain its market competitiveness and create value for the customers and the society? In this paper, Renault Automobile Company was selected as the decision making unit (DMU) to avail Grey Forecasting Theory and DEA Analysis method to help the company seek the most suitable strategic alliance partner to enhance alliance benefits, promote automobile sales and realize profit growth.

2 Literature review

In such a world that is fast changing and full of uncertainty, the global environment makes it harder for enterprises to maintain its competitive advantage and promote the rapid growth of the cooperation and alliance between independent enterprises [1]. Thus, strategic alliance is one of the crucial parts of an enterprise’s global strategy [2, 3]. Meanwhile, strategic alliance also becomes one of the important methods to realize rapid development featuring high growth, high earnings ratio and high market value.

The rising of strategic alliances changes the boundary of traditional enterprises and the operation environment. With the progress of global economic integration, the international strategic alliances between enterprises witness rapid and continuous growth. James believed that the alliance would promote the success of a series of companies including and etc., [4]. However, due to the motivational conflicts between the partners, the alliance has always been easy to fail. The alliance consisting of enterprises from different countries would be more likely to fail. Yuan Lei believed that strategic motivation and partner selection were the two most crucial factors and they were closely related to each other [5]. Bierly and Gallagher pointed out that the compatibility of strategic business was of the main incentive factors for each enterprise to select partner. The partner selection based on the compatibility of strategic business could only be applied to specific decision making environment. When uncertainty existed, over simplified partner selection would cause a series of problems [6].

After the studies on the partnership selection among enterprises from the perspective of strategic coordination, the author believes that coordination between key enterprise and its potential partner is the important basis to make partner selection decisions. One enterprise can select the enterprise that can strategically match with and support each other as the cooperative partner to promote partnership and jointly create value. Das believed that if one enterprise selected the enterprise with different objectives as the cooperative partner, they would be more likely to meet obvious barriers during the cooperation process [7 –12]. The reason is that the current partner selection may influence the future cooperation. The problems caused by inconsistent objectives might be magnified during the interaction process after the partnership has been established. Thus, we can conclude that the partner selection process is very hard but it does be the crucial element to obtain success for international strategic alliance.

Grey System Theory was first put forward in 1982 by Chinese Professor Deng Julong, with the uncertain system consisting of small sample and poor information as the study object. This system can process the original data and establish grey model to find and grasp the law of system development to quantitatively and scientifically forecast the future state of the system. The GM (1, 1) [13] model with X (n) as the initial condition put forward by Dang is the most widely used model. For example, based on the data from Britain and America, Chirwa used GM (1, 1) to predict car accident risk [14]. Cempel used grey forecasting model to check mechanic vibration state [15]. Wang Xuliang used grey forecasting model to forecast fatigue endurance of machine part to sharply reduce the forecast error [16]. At big data era, grey system forecasting method based on the dig of small data has become an effective tool to extract effective information from mass data.

Efficiency evaluation was initially put forward by Farrell on the basis of the previous studies made by Debreu. On this basis, in 1978, Charnes, Cooper and Rhodes put forward the first DEA model to evaluate the efficiency of the production units with multiple input and output units to realize decision-making objectives. In DEA theory, judging the DEA validity of each DMU, in essence, was to judge whether the DMU fell behind the production frontiers of production possibility set. Astrid Cullmann used DEA to evaluate the average power distribution efficiency of Germany Power Distribution Company in western and eastern France with labor, capital and peak responsibility as the input indicators and sales per unit and the number of customers as the output indicators. The result showed that the efficiency of the eastern part was obviously higher than that of the western part [17]. SeongKon Lee used analytic hierarchy process and DEA model to evaluate the relative technical efficiency of hydrogen energy to offer reference basis to realize the economic benefit of hydrogen energy and promote national energy security [18]. V. J. Thomas studied the sum of R&D efficiency of 50 states in America. Then, after the comparison of the R&D efficiency of each country from 2004 to 2008, it was found that the R&D efficiency of China, Korea, Brazil and India had been obviously on the rise and the R&D efficiency greatly influenced by the number of patent applications. Based on the data collected from field research [19], Zhao Shukuan, Yu Haiqing and Gong Shunlong made use of DEA model to analyze innovation performance with 151 high and new technology enterprises in Jilin Province as the study objects [20]. Yao Lushi and Zhao Meng used ultra-efficient DEA model to investigate innovation performance of each enterprise in the past two years with the first and second batches of innovation-oriented enterprises as the samples [21].

Based on the above reasons, integrating Grey System Theory and DEA model is a new and effective method to make decisions about selecting alliance partner for not only can it be used to predict future operation data but also predict operation efficiency through standard input and output variables. Thus, it can offer important basis to automobile manufacturers to seek for suitable strategic alliance partners.

3 Research design

3.1 Selection of indicators and samples

The paper studies the reports of Bloomberg Newsweek on the top 19 auto-manufactures among Global 500 in consecutive four fiscal years (2012 to 2015). Those enterprises are representatives of the whole automobile manufacturing industry in global market, because they keep operating smoothly and provide relatively integral data for study. As shown in Table 1, Group Renault (DMU13) is selected as the subject of this study. For Renault, the selection of a strategic partner will become part of its effective corporate strategies, since it not only helps bring a high growth rate, a high yield and a high market value to the corporation, but also facilitates the rapid development of it.

Table 1
List of top 500 automotive manufacturers in the world

NO. DMUS Corporate name

1 DMU1 Volkswagen Group AG

2 DMU2 Toyota Motors

3 DMU3 Daimler AG

4 DMU4 General Motors

5 DMU5 Ford Motor

6 DMU6 Honda Motor

7 DMU7 BMW Group

8 DMU8 Nissan Motor

9 DMU9 SAIC Motor

10 DMU10 Hyundai Motor

11 DMU11 DongFeng Motor Group

12 DMU12 PSA Peugeot Citroen

13 DMU13 Renault S.A

14 DMU14 Kia Motors

15 DMU15 TaTa Motors

16 DMU16 Volvo Group

17 DMU17 GAC Group

18 DMU18 Mazda Motor

19 DMU19 Suzuki Motor

NO.	DMUS	Corporate name
1	DMU1	Volkswagen Group AG
2	DMU2	Toyota Motors
3	DMU3	Daimler AG
4	DMU4	General Motors
5	DMU5	Ford Motor
6	DMU6	Honda Motor
7	DMU7	BMW Group
8	DMU8	Nissan Motor
9	DMU9	SAIC Motor
10	DMU10	Hyundai Motor
11	DMU11	DongFeng Motor Group
12	DMU12	PSA Peugeot Citroen
13	DMU13	Renault S.A
14	DMU14	Kia Motors
15	DMU15	TaTa Motors
16	DMU16	Volvo Group
17	DMU17	GAC Group
18	DMU18	Mazda Motor
19	DMU19	Suzuki Motor

3.2 Selection of evaluation methods

3.2.1 GM (1, 1) model

To obtain the grey predict model GM (1, 1), the original irregular data are first accumulated to generate relatively regular sequences which are then employed for modeling. After that, data obtained from the generated model undergo the inverse accumulated generating operation so as to work out the predicted values of original data [22].

The original data sequence is assumed as follows: $X^{(0)} = (X^{(0)} (1), X^{(0)} (2), \dots, X^{(0)} (n))$

Where X⁽⁰⁾ (k)≥0, k = 1, 2, …, n ; X⁽¹⁾ is 1-AGO Sequence of the original sequence X⁽⁰⁾: $X^{(1)} = (X^{(1)} (1), X^{(1)} (2), \dots, X^{(1)} (n))$

Where $X^{(1)} (k) = \sum_{i = 1}^{k} X^{(0)} (i), k = 1, 2, \dots, n$ ;

After the accumulation of original data, the data randomness is lowered. If the original sequence X⁽⁰⁾ and 1-AGO sequence X⁽¹⁾ meet the requirements of quasi-smoothness test:

$ρ (k) = \frac{X^{(0)} (k)}{X^{(1)} (k - 1)} < 0.5$ , quasi-exponent law test:

$δ (k) = \frac{x^{(1)} (k)}{x^{(1)} (k - 1)} \in [1, 1.5]$ , and class-compare verification: $σ (k) = \frac{x^{(0)} (k)}{x^{(0)} (k - 1)} \in (e^{- \frac{2}{n + 1}}, e^{\frac{2}{n + 1}})$

X⁽¹⁾ Sequence denotes the law of exponential growth; in other words, it can be represented by the linear first-order differential equation as below: $\frac{{dx}^{(1)} (k)}{dt} + α X^{(1)} (k) = μ$ (1)

In the equation, a is the development coefficient which reflects the developing trend of X⁽¹⁾ and original sequence X⁽⁰⁾; μ is the internal control grey number indicating changes in relation among data.

To work out α and μ, $\overset{\land}{α} = {[α, μ]}^{T}$ is set as the vector to be estimated; since the analyzed sequence is discrete, through the discretization of $\frac{{dx}^{(1)} (k)}{dt}$ in Formula (1) the following formula is obtained: $\frac{{dx}^{(1)} (k)}{dt} = X^{(1)} (k) - X^{(1)} (k - 1), (k = 2, 3, \dots, n)$ (2)

Let if: $Z^{(1)} (k) = μ X^{(1)} (k) + (1 - μ) X^{(1)} (k - 1)$ (3)

In the formula (3), Z⁽¹⁾ (k) is known as the background value of formula (1), and the weighting coefficient μ ∈ [0, 1].

If μ is set as 0.5, then $Z^{(1)} (k) = \frac{1}{2}$ (4)

At this point, through the discretization of Formula (1), the following is obtained: $X^{(1)} (k) - X^{(1)} (k - 1) + α Z^{(1)} (k) = μ$ (5)

By adopting the least squares method to solve Formula (5), the following is obtained: $\overset{\land}{α} = (B^{T} B)^{- 1} B^{T} Y_{n}$ (6)

Where $B = [\begin{matrix} - z^{(1)} (2) & 1 \\ - z^{(1)} (3) & 1 \\ ⋮ & ⋮ \\ - z^{(1)} (n) & 1 \end{matrix}]$ $= [\begin{matrix} - \frac{1}{2} [x^{(1)} (1) + x^{(1)} (2)] & 1 \\ - \frac{1}{2} [x^{(1)} (2) + x^{(1)} (3)] & 1 \\ ⋮ & ⋮ \\ - \frac{1}{2} [x^{(1)} (n - 1) + x^{(1)} (n)] & 1 \end{matrix}], Y_{n} = [\begin{matrix} x^{(0)} (2) \\ x^{(0)} (3) \\ ⋮ \\ x^{(0)} (n) \end{matrix}]$

After the calculation of α and μ, we continue to solve the Differential Equation (1) and the following formula is obtained [23]: $\overset{\land}{X^{(1)}} = {ce}^{- α t} + \frac{μ}{α}$ (7)

In the formula, $\overset{\land}{X^{(1)}}$ represents the predicted values of Sequence X⁽¹⁾, with c as the undefined constant.

The discretization of Formula (7) leads to Formula (8) as below: $\overset{\land}{X^{(1)}} (k + 1) = {ce}^{- α t} + \frac{μ}{α} (k = 0, 1, \dots, n - 1)$ (8)

To work out constant c, an initial value is determined beforehand, and it is assumed that $\overset{\land}{X^{(1)}} (1) = X^{(0)} (1)$ ; as a result, the following formula is obtained: $c = X^{(0)} (1) - \frac{μ}{α}$ (9)

By substituting Formula (9) into Formula (8), the following is obtained: $\overset{\land}{X^{(1)}} (k + 1) = (X^{(0)} (1) - \frac{μ}{α}) e^{- α t} + \frac{μ}{α}$ (10)

Through the inverse accumulated generating operation of Formula (10), the grey prediction model of original sequence X⁽⁰⁾ is obtained as follows: $\overset{\land}{X^{(0)}} (k + 1) = (X^{(0)} (1) - \frac{μ}{α}) e^{- α t} (1 - e^{α})$ (11)

3.2.2 Non-radial super-efficiency DEA model

The selection of strategic alliance partners is rather a complicated decision-making process. Traditional DEA models (CCR and BCC Model) are unable to well recognize decision-making units whose efficiency value is 1 [24], and the input factor is required to be non-radial [25]. Therefore, in this study, a non-radial super-efficiency SBM model is selected, so that the slackness of factor inputs and outputs can be fully taken into account in relevant analysis and evaluation.

If we assume the number of DMU is nand numbers of the input and output types for each DMU_j are respectively m and s, we obtain x_j = (x_1j, x_2j, …, x_mj) ^T, y_j = (y_1j, y_2j, …, y_sj) ^T in which χ_ij > 0 represents the input of the i^th type for the j^thDMU_j, and y_rj > 0 represents the output of the r^th type for the j^thDMU_j(j = 1, 2, …, n ; n ; i = 1, 2, …, m ; r = 1, 2, …, s). Si^- and $S_{r}^{+}$ are respectively surplus and slack variables, λ_j is the weight vector, and χ₀, y₀ are respectively the input and output of the decision-making unit DMU₀. Therefore, to determine the efficiency of a selected DMU₀, the non-radial DEA model will be as follows: $min ρ = \frac{1 + \frac{1}{m} \sum_{i = 1}^{m} \frac{s^{-} i}{x_{i 0}}}{1 \frac{1}{s} \sum_{r - 1}^{s} \frac{s_{r}^{+}}{y_{r 0}}}$ (12) $\begin{matrix} s . t \sum_{j = 1, \neq 0}^{n} λ_{j} x_{j} - S^{-} \leq x_{0}, \\ \sum_{j = 1, \neq 0}^{n} λ_{j} x_{j} + S^{+} \leq y_{0} \end{matrix}$ (13)

eλ = 1, λ, S^-, S⁺ ≥ 0, ρ is the effective value of DMU₀. When ρ ≥ 1, DMU₀ is of relative efficiency in DEA; when ρ < 1, DMU₀ is not efficient in DEA, which means necessary upgrades should be made to inputs and outputs.

3.2.3 Selection of indicators

In order to fully measure the efficiency of the DEA model and meanwhile find the suitable alliance partner for the target decision-making unit, this paper, based on the input-output correlation, set fixed assets (Fix.as), costs of sales (Cogs), operating expenses (O.exp) and long-term investment (L.inv) as input factors, and revenue (Rev), total equity (T.eq) and net income (Net.in) as output factors. For proprietors and investors, these indicators can be employed to evaluate the operation and revenue of an enterprise, and on this basis, they can decide whether they will form alliance with the enterprise. The indicators are show in Table 2.

Table 2
Inputs and outputs data of all DMUS in 2015

DMUS Inputs (1,000,000 U.S Dollars) Outputs (1,000,000 U.S Dollars)

(I) Fix.as (I) Cogs (I) O.exp (I) L.inv (O) Rev (O) T.eq (O) Net.in

DMU1 104,410.90 83,262.30 10,300.40 4,480.30 80,861 26,804.80 –6,066.50

DMU2 84,506.54 190,148.75 24,020.74 30,523.35 247,586.56 160,430.26 20,980.95

DMU3 26,754.20 129,437 13,361.70 5,582.50 164,413.70 60,086.40 9,582.10

DMU4 31,229 128,321 13,405 7,874 152,356 40,323 9,615

DMU5 30,163 124,041 14,999 41,279 149,558 28,657 7,371

DMU6 28,995.56 93,916.22 15,641.45 5,892.77 121,164.54 67,116.56 5,100.89

DMU7 19,534.90 81,447.30 9,496.30 6,477.90 101,392.50 47,040.40 7,035.60

DMU8 61,166.49 84,012.19 14,039.14 4,666.07 103,410.97 46,127.18 4,159.76

DMU9 5,952.40 90,128.14 5,467.31 9,079.95 103,145.88 32,448.81 6,165.23

DMU10 22,959.14 58,961.04 9,519.63 233.14 73,566.99 53,505.12 5,207.33

DMU11 1,989.08 16,867.23 1,099.08 469.23 19,471.69 14,074.46 1,955.69

DMU12 11,983.40 48,959.90 6,133.60 1,785.30 60,143.60 13,440.90 1,322.20

DMU13 12,288.10 39,724.30 5,300.90 3,353.90 49,859.70 31,321.40 3,256

DMU14 10,433.70 31,723.02 3,769.37 3,131.69 39,617.16 19,363.22 2,104.48

DMU15 6,274.71 28,312.12 3,258.12 1,474.24 36,766.47 10,071.76 8,454.35

DMU16 6,165.90 27,319.19 2,989.25 758.5 36,128.90 9,897.11 8,307.75

DMU17 1,223.50 3,817.87 285.46 664.92 4,525.88 6,067.30 616.44

DMU18 11,500.29 27,411.22 7,113.30 1,165.22 36,998.77 209.95 1,936.68

DMU19 6,623.05 18,226.76 5,373.45 1,603.52 25,093.30 11,356.89 806.04

DMUS	Inputs (1,000,000 U.S Dollars)	Outputs (1,000,000 U.S Dollars)
DMU1	104,410.90	83,262.30	10,300.40	4,480.30	80,861	26,804.80	–6,066.50
DMU2	84,506.54	190,148.75	24,020.74	30,523.35	247,586.56	160,430.26	20,980.95
DMU3	26,754.20	129,437	13,361.70	5,582.50	164,413.70	60,086.40	9,582.10
DMU4	31,229	128,321	13,405	7,874	152,356	40,323	9,615
DMU5	30,163	124,041	14,999	41,279	149,558	28,657	7,371
DMU6	28,995.56	93,916.22	15,641.45	5,892.77	121,164.54	67,116.56	5,100.89
DMU7	19,534.90	81,447.30	9,496.30	6,477.90	101,392.50	47,040.40	7,035.60
DMU8	61,166.49	84,012.19	14,039.14	4,666.07	103,410.97	46,127.18	4,159.76
DMU9	5,952.40	90,128.14	5,467.31	9,079.95	103,145.88	32,448.81	6,165.23
DMU10	22,959.14	58,961.04	9,519.63	233.14	73,566.99	53,505.12	5,207.33
DMU11	1,989.08	16,867.23	1,099.08	469.23	19,471.69	14,074.46	1,955.69
DMU12	11,983.40	48,959.90	6,133.60	1,785.30	60,143.60	13,440.90	1,322.20
DMU13	12,288.10	39,724.30	5,300.90	3,353.90	49,859.70	31,321.40	3,256
DMU14	10,433.70	31,723.02	3,769.37	3,131.69	39,617.16	19,363.22	2,104.48
DMU15	6,274.71	28,312.12	3,258.12	1,474.24	36,766.47	10,071.76	8,454.35
DMU16	6,165.90	27,319.19	2,989.25	758.5	36,128.90	9,897.11	8,307.75
DMU17	1,223.50	3,817.87	285.46	664.92	4,525.88	6,067.30	616.44
DMU18	11,500.29	27,411.22	7,113.30	1,165.22	36,998.77	209.95	1,936.68
DMU19	6,623.05	18,226.76	5,373.45	1,603.52	25,093.30	11,356.89	806.04

Sources: Official websites of the above-mentioned automobile manufacturers.

4 Analysis of results

4.1 Results of prediction

In this paper, a GM (1, 1) model is adopted to predict the input and output variables in several years in the future. In this part the fixed asset (Fix.as) of DMU13 is verified as a sample, and the verification of other variables is also made in the following procedures:

Therefore, we can set up the original data sequence as below: $X^{(0)} = (12, 687.4; 12, 070.3; 11, 881.1; 12, 288.1)$

The original data undergo accumulated generating operation (AGO): $X^{(1)} = (12, 687.4; 24, 757.7; 36, 638.8; 48, 926.9)$

If μ is of a value of 0.5, the sequence of mean generation with consecutive neighbors is obtained. $Z^{(1)} (k) = (8, 722.55; 30, 698.25; 42, 782.85)$

By (6) formula is obtained as follows: $\begin{matrix} B & = & [\begin{matrix} - 18, 722.55 & 1 \\ - 30, 698.25 & 1 \\ - 42, 782.85 & 1 \end{matrix}], Y_{n} = [\begin{matrix} 12, 070.3 \\ 11, 881.1 \\ 12, 288.1 \end{matrix}] \\ \overset{\land}{α} & = & {[α, μ]}^{T} = {(B^{T} B)}^{- 1} B^{T} Y_{n} \end{matrix}$

Then, α = -0.00908958, μ = 11, 800.46921115. By substituting it into Formula (10), we obtain the grey prediction model as follows: $\begin{matrix} \overset{\land}{X^{(1)}} (k + 1) = (X^{(0)} (1) - \frac{μ}{α}) e^{- α t} + \frac{μ}{α} \\ = 1, 310, 928.82 \times e^{0.00908958} - 1, 298, 241.42 \end{matrix}$

Through the inverse accumulated generating operation (IAGO).

Based on the above data, we can obtain the results of prediction for the upcoming years, as shown in Table 3 and Table 4.

Table 3
DMU11’s Inputs/Outputs data from 2012 to 2015

DMU11 Inputs (1,000,000 U.S Dollars) Outputs (1,000,000 U.S Dollars)

(I) Fix.as (I) Cogs (I) O.exp (I) L.inv (O) Rev (O) T.eq (O) Net.in

2012 12,687.40 37,501.20 4,987.40 1,725.90 45,397 27,001.70 1,908.50

2013 12,070.30 36,972.10 4,693.70 2,996.40 45,025.20 25,535.40 764.5

2014 11,881.10 36,641 4,856.50 3,063.50 45,160.50 27,387.80 2,197.80

2015 12,288.10 39,724.30 5,300.90 3,353.90 49,859.70 31,321.40 3,256

DMU11	Inputs (1,000,000 U.S Dollars)	Outputs (1,000,000 U.S Dollars)
2012	12,687.40	37,501.20	4,987.40	1,725.90	45,397	27,001.70	1,908.50
2013	12,070.30	36,972.10	4,693.70	2,996.40	45,025.20	25,535.40	764.5
2014	11,881.10	36,641	4,856.50	3,063.50	45,160.50	27,387.80	2,197.80
2015	12,288.10	39,724.30	5,300.90	3,353.90	49,859.70	31,321.40	3,256

Table 4

Forecast values for year 2019–2020, inputs (1,000,000 U.S Dollars)

DMUS	(I) Fix.as		(I) Cogs		(I) O.exp		(I) L.inv
	2019	2020	2019	2020	2019	2020	2019	2020
DMU1	189,798.47	219,585.26	124,176.61	137,701.20	25,573.38	32,427.96	5,455.26	5,724.95
DMU2	112,625.89	122,042.07	184,383.40	183,710.39	27,851.58	28,858.43	64,779.77	78,448.98
DMU3	33,392.02	35,277.86	209,520.14	236,815.21	16,129.73	16,913.67	5,746.47	5,805.35
DMU4	45,437.90	49,998.01	118,448.97	115,606.58	15,532.50	16,186.28	8,346.39	8,524.86
DMU5	36,275.36	37,863.54	121,821.40	121,240.97	19,724.08	20,944.48	2,457.90	1,297.31
DMU6	49,426.92	56,462.39	181,485.20	212,859.18	22,664.83	24,954.44	3,940.23	3,562.90
DMU7	26,858.69	28,991.78	120,633.48	133,621.65	13,423.74	14,642.85	4,935.36	4,623.83
DMU8	101,613.72	115,192.75	111,440.56	119,585.42	28,110.87	33,386.16	4,531.00	4,474.64
DMU9	11,779.69	14,007.63	127,957.06	139,473.08	5,963.18	6,026.10	10,146.81	10,353.07
DMU10	41,486.46	48,410.68	69,422.24	72,365.10	10,889.97	11,257.25	201.62	193.42
DMU11	3,690.18	4,289.99	134,536.88	227,030.53	9,272.70	16,020.93	2,699.57	4,095.27
DMU12	11,910.25	11,898.74	45,042.42	44,300.48	4,520.65	4,205.57	2,379.89	2,589.27
DMU13	12,641.06	12,756.49	45,424.19	47,135.22	6,734.77	7,164.79	4,179.87	4,427.83
DMU14	18,799.25	21,938.91	35,266.30	36,273.41	4,221.15	4,370.55	42,177.92	86,626.93
DMU15	47,232.76	58,992.73	4,651.70	5,582.40	672.48	707.62	14,216.55	18,074.18
DMU16	6,708.46	6,797.56	36,168.29	38,532.49	3,047.97	3,003.56	9,301.78	15,313.16
DMU17	1,435.90	1,490.70	8,421.09	10,318.51	750.08	942.71	2,810.17	4,013.20
DMU18	16,607.38	18,200.63	46,143.08	52,546.30	13,432.83	15,719.22	2,096.29	2,377.59
DMU19	7,003.92	7,084.85	15,140.39	14,350.03	5,351.48	5,306.31	1,477.58	1,423.93

Sources: Obtained from annual reports of the 19 enterprises.

Table 5

Forecast values for year 2019–2020, outputs (1,000,000 U.S Dollars)

DMUS	(O) Rev		(O) T.eq		(O) Net.in
	2019	2020	2019	2020	2019	2020
DMU1	101,440.80	107,418.99	25,149.51	24,467.18	25,594.23	37,722.68
DMU2	273,663.67	281,294.07	222,915.73	243,146.16	62,802.95	82,164.52
DMU3	263,633.88	297,211.68	95,598.63	108,011.76	9,038.16	9,032.93
DMU4	147,106.84	145,659.07	32,999.41	31,783.15	42,924.50	64,387.81
DMU5	153,664.12	155,065.37	32,997.71	34,479.84	9,304.62	9,404.40
DMU6	217,317.44	250,244.22	111,144.30	126,066.67	9,772.80	11,230.52
DMU7	148,635.18	164,040.34	67,720.71	74,405.87	10,122.56	11,091.49
DMU8	144,187.00	156,690.82	58,236.97	61,735.60	7,418.71	8,587.69
DMU9	144,886.68	157,507.91	55,027.10	62,818.45	7,830.15	8,305.13
DMU10	81,530.56	83,679.55	74,771.01	81,207.18	2,727.52	2,321.18
DMU11	157,523.65	266,811.38	28,659.87	34,298.67	2,829.54	3,073.76
DMU12	60,460.12	60,798.32	2,817.60	2,316.21	98.06	58.53
DMU13	60,659.04	63,936.62	47,059.53	52,228.37	31,512.94	55,541.22
DMU14	42,539.73	43,408.24	27,640.49	30,186.06	946.84	780.96
DMU15	85,701.21	100,549.82	1,683.81	1,500	4,583.74	5,343.63
DMU16	48,128.95	51,601.93	12,295.93	12,941.64	12,048.30	13,205.97
DMU17	25,508.63	39,575.70	10,696.13	12,287.22	1,579.62	2,010.88
DMU18	69,261.09	80,870.97	703.82	969.55	14,946.13	24,497.47
DMU19	21,913.09	21,016.96	9,286.87	8,795.72	795.61	775.97

Sources: Obtained from annual reports of the 19 enterprises.

4.2 Accuracy of prediction

The GM (1, 1) method mainly predicts future results with the current imperfect information. In this method, the mean absolute percent error (MAPE) is adopted to measure data precision. A low MAPE indicates that the predicted values are reasonable. The MAPE values of all 19 DMUS are show below in Table 6.

Table 6
Mean absolute percent errors of decision-making units

DMUS MAPE DMUS MAPE

DMU1 12.57% DMU11 8.22%

DMU2 2.30% DMU12 7.79%

DMU3 1.78% DMU13 2.92%

DMU4 4.72% DMU14 3.91%

DMU5 5.83% DMU15 3.20%

DMU6 2.91% DMU16 3.71%

DMU7 2.47% DMU17 3.69%

DMU8 6.63% DMU18 7.58%

DMU9 1.51% DMU19 3.46%

DMU10 1.02%

19DMUs MAPE 4.53936%

DMUS	MAPE	DMUS	MAPE
DMU1	12.57%	DMU11	8.22%
DMU2	2.30%	DMU12	7.79%
DMU3	1.78%	DMU13	2.92%
DMU4	4.72%	DMU14	3.91%
DMU5	5.83%	DMU15	3.20%
DMU6	2.91%	DMU16	3.71%
DMU7	2.47%	DMU17	3.69%
DMU8	6.63%	DMU18	7.58%
DMU9	1.51%	DMU19	3.46%
DMU10	1.02%
19DMUs MAPE	4.53936%

As shown in Table 6, most MAPE values are lower than 10% and their average is 4.53936%, which reflects that the predicted values are reasonable and relatively accurate. In the table, the MAPE value of DMU1 reaches as high as 12.573%. In 2015 the Volkswagen AG saw a growth of $239.5 billion in revenue and an increase of $14.4 billion in operating profit; however, the emission scandal caused a loss of $18.2 billion to the corporation, and consequently the corporation had a negative net income that year.

4.3 Pearson correlation test

Homogeneity and isotonicity are the two assumptions on which DEA is based. The former ensures the comparability of different DMUs and the fairness of evaluation results, and the latter requires a positive correlation between input and output data. Pearson correlation test is made to measure the correlation (linear dependence) between two variables. In general, correlation coefficients are within the range of [–1, +1], and the larger the absolute value of a coefficient is, the stronger the correlation is. In other words, the closer a coefficient is to 1 or –1, the stronger the correlation is; and the closer it is to 0, the weaker the correlation is [26].

Tables 7 to 10 demonstrates the correlation coefficients between input and output variables, showing a positive correlation between them. The positive correlation proves that the input and output variables are properly selected, and it is also the premise of employing DEA model for analysis.

Table 7
Input/Output data correlation coefficient in 2012

Fix.as Cogs O.exp L.inv Rev T.eq Net.in

Fix.as 1 0.76574 0.7607143 0.0673521 0.7684515 0.8948227 0.2206499

Cogs 0.76574 1 0.940183 0.3701964 0.9919036 0.8168755 0.4961964

O.exp 0.7607143 0.940183 1 0.23272 0.9445109 0.85683 0.3763975

L.inv 0.0673521 0.3701964 0.23272 1 0.373946 0.0425716 0.2221469

Rev 0.7684515 0.9919036 0.9445109 0.373946 1 0.8321341 0.4956921

T.eq 0.8948227 0.8168755 0.85683 0.0425716 0.8321341 1 0.2339922

Net.in 0.2206499 0.4961964 0.3763975 0.2221469 0.4956921 0.2339922 1

	Fix.as	Cogs	O.exp	L.inv	Rev	T.eq	Net.in
Fix.as	1	0.76574	0.7607143	0.0673521	0.7684515	0.8948227	0.2206499
Cogs	0.76574	1	0.940183	0.3701964	0.9919036	0.8168755	0.4961964
O.exp	0.7607143	0.940183	1	0.23272	0.9445109	0.85683	0.3763975
L.inv	0.0673521	0.3701964	0.23272	1	0.373946	0.0425716	0.2221469
Rev	0.7684515	0.9919036	0.9445109	0.373946	1	0.8321341	0.4956921
T.eq	0.8948227	0.8168755	0.85683	0.0425716	0.8321341	1	0.2339922
Net.in	0.2206499	0.4961964	0.3763975	0.2221469	0.4956921	0.2339922	1

Table 8

Input/Output data correlation coefficient in 2013

	Fix.as	Cogs	O.exp	L.inv	Rev	T.eq	Net.in
Fix.as	1	0.6747926	0.6817668	0.1166557	0.7452457	0.859656	0.560572
Cogs	0.6747926	1	0.9227841	0.4596575	0.9806112	0.7911696	0.7731995
O.exp	0.6817668	0.9227841	1	0.3876464	0.9297621	0.8398558	0.7262106
L.inv	0.1166557	0.4596575	0.3876464	1	0.4194766	0.0938967	0.3084335
Rev	0.7452457	0.9806112	0.9297621	0.4194766	1	0.8600308	0.80242
T.eq	0.859656	0.7911696	0.8398558	0.0938967	0.8600308	1	0.7378218
Net.in	0.560572	0.7731995	0.7262106	0.3084335	0.80242	0.7378218	1

Table 9

Input/Output data correlation coefficient in 2014

	Fix.as	Cogs	O.exp	L.inv	Rev	T.eq	Net.in
Fix.as	1	0.5784363	0.5853364	0.3058545	0.5700005	0.578594	0.4028715
Cogs	0.5784363	1	0.9311988	0.6382473	0.9846181	0.7992512	0.7909706
O.exp	0.5853364	0.9311988	1	0.6351077	0.9383312	0.8498774	0.8095956
L.inv	0.3058545	0.6382473	0.6351077	1	0.6333325	0.3640903	0.7113061
Rev	0.5700005	0.9846181	0.9383312	0.6333325	1	0.8377586	0.8276574
T.eq	0.578594	0.7992512	0.8498774	0.3640903	0.8377586	1	0.7967409
Net.in	0.4028715	0.7909706	0.8095956	0.7113061	0.8276574	0.7967409	1

Table 10

Input/Output data correlation coefficient in 2015

	Fix.as	Cogs	O.exp	L.inv	Rev	T.eq	Net.in
Fix.as	1	0.6443792	0.7135203	0.3910409	0.6023341	0.5946827	0.3242176
Cogs	0.6443792	1	0.9212749	0.7158512	0.9939685	0.8228946	0.7617504
O.exp	0.7135203	0.9212749	1	0.6681202	0.9312986	0.8430454	0.6744677
L.inv	0.3910409	0.7158512	0.6681202	1	0.7166668	0.5289074	0.5870217
Rev	0.6023341	0.9939685	0.9312986	0.7166668	1	0.8565835	0.803273
T.eq	0.5946827	0.8228946	0.8430454	0.5289074	0.8565835	1	0.8019036
Net.in	0.3242176	0.7617504	0.6744677	0.5870217	0.803273	0.8019036	1

4.4 Pre-alliance analysis

Super-SBM-I-V Model is adopted to measure the actual data of the 19 DMUs in 2015. And the efficiency ranking before alliance is obtained as shown in Table 11.

Table 11
Pre-alliance efficiency values and their ranking

Rank DMU Score Rank DMU Score

1 DMU17 2.7234515 11 DMU2 1

2 DMU10 1.913897 12 DMU13 0.8980208

3 DMU11 1.7154632 13 DMU12 0.8798003

4 DMU9 1.5579631 14 DMU7 0.8692622

5 DMU3 1.4068699 15 DMU4 0.8420594

6 DMU16 1.2540602 16 DMU14 0.7047184

7 DMU15 1.0396353 17 DMU5 0.651358

8 DMU6 1.0183545 18 DMU8 0.6391677

9 DMU19 1.0137305 19 DMU1 0.517415

10 DMU18 1.0044126

Rank	DMU	Score	Rank	DMU	Score
1	DMU17	2.7234515	11	DMU2	1
2	DMU10	1.913897	12	DMU13	0.8980208
3	DMU11	1.7154632	13	DMU12	0.8798003
4	DMU9	1.5579631	14	DMU7	0.8692622
5	DMU3	1.4068699	15	DMU4	0.8420594
6	DMU16	1.2540602	16	DMU14	0.7047184
7	DMU15	1.0396353	17	DMU5	0.651358
8	DMU6	1.0183545	18	DMU8	0.6391677
9	DMU19	1.0137305	19	DMU1	0.517415
10	DMU18	1.0044126

In Table 11, DMU10 is the most efficient decision-making unit, with a score of 5.8198003, and DMU17 and DMU11 are respectively in the second and the third place. The target decision-making unit is ranked at the 12th and its efficiency scores 0.8980208 (0.8980208 < 1). Apparently, it is necessary for the subject corporation to look for suitable strategic partners who can help enhance its efficiency of operation.

4.5 Post-alliance analysis

An analysis is made to verify whether the alliance with strategic partners can help the subject corporation to enhance its operating efficiency, and meanwhile to explore new opportunities from the newly established innovative alliance. In the analysis, DMU13 is paired with each of the other 18 DMUs, and a total of 37 DMUs are thus obtained, including the 19 original DMUs and the 18 DMUs of virtual alliances. Afterwards, Super-SBM-I-V Model and DEA Model are adopted for efficiency evaluation of the 37 DMUs. The rankings and scores of virtual alliances are demonstrated in Table 12.

Table 12
Rankings and scores of the efficiency of virtual DMUs

Rank DMU Score Rank DMU Score

1 DMU17 2.7234515 20 DMU6 1.0015574

2 DMU13+DMU8 2.3551355 21 DMU13+DMU2 1

3 DMU10 1.913897 22 DMU13+DMU19 0.9461806

4 DMU11 1.7203141 23 DMU13+DMU7 0.9139475

5 DMU9 1.338545 24 DMU13 0.8883958

6 DMU13+DMU10 1.2982582 25 DMU13+DMU4 0.8871692

7 DMU13+DMU3 1.2555027 26 DMU12 0.8798003

8 DMU16 1.2540088 27 DMU7 0.8580452

9 DMU3 1.0936902 28 DMU13+DMU18 0.8492931

10 DMU13+DMU9 1.0901715 29 DMU4 0.8318275

11 DMU13+DMU11 1.0634411 30 DMU13+DMU14 0.824048

12 DMU13+DMU16 1.044608 31 DMU13+DMU12 0.8039628

13 DMU15 1.0236682 32 DMU14 0.7044297

14 DMU13+DMU15 1.014012 33 DMU13+DMU5 0.7033756

15 DMU19 1.0137305 34 DMU5 0.6491933

16 DMU13+DMU6 1.0128933 35 DMU8 0.6391677

17 DMU2 1.0108327 36 DMU13+DMU1 0.5719271

18 DMU18 1.0044126 37 DMU1 0.517415

19 DMU13+DMU17 1.0017428

Rank	DMU	Score	Rank	DMU	Score
1	DMU17	2.7234515	20	DMU6	1.0015574
2	DMU13+DMU8	2.3551355	21	DMU13+DMU2	1
3	DMU10	1.913897	22	DMU13+DMU19	0.9461806
4	DMU11	1.7203141	23	DMU13+DMU7	0.9139475
5	DMU9	1.338545	24	DMU13	0.8883958
6	DMU13+DMU10	1.2982582	25	DMU13+DMU4	0.8871692
7	DMU13+DMU3	1.2555027	26	DMU12	0.8798003
8	DMU16	1.2540088	27	DMU7	0.8580452
9	DMU3	1.0936902	28	DMU13+DMU18	0.8492931
10	DMU13+DMU9	1.0901715	29	DMU4	0.8318275
11	DMU13+DMU11	1.0634411	30	DMU13+DMU14	0.824048
12	DMU13+DMU16	1.044608	31	DMU13+DMU12	0.8039628
13	DMU15	1.0236682	32	DMU14	0.7044297
14	DMU13+DMU15	1.014012	33	DMU13+DMU5	0.7033756
15	DMU19	1.0137305	34	DMU5	0.6491933
16	DMU13+DMU6	1.0128933	35	DMU8	0.6391677
17	DMU2	1.0108327	36	DMU13+DMU1	0.5719271
18	DMU18	1.0044126	37	DMU1	0.517415
19	DMU13+DMU17	1.0017428

As shown in Table 12, after the alliance, DMU13 and DMU8 manage to get the highest efficiency score (namely their respective score is higher than 1.

Later these virtual alliances will be divided into two groups for a comparison of their efficiency, as shown in Table 13:

Table 13

High/low efficiency alliance partners

Grouping and sorting	virtual alliance	DMU13	DM13	League ranking- League post ranking
		League ranking	League post ranking
First group	High Efficiency Alliance
1	DMU13+DMU8	24	2	22
2	DMU13+DMU10	24	6	18
3	DMU13+DMU3	24	7	17
4	DMU13+DMU9	24	10	14
5	DMU13+DMU11	24	11	13
6	DMU13+DMU16	24	12	12
7	DMU13+DMU15	24	14	10
8	DMU13+DMU6	24	16	8
9	DMU13+DMU17	24	19	5
10	DMU13+DMU2	24	21	3
11	DMU13+DMU19	24	22	2
12	DMU13+DMU7	24	23	1
Second group	Low Efficiency Alliance
1	DMU13+DMU4	24	25	–1
2	DMU13+DMU18	24	28	–4
3	DMU13+DMU14	24	30	–6
4	DMU13+DMU12	24	31	–7
5	DMU13+DMU5	24	33	–9
6	DMU13+DMU1	24	36	–12

In the first group, after the alliance with 12 DMUs,including DMU8, DMU10, DMU3, DMU9, DMU11, DMU16, DMU15, DMU6, DMU17, DMU2, DMU19, DMU7, the efficiency of DMU13 has been enhanced, which indicates that DMU13 will be benefited from these alliances. Therefore, the 12 DMUS candidates will be the first choice of DMU13 in forming an alliance, particularly the ideal candidate falls on DMU8. The rankings of DMU13 before and after alliance are of the largest difference (22) when it allied with DMU8, which makes DMU8 the ideal partner. The second group includes 6 DMUs and it is clear that DMU13’s alliance with them will lead to a lowering of its own efficiency. In the long run, these DMUs will not contribute to the enhancement of DMU13’s efficiency. Therefore, corresponding enterprises should not be on the list of strategic alliance partners for DMU13.

4.6 Selection of alliance partners

In the above analysis, the best alliance partner is determined by the ranking of the efficiency value of DMU13. Apparently, to select an alliance partner solely by the efficiency ranking is far from sufficient, and we need to further analyze the feasibility of alliance with a selected partner. As shown in Table 12, although there are 12 potential partners on the list for selection, they normally lack a motivation to ally with DMU13 because the target decision-making unit DMU13 is at a relatively low ranking (the 24th place).

Integrating Tables 11 to 13, Fig. 2 is obtained from a comparison among the rankings of the virtual alliances formed by DMU13 with each of the other 18 DMUs. As shown in Fig. 2, the blue line (pre-alliance) is closer to the center than the red line (post-alliance). That means most of the DMUs have a high efficiency before alliance while still some others are of a low efficiency before alliance.

Fig.2

Rankings of the virtual alliances.

From Fig. 2, we can see that Group Renault (DMU13) and Nissan Motor Company (DMU8) are both of a relatively low efficiency before their alliance, namely 0.8883958 and 0.6391677 (both are less than 1), and they are ranked respectively at the 24th and the 35th place then. However, after Renault (DMU13) allied with Nissan (DMU8), the efficiency of their alliance is largely improved to 2.399553485 (higher than 1), and their alliance is ranked at the 2nd place. After its alliance with Daimler AG (DMU3), the efficiency of Renault goes up from 1.0936902 to 1.2555027, and its ranking goes up to the 7th. That means the alliance not only benefits Renault, but also brings opportunities for Nissan and Daimler AG. In other words, Nissan-Renault alliance and Renault-Daimler alliance would enable the corporations to manage and integrate their resources more efficiently. Therefore, Nissan Motor Company and Daimler AG will have a strong motivation to ally with Renault.

In fact, the Renault-Nissan alliance has been maintained since 1999. The three leading auto-manufacturers, Renault of France, Nissan of Japan and Daimler AG of Germany, established a “triple alliance” on April 7, 2010. These alliances proved that the results of our study are valid and feasible. It is the triple alliance of Renault, Nissan and Daimler that has greatly changed the pattern of global automobile industry. The alliance has immediately become the third largest auto-alliance in the world, second to Toyota-Suzuki and Volkswagen-Suzuki alliance. The triple alliance involves not only the three giants in auto-industry, but also the blending of Eastern and Western cultures. Thanks to the cultural blending, the costs of purchase and manufacturing could be lowered to achieve “the maximization of interests in cooperation”, and the three corporations would share a closer relation in different links including technology, product platform, marketing, manufacturing and R&D, etc. Therefore, the alliance is in line with the global trend of inter-organizational collaboration.

5 Conclusions

Based on the real data released in the annual reports of the top 19 auto-manufacturers from 2012 to 2015, this paper selects Group Renault of France as the target decision-making unit (DMU13) and adopts GM (1, 1) model to predict the changes in the future values of input and output variables. Besides, through the MAPE test, it is found that the prediction is of an accuracy of 4.53936% which proves the reasonability of the predicted values. In Pearson correlation test, the positive correlation between input and output variables is obtained. The positive correlation indicates that the selected input and out variables in this study are appropriate, and it is also the premise of making analysis with DEA model.

By employing a non-radial super-efficiency DEA model to evaluate the efficiency values of 19 corporations and of DMU13’ alliances with other 18 DMUs, we find that Renault can form an alliance with 12 relatively appropriate partners. However, after the feasibility test, it is clear that the most suitable and realistic alliance partners for Renault (DMU13) are Nissan Motor Company (DMU8) and Daimler AG (DMU3).

Based on the study, the paper reaches the conclusion that in practice the selection of a strategic alliance partner does not mean pursuing cooperation with the largest or the highest-ranked enterprise; instead, a corporation should ally with the most suitable partner. Currently many industries including auto-manufacturing are faced with great challenges in exploring new markets with a competitive edge, acquiring new technologies and resources, and reducing risks and R&D costs. To solve those problems, this paper, by integrating grey system theory with a non-radial super-efficiency DEA model, proposes a novel decision-making model with high accuracy to predict and evaluate the selection of appropriate alliance partners for automobile enterprises. Further studies are still needed to explore whether this model can also be applied to the selection of alliance partners in other industries.

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