# Dynamic Assessment of Sustainable Manufacturing Capability for CNC Machining Systems in Cloud Manufacturing

Luqiong Xie, Xuemei Jiang, Wenjun Xu, Qin Wei, Ruifang Li, Zude Zhou

<figure><img src="image_1.png" /></figure>

## To cite this version:

Luqiong Xie, Xuemei Jiang, Wenjun Xu, Qin Wei, Ruifang Li, et al.. Dynamic Assessment of Sustainable Manufacturing Capability for CNC Machining Systems in Cloud Manufacturing. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2015, Tokyo, Japan. pp.396-403, 10.1007/978-3-319-22759-7_46 . hal-01431121

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Submitted on 10 Jan 2017

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<figure><img src="image_2.png" /></figure>
Dynamic Assessment of Sustainable Manufacturing
Capability for CNC Machining Systems in Cloud
Manufacturing

Luqiong Xie¹,², Xuemei Jiang¹,², Wenjun Xu¹,², Qin Wei¹,²,

Ruifang Li¹,², Zude Zhou¹,²

¹School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China

²Key Lab. of Fiber Sensing Technology and Information Processing, Ministry of Education, China

xieluqiong_whut@163.com, jxm2001@whut.edu.cn, xuwenjun@whut.edu.cn

qinwei@whut.edu.cn, liruifang@whut.edu.cn, zudezhou@whut.edu.cn

**Abstract.** Sustainability has been attracted extensive attention in manufacturing industry for the increasing excessive resource consumption and serious environmental pollution. The assessment of sustainable manufacturing capability is a vital factor, especially in cloud manufacturing, in which the capability assessment of the manufacturing resources is the premise of selecting the optimal manufacturing services. While the CNC machining tools are the basic manufacturing resources in production process, so the dynamic assessment of their sustainable manufacturing capabilities is investigated in this paper. A set of indicators is established considering manufacturing sustainability and a new dynamic assessment model is proposed based on a modified “vertical and horizontal” method. The model is verified through a case study and it can comprehensively evaluate the capability performance of the CNC machining systems, and also effectively follow the dynamics of their production activities.

**Keywords:** Sustainable manufacturing capability; CNC machining systems; dynamic assessment; “vertical and horizontal” method

# 1 Introduction

Currently, cloud manufacturing becomes a new manufacturing model under the promotion of manufacturing informatization. The capabilities of manufacturing resources are presented in the form of services consumers can share together globally. Selecting the optimal manufacturing resource from the global shared resource pool becomes a vital issue under cloud manufacturing. Meanwhile, sustainability has been the focus of heated discussion in recent years. There're many definitions about sustainability. The most acceptable one is defined at 1987 World Commission on Environment and Development [1], which states, “Meeting the needs of the present without compromising
ing the ability of future generations to meet their own needs.” Generally, sustainable manufacturing is the reflection of sustainability in manufacturing. Meanwhile, manufacturing informatization makes digital design and manufacture become a way to improve manufacturing capability. CNC machining tools are widely used and they can solve many parts processing problems (e.g., high-precision, small batch and multi varieties production). They are the key to parts processing, which will greatly affect the processing quality, cost, time, energy, wastes, etc. So the assessment of manufacturing capability for CNC machining systems is of great significance.

## 2 Related Works

The concept of manufacturing capability was first proposed by Skinner in 1969[2]. He stated that manufacturing capability is a kind of ability for enterprises to achieve manufacturing strategy and is composed of costs, quality, time and the relationship between these elements. Corbett [3] pointed out that manufacturing capability is consist of quality, cost, delivery speed, flexibility and innovation. Reference [4] defined manufacturing capability as time, quality, cost, technology, service, corporate performance etc. when selecting virtual enterprise partners. In the field of sustainable manufacturing, some scholars have applied sustainability assessment to manufacturing decision making from economic, environmental and social aspects [5, 6].

The relative assessment methods mainly have two categories: One is the subjective method which has certain subjectivity. The other is the objective method which cannot reflect the preferences of decision makers. So far, most assessment models are static. The dynamic assessments have already made some achievements [7, 8], which have two classifications. One is a twice-weighted method which confirms the weights at different times; the other is dynamically dealing with the time series data, by which the weights are updated along with the update of data. For the former, reference [9] proposed a dynamic method based on Time Entropy to assess manufacturing capability, while it only considers subjective weights ignoring the effect of objective data.

Overall, the existing relative researches mainly have two shortages. Firstly, the researches solely focus on economic benefits without considering environmental impact and resource consumption. Secondly, most assessment methods are static which cannot reflect the capability dynamically. Therefore, this paper establishes a set of indicators system of sustainable manufacturing capability for CNC machining systems. A dynamic assessment method is proposed, which combine the advantages of subjective and objective assessment methods. Finally, “time-value coefficients” are introduced to aggregate data to obtain comprehensive capability value.

## 3 Assessment Model and Indicators

### 3.1 Assessment Model

For CNC machining systems, the indicator values are changing dynamically. Therefore, the issue of manufacturing capability assessment is a multidimensional
decision making problem of three dimensions with indicators space, object space and time space. It can be supposed that there are *n* alternatives $s_1, s_2, \cdots, s_n$, *m* indicators $x_1, x_2, \cdots, x_m$ (suppose all the indicators are standardized), and *N* historical task orders drawn from *N* recent time periods in chronological order. The original data can be got as $x_{ij}(t_k)$, constituting a time series database shown in Tab.1. Based on the dynamic time series data, the connotation of manufacturing capability and sustainable manufacturing, this paper mainly concern economic and environmental aspects. A dynamic assessment model is proposed as Fig.1.

<table><caption>**Table 1.** Dynamic timing database</caption><thead><tr><th rowspan="2">Alternatives</th><th colspan="3">t<sub>1</sub></th><th colspan="3">t<sub>2</sub></th><th colspan="3">...</th><th colspan="3">t<sub>N</sub></th></tr><tr><th>x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>m</sub></th><th></th><th></th><th>x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>m</sub></th><th></th><th></th><th></th><th>x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>m</sub></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>s<sub>1</sub></td><td>x<sub>11</sub> t<sub>1</sub> x<sub>12</sub> t<sub>1</sub> ... x<sub>1m</sub> t<sub>1</sub></td><td>x<sub>11</sub> t<sub>2</sub> x<sub>12</sub> t<sub>2</sub> ... x<sub>1m</sub> t<sub>2</sub></td><td>x<sub>11</sub> t<sub>3</sub> x<sub>12</sub> t<sub>3</sub> ... x<sub>1m</sub> t<sub>3</sub></td><td>x<sub>11</sub> t<sub>N</sub></td><td>x<sub>12</sub> t<sub>N</sub></td><td>x<sub>13</sub> t<sub>N</sub></td><td>x<sub>11</sub> t<sub>N</sub></td><td>x<sub>12</sub> t<sub>N</sub></td><td>x<sub>13</sub> t<sub>N</sub></td><td>x<sub>11</sub> t<sub>N</sub></td><td>x<sub>12</sub> t<sub>N</sub></td><td>x<sub>13</sub> t<sub>N</sub></td></tr><tr><td>s<sub>2</sub></td><td>x<sub>21</sub> t<sub>1</sub> x<sub>22</sub> t<sub>1</sub> ... x<sub>2m</sub> t<sub>1</sub></td><td>x<sub>21</sub> t<sub>2</sub> x<sub>22</sub> t<sub>2</sub> ... x<sub>2m</sub> t<sub>2</sub></td><td>x<sub>21</sub> t<sub>3</sub> x<sub>22</sub> t<sub>3</sub> ... x<sub>2m</sub> t<sub>3</sub></td><td>x<sub>21</sub> t<sub>N</sub></td><td>x<sub>22</sub> t<sub>N</sub></td><td>x<sub>23</sub> t<sub>N</sub></td><td>x<sub>21</sub> t<sub>N</sub></td><td>x<sub>22</sub> t<sub>N</sub></td><td>x<sub>23</sub> t<sub>N</sub></td><td>x<sub>21</sub> t<sub>N</sub></td><td>x<sub>22</sub> t<sub>N</sub></td><td>x<sub>23</sub> t<sub>N</sub></td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>s<sub>N</sub></td><td>x<sub>n1</sub> t<sub>1</sub> x<sub>n2</sub> t<sub>1</sub> ... x<sub>nm</sub> t<sub>1</sub></td><td>x<sub>n1</sub> t<sub>2</sub> x<sub>n2</sub> t<sub>2</sub> ... x<sub>nm</sub> t<sub>2</sub></td><td>x<sub>n1</sub> t<sub>N</sub></td><td>x<sub>n2</sub> t<sub>N</sub></td><td>x<sub>n3</sub> t<sub>N</sub></td><td>x<sub>n4</sub> t<sub>N</sub></td><td>x<sub>n1</sub> t<sub>N</sub></td><td>x<sub>n2</sub> t<sub>N</sub></td><td>x<sub>n3</sub> t<sub>N</sub></td><td>x<sub>n4</sub> t<sub>N</sub></td><td>x<sub>n1</sub> t<sub>N</sub></td><td>x<sub>n2</sub> t<sub>N</sub></td><td>x<sub>n3</sub> t<sub>N</sub></td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Assessment Model</figcaption></figure>

## 3.2 Assessment Indicators

According to the connotation of manufacturing capability and the demands of sustainable manufacturing, besides quality, time and cost, the basic elements of manufacturing capability, resource consumption and environmental impact are also considered in this paper. Given the actual processing of machining system, the five factors can be decomposed to establish the indicator system shown in Table2.
<table><caption>**Table 2.** Indicators for sustainable manufacturing capability assessment</caption><thead><tr><th>Goal</th><th>Indexes</th><th>Sub-indexes</th></tr></thead><tbody><tr><td rowspan="10">Assessment of Sustainable Manufacturing Capability for CNC Machining Systems</td><td rowspan="3">Processing quality</td><td>Dimension machining precision</td></tr><tr><td>Surface machining precision</td></tr><tr><td>Shape machining precision</td></tr><tr><td rowspan="4">Processing cost</td><td>Workers' wages</td></tr><tr><td>Equipment depreciation</td></tr><tr><td>Operation expenses</td></tr><tr><td>Maintenance cost</td></tr><tr><td>Material cost</td></tr><tr><td rowspan="2">Processing time</td><td>Machining time</td></tr><tr><td>Auxiliary time</td></tr><tr><td rowspan="3">Resource consumption</td><td>Main material consumption</td></tr><tr><td>Auxiliary materials consumption</td></tr><tr><td>Energy consumption</td></tr><tr><td rowspan="4">Environmental impact</td><td>Air pollution</td></tr><tr><td>Cutting liquid pollution</td></tr><tr><td>Noise</td></tr><tr><td>Wastes</td></tr></tbody></table>

# 4 Dynamic Assessment Based on Timing Sequence

## 4.1 Subjective Weight Calculation Based on AHP

Analytic hierarchy process (AHP) was first put forward by Saaty as multi criteria decision tool that quantifies the qualitative analysis [10]. It is used in this paper to determine the subjective weights. The method consists of the following steps:

1. Firstly, define the problem and find the indicators related to the decision goal.

2. Establish a hierarchical structure according to the subordinate relations between the indicators: top level is the goal of the decision; intermediate levels represent criteria or sub-criteria; and the bottom level represents the alternatives, such as Table 2.

3. Construct the comparison matrices by conducting pairwise comparison between the elements of each level with respect to each element in the immediate upper level.

4. Calculate the eigenvector of each matrix to find element's relative weight and check consistency index CI and consistency ratio CR for each eigenvector. Due to the length limitation, further details can refer to reference [10].

Based on Table 2, the subjective weight vector $w$ ($w_1, w_2, \dots, w_m$) can be obtained by AHP. Then the weighted timing database can be got by Eq. (1)

$$x_{ij}(t_k) \quad w_j x_{ij}(t_k), i, 1, 2, \dots, n; j, 1, 2, \dots, m \qquad (1)$$
## 4.2 Objective Weights Calculation Based on “Vertical and Horizontal”

Based on Eq. (1) and Table 1, “vertical and horizontal” method [7] is used here for dynamic assessment. For time $t_k(k = 1, 2, \dots, N)$, the linear function can be defined as:

$$y_i(t_k) = \sum_{j=1}^{m} w_j x_{ij}(t_k), k = 1, 2, \dots, N; i = 1, 2, \dots, n \quad (2)$$

$y_i(t_k)$ is the assessment result of system $s_i$ at time $t_k$; $w$ ($w_1, w_2, \dots, w_m$) is the subjective dynamic weight vector. The principle of determining $w_j$ is to maximize the difference between systems $s_1, s_2, \dots, s_m$, which can be described by Eq. (3).

$$\sum_{k=1}^{N} \sum_{i=1}^{n} (y_i(t_k) - \bar{y})^2 w \left( \sum_{k=1}^{N} A_k A_k + N \bar{x} \bar{x} \right) w H w \quad (3)$$

where $H = \sum_{k=1}^{N} H_k$ $nN\bar{x} = H_k$, $A_k = \sum_{k=1}^{N} A_k A_k$ ($k = 1, 2, \dots, N$), $A_k$ is the matrix of $x_{ij}(t_k)$; $\bar{x} = (\bar{x}_1, \bar{x}_2, \dots, \bar{x}_m)$, $\bar{x}_j = \frac{1}{N} \sum_{k=1}^{N} \frac{1}{n} x_{ij}(t_k)$, $\bar{y} = \frac{1}{N} \sum_{k=1}^{N} \frac{1}{n} y_i(t_k)$.

Obviously, $^2$ have no upper limit if $w$ isn't limited. Limit $w$ $w = 1$. When $w$ is the corresponding eigenvector of the largest eigenvalue $\max(H)$, $^2$ reaches the maximum. If $w = 0$, normalize $w$ to make it satisfy $\sum_{j=1}^{m} w_j = 1$. If $j = (1, 2, \dots, m)$, $w_j = 0$, $w$ can be obtained by the following nonlinear programming problem:

$$\begin{array}{l} \max w H w \\ \text{s.t. } w w = 1, w = 0 \end{array} \quad (4)$$

## 4.3 Obtaining Time-value Coefficient

The system capability of different time $y_i(t_k)$ has been obtained from Eq. (2). The linear comprehensive assessment function can be defined as

$$y_i = \sum_{k=1}^{N} v_k y_i(t_k), i = 1, 2, \dots, n \quad (5)$$

$v$ is the time weighting vector. Furthermore, time-degree factor $\sum_{k=1}^{N} \frac{N}{N-1} v_k$ is introduced to characterize the preference degree to time series. The closer to 0, it indicates the more attention to the recent data. The closer to 1, it indicates the more attention to the distant data. The principle of determining $v$ is to find a set of stable time weights which have small fluctuation. It can be described by the variance of $v$, which can be calculated by the following mathematical programming problem. The solution of this problem can be easily got in reference [11].
$$
\begin{array}{l}
\min(D^2(v)) \quad \frac{1}{N} \sum_{k=1}^{N} v_k^2 - \frac{1}{N^2} \\
\text{s.t.} \quad \sum_{k=1}^{N} \frac{N}{N} \frac{k}{1} v_k, \quad w_k, 1, w_k, 0, 1, k, 1, 2, \dots, N
\end{array}
\qquad (6)
$$

5 A Case Study and Implementation

5.1 A Case Study

The case about selecting the machining system which has the optional sustainable
manufacturing capability for machining a batch of shafting parts is presented.
s₁, s₂, s₃ are the matched alternatives. Based on Table 1, pruning some indicators
with small difference comparatively, 11 indicators are selected: quality( x₁ dimension
machining precision; x₂ surface machining precision; x₃ shape machining precision ),
time( x₄ processing time; x₅ auxiliary time), cost( x₆ operation expenses; equipment
depreciation), resource consumption( x₈ electricity), environmental impact( x₉ noise;
x₁₀ cuttings; x₁₁ liquid wastes). The original data are shown in Table 3.

<table><caption>**Table 3.** The value of indicators</caption>
  <thead>
    <tr>
      <th></th>
      <th></th>
      <th>x<sub>1</sub></th>
      <th>x<sub>2</sub></th>
      <th>x<sub>3</sub></th>
      <th>x<sub>4</sub></th>
      <th>x<sub>5</sub></th>
      <th>x<sub>6</sub></th>
      <th>x<sub>7</sub></th>
      <th>x<sub>8</sub></th>
      <th>x<sub>9</sub></th>
      <th>x<sub>10</sub></th>
      <th>x<sub>11</sub></th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td rowspan="3">t<sub>1</sub></td>
      <td>s<sub>1</sub></td>
      <td>0.05</td>
      <td>0.05</td>
      <td>0.05</td>
      <td>20</td>
      <td>10</td>
      <td>50.8</td>
      <td>1.0</td>
      <td>5.02</td>
      <td>80.2</td>
      <td>1.23</td>
      <td>6</td>
    </tr>
    <tr>
      <td>s<sub>2</sub></td>
      <td>0.09</td>
      <td>0.09</td>
      <td>0.09</td>
      <td>30</td>
      <td>13</td>
      <td>32.5</td>
      <td>1.5</td>
      <td>5.25</td>
      <td>75.3</td>
      <td>2.28</td>
      <td>5.5</td>
    </tr>
    <tr>
      <td>s<sub>3</sub></td>
      <td>0.06</td>
      <td>0.06</td>
      <td>0.05</td>
      <td>18</td>
      <td>10</td>
      <td>30</td>
      <td>0.8</td>
      <td>5.50</td>
      <td>82.6</td>
      <td>1.35</td>
      <td>6.1</td>
    </tr>
    <tr>
      <td rowspan="3">t<sub>2</sub></td>
      <td>s<sub>1</sub></td>
      <td>0.05</td>
      <td>0.06</td>
      <td>0.05</td>
      <td>21</td>
      <td>10</td>
      <td>51.8</td>
      <td>1.2</td>
      <td>5.08</td>
      <td>82.2</td>
      <td>1.25</td>
      <td>5.8</td>
    </tr>
    <tr>
      <td>s<sub>2</sub></td>
      <td>0.08</td>
      <td>0.09</td>
      <td>0.09</td>
      <td>32</td>
      <td>14</td>
      <td>34.5</td>
      <td>1.6</td>
      <td>5.25</td>
      <td>76.5</td>
      <td>2.01</td>
      <td>5.4</td>
    </tr>
    <tr>
      <td>s<sub>3</sub></td>
      <td>0.05</td>
      <td>0.06</td>
      <td>0.06</td>
      <td>20</td>
      <td>11</td>
      <td>32</td>
      <td>1.4</td>
      <td>5.48</td>
      <td>85.0</td>
      <td>1.59</td>
      <td>6.5</td>
    </tr>
    <tr>
      <td rowspan="3">t<sub>3</sub></td>
      <td>s<sub>1</sub></td>
      <td>0.07</td>
      <td>0.06</td>
      <td>0.05</td>
      <td>21</td>
      <td>10</td>
      <td>52.8</td>
      <td>1.0</td>
      <td>5.02</td>
      <td>82</td>
      <td>1.85</td>
      <td>6.2</td>
    </tr>
    <tr>
      <td>s<sub>2</sub></td>
      <td>0.10</td>
      <td>0.09</td>
      <td>0.08</td>
      <td>33</td>
      <td>13</td>
      <td>32.5</td>
      <td>1.5</td>
      <td>6.25</td>
      <td>78</td>
      <td>2.30</td>
      <td>5.9</td>
    </tr>
    <tr>
      <td>s<sub>3</sub></td>
      <td>0.06</td>
      <td>0.07</td>
      <td>0.07</td>
      <td>19</td>
      <td>12</td>
      <td>30</td>
      <td>1.2</td>
      <td>5.88</td>
      <td>83</td>
      <td>1.50</td>
      <td>6.5</td>
    </tr>
    <tr>
      <td rowspan="3">t<sub>4</sub></td>
      <td>s<sub>1</sub></td>
      <td>0.08</td>
      <td>0.07</td>
      <td>0.05</td>
      <td>20</td>
      <td>10</td>
      <td>41.8</td>
      <td>1.2</td>
      <td>5.02</td>
      <td>82</td>
      <td>1.72</td>
      <td>5.6</td>
    </tr>
    <tr>
      <td>s<sub>2</sub></td>
      <td>0.09</td>
      <td>0.10</td>
      <td>0.09</td>
      <td>29</td>
      <td>14</td>
      <td>42.5</td>
      <td>1.3</td>
      <td>5.25</td>
      <td>76</td>
      <td>2.30</td>
      <td>4.7</td>
    </tr>
    <tr>
      <td>s<sub>3</sub></td>
      <td>0.08</td>
      <td>0.06</td>
      <td>0.08</td>
      <td>19</td>
      <td>10</td>
      <td>32</td>
      <td>1.1</td>
      <td>5.88</td>
      <td>84</td>
      <td>1.35</td>
      <td>5.8</td>
    </tr>
    <tr>
      <td rowspan="3">t<sub>5</sub></td>
      <td>s<sub>1</sub></td>
      <td>0.08</td>
      <td>0.07</td>
      <td>0.09</td>
      <td>25</td>
      <td>12</td>
      <td>58</td>
      <td>0.8</td>
      <td>4.84</td>
      <td>77.9</td>
      <td>1.19</td>
      <td>5.8</td>
    </tr>
    <tr>
      <td>s<sub>2</sub></td>
      <td>0.09</td>
      <td>0.07</td>
      <td>0.09</td>
      <td>24</td>
      <td>12</td>
      <td>59</td>
      <td>0.7</td>
      <td>5.04</td>
      <td>80</td>
      <td>1.98</td>
      <td>5.7</td>
    </tr>
    <tr>
      <td>s<sub>3</sub></td>
      <td>0.09</td>
      <td>0.08</td>
      <td>0.07</td>
      <td>25</td>
      <td>12</td>
      <td>60</td>
      <td>0.8</td>
      <td>5.84</td>
      <td>79</td>
      <td>1.28</td>
      <td>5.5</td>
    </tr>
  </tbody>
</table>

Firstly, standardize the data and use AHP to calculate the weights (normalized)

w (0.089,0.183,0.049,0.156,0.104,0.140,0.07,0.09,0.055,0.029 0.036)

Then we can get the weighted time series database $x_{ij}(t_k)$ by using Eq. (1). The
objective weight vector is calculated by Matlab based on Eq. (4)
w (0.113, 0.251, 0.081, 0.242, 0.177, 0.004, 0.055, 0.029, 0.004, 0.040, 0.004)

So we get $y_i(t_k)$ by using Eq. (5). Let $v$ (0.04,0.12,0.2,0.28,0.36) is obtained based on Eq. (6). The assessment results are shown in Table 4 by the expansion without affecting the ranking. From the results, we see $s_1$ is the optimal.

<table><caption>**Table 4.** Alternative value table</caption><thead><tr><th></th><th>t<sub>1</sub></th><th>t<sub>2</sub></th><th>t<sub>3</sub></th><th>t<sub>4</sub></th><th>t<sub>5</sub></th><th>Comprehensive value</th><th>Capability Ranking</th></tr></thead><tbody><tr><th>s<sub>1</sub></th><td>11.72</td><td>10.44</td><td>10.07</td><td>9.18</td><td>6.85</td><td>8.77</td><td>1</td></tr><tr><th>s<sub>2</sub></th><td>2.63</td><td>1.84</td><td>1.58</td><td>1.60</td><td>6.83</td><td>3.55</td><td>3</td></tr><tr><th>s<sub>3</sub></th><td>11.12</td><td>9.98</td><td>8.58</td><td>9.94</td><td>5.72</td><td>8.20</td><td>2</td></tr></tbody></table>

## 5.2 Results Analysis

1. The dynamic assessment method proposed considers both the references of decision makes and the impact of objective data. The weights at different time are consistent, so we can compare the capabilities of alternatives at the same time from the horizontal and get the capability trends with time from the vertical. The capabilities of three alternatives are shown in Fig.2. We can know that $s_1$ is on the decline but it is optimal overall. $s_2$ improves much at $t_5$. Finding out the possible causes of the improvement can provide guidance for improving capability.

2. The proposed dynamic assessment method is based on the time series data. If the data are updated, the weights change correspondingly. So it effectively follows the dynamics of manufacturing process. The weight vector of each time can be calculated by Matlab within seconds for one time, so it has less computation.

3. From $w$, we can know $x_2$ and $x_4$ are the key factors of capability. More attention should be attached to them to improve the sustainable manufacturing capability.

4. The time-value factor can affect the comprehensive assessment value. Take as 0, 0.2, 0.4, 0.6, 0.8, and 1 respectively, the corresponding capabilities are shown in Fig.3. How to adjust the time-value coefficients to forecast the capability of machining system at next time is the next research content.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Trend of capability for alternatives</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** The capabilities of different</figcaption></figure>
# 6 Conclusion

This paper focuses on the dynamic assessment of sustainable manufacturing capability for CNC machining systems. A set of indicators system is established from quality, time, cost, resource consumption and environmental impacts. Then a dynamic assessment method based on “vertical and horizontal” method and AHP considering “time-value coefficients” is proposed to assess the capability dynamically and effectively. Its application in a case study verified its advantages and effectiveness. The dynamic assessment model is also applicable to other dynamic decision making problems, such as economic decision-making, performance assessment of systems, etc.

# Acknowledgements

This research is supported by National Natural Science Foundation of China (Grant No. 51305319), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120143110017), and the Key Project of Natural Science Foundation of Hubei Province of China (Grant No. 2013CFA044).

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