How Grey Relational Analysis Optimizes Coal Mine Management Evaluation

Case Study

This example explains the grey comprehensive evaluation method using the assessment of a coal‑enterprise's management level.

Many factors affect production, making it difficult to evaluate coal‑mine management. Accurately assessing each mine’s management level and the gaps between them helps improve individual mine management and provides reliable bases for corporate assessments. Common methods include qualitative analysis, single‑indicator comparison, multi‑objective analysis, and fuzzy comprehensive evaluation, but most cannot reflect the overall situation and are cumbersome to compute. Grey relational analysis overcomes these shortcomings by converting incomparable indicators into comparable ones, especially effective for multi‑indicator systems.

Selection of the coal‑mine management indicator system For multi‑indicator evaluation, comparable mines are selected and common indicators are analyzed to judge management levels. The indicator system must reflect the actual situation of the evaluated mines. Six indicators representing coal‑mine production characteristics are chosen:

Production: percentage of planned production achieved (higher is better).

Advancement: percentage of planned advance length achieved (higher is better).

Labor efficiency: percentage of planned overall employee efficiency achieved (higher is better).

Quality: planned ash content set to 100; lower actual ash content is better.

Cost: planned cost per ton of coal set to 100; lower actual cost is better.

Safety: planned accident rate set to 100; lower actual accident rate is better.

The weights for these six indicators follow the order of appearance.

Evaluation data A mining bureau has five pairs of mines; the year‑end assessment data for each mine are listed in the table below.

Indicator calculation Construct an ideal object by taking the best value of each indicator among the evaluated objects. For different factors, some indicators are better when larger, others when smaller; the ideal values serve as the reference.

Only the weighted relational degree between one mine and the ideal object is shown as an example.

(1) Calculate the relational coefficient for each indicator.

(2) Calculate the weighted relational degree.

Using the same method, weighted relational degrees for the other mines can be computed.

Based on these degrees, a ranking sequence is established.

Step Summary

The specific steps of grey relational analysis are:

(1) Determine the comparison series (evaluation objects) and the reference series (evaluation standards). Let there be n evaluation objects and m indicators.

Reference series:

(2) Determine the weight of each indicator, which can be obtained by methods such as Analytic Hierarchy Process.

Here, w_j denotes the weight of the j ‑th indicator.

(3) Compute the grey relational coefficient.

The coefficient measures the relative difference between the comparison and reference series for each indicator.

(4) Compute the grey weighted relational degree using the formula:

where γ_i is the grey weighted relational degree of the i ‑th evaluation object to the ideal object.

(5) Evaluation analysis: rank the evaluation objects according to their grey weighted relational degrees; a larger degree indicates better performance.

Reference:

"Modern Comprehensive Evaluation Methods and Selected Cases" by Du Dong, Pang Qinghua, Wu Yan.