Page 92 - Advances In Productive, Safe, and Responsible Coal Mining

Optimization of coal recovery and production rate as a function of panel dimensions 77

and matrices that correspond to Eq. (5.4). In this case, MATLAB functions were writ-
ten to take input (e.g., number of strips, number of panel widths under consideration
and their widths, and production rates for each panel width from DES) and convert the
model (Eq. 5.2) into equivalent matrices and vectors in Eq. (5.4). This approach is
adequate for small problems where the number of strips is few and the number of pos-
sible cutting patterns is not prohibitively high:

T
min c x
Ax b
A eq x ¼ b eq (5.4)
l x u
x is an integer

In the case study problem where there are many strips and panel widths are small rel-
ative to the width of strips (i.e., there are many possible patterns to consider), the lit-
erature shows that the solution approach used will be computationally expensive [11,
13]. In such instances, the branch-and-price algorithm, which only incorporates a few
patterns at a time and generates additional columns as the solution progresses, has
been shown to be more promising [14]. Future work should focus on developing
branch-and-price algorithms to solve the coal recovery problem. This will require
finding means to perform the Dantzig-Wolfe decomposition of the linear program-
ming relaxation of the problem. If successful, this line of research will ensure that real-
istic instances of the problem (Eq. 5.2) with many strips can be solved in reasonable
time making this approach much more useful for mine planning and design.

5.3.3 Case study

To illustrate the coal recovery optimization problem, a case study with 10 strips is
used. Table 5.3 shows strip widths, panel widths, and production indexes. The situa-
tion where all six panel widths in the simulation experiments are considered to be fea-
sible is taken into account. This may not necessarily be the case in a real application.
Engineers and managers may want to limit the number of panel widths used in the
mine so that production practices do not vary significantly. This will actually make
the problem easier to solve as there will be fewer feasible patterns. In this case study,
it was assumed that all barrier pillars are 80ft. wide regardless of panel width. The
problem is solved for η¼0.05, 0.10, 0.15, 0.30, 1.00.
Table 5.4 shows optimization results for the case study. These solutions show that
the model works as intended and can be useful for mine engineers and managers dur-
ing R&P mine planning.
Based on the sensitivity of the result to η, it can be concluded that the model truly
behaves as a dual-objective optimization model. The reader can observe that for
η 0.1, the 17-entry wide panel, which is the panel width with the highest production
rate, is the preferred panel width. It dominates the solution and is to be used on every
strip and is used exclusively to mine strips 9 and 10. These solutions obviously pri-
oritize production rate and only use other panel widths when one with a higher