11 Economy-Wide Material Flow Analysis and Its Projection …
165
output materials on the DMI basis given in the form of I and M are computed in the
following equation.
I =
I j
(11.2)
M =
M k
(11.3)
Subsequently, S j is introduced as the specific TMR of each of input materials.
Based on the concept of Eq. (11.1), the total weight of input materials on the TMR
basis (T ) is obtained in the following equation.
T =
I j × S j
(11.4)
Since the total weight of input materials on the TMR basis is put on the shoulder of
all output materials, it has to be properly allocated to each output material to identify
the specific TMR. This study utilizes the monetary value of each output material
as an allocation method, since the value of commodity is a major driving force of
mining activities (Kosai et al. 2018). P k is introduced as an unit price of each output
material and the allocation rate (r k ) is obtained in the following equation.
r k =
M k × P k
(M k × P k )
(11.5)
The weight of each output material on the TMR basis (T k ) is obtained in the
following equation.
T k = (T − M ) × r k + M k
(11.6)
The specific TMR of each output material (S k ) is computed in the following
equation.
S k =
T k
M k
(11.7)
A set of process for obtaining specific TMR is applied to the 3rd classification.
After obtaining the weight on the DMI basis and the estimated specific TMR in each
of 3rd classifications, the weight on the TMR basis is obtained by using Eq. (11.1).
Subsequently, 1st and 2nd classification on both DMI and TMR basis is computed
in the form of DMI c and TMR c respectively.
DMI c =
c
x
M x
(11.8)
165
output materials on the DMI basis given in the form of I and M are computed in the
following equation.
I =
I j
(11.2)
M =
M k
(11.3)
Subsequently, S j is introduced as the specific TMR of each of input materials.
Based on the concept of Eq. (11.1), the total weight of input materials on the TMR
basis (T ) is obtained in the following equation.
T =
I j × S j
(11.4)
Since the total weight of input materials on the TMR basis is put on the shoulder of
all output materials, it has to be properly allocated to each output material to identify
the specific TMR. This study utilizes the monetary value of each output material
as an allocation method, since the value of commodity is a major driving force of
mining activities (Kosai et al. 2018). P k is introduced as an unit price of each output
material and the allocation rate (r k ) is obtained in the following equation.
r k =
M k × P k
(M k × P k )
(11.5)
The weight of each output material on the TMR basis (T k ) is obtained in the
following equation.
T k = (T − M ) × r k + M k
(11.6)
The specific TMR of each output material (S k ) is computed in the following
equation.
S k =
T k
M k
(11.7)
A set of process for obtaining specific TMR is applied to the 3rd classification.
After obtaining the weight on the DMI basis and the estimated specific TMR in each
of 3rd classifications, the weight on the TMR basis is obtained by using Eq. (11.1).
Subsequently, 1st and 2nd classification on both DMI and TMR basis is computed
in the form of DMI c and TMR c respectively.
DMI c =
c
x
M x
(11.8)