54
4 Sefficiency (Sustainable Efficiency)
C1 =
C
I
, R1 =
R
I
, C1 + R1 = 1
W C1 =
W dC
W d I
, W R1 =
W d R
W d I
, d = b, q, s
(4.14)
C1 is Consumption fraction, R1 is Return fraction, WC1 is desirable Consumption
fraction, and WR1 is desirable Return fraction. For example, if d = b, WC1 is
beneficial Consumption fraction. Applying Eq. (4.14) to Eq. (4.8), we get Eq. (4.15).
S E =
W C1 ∗ C1 + ic ∗ W R1 ∗ R1
1 − (1 − ic) ∗ W R1 ∗ R1
, ic = {0, 1}
(4.15)
Equation (4.15) and C1 + R1 = 1 form a 4D problem: C1 or R1, WC1, WR1 and
SE (for d = b, we should use the symbol SE b ). This is still difficult to visualize, but
keeping one of the variables constant, contour lines of iSE and cSE can be shown as
in Figs. 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16 and 4.17 (MatLab
(MathWorks 2018) was used, with special thanks to Rui M.S. Pereira). These figures
give trade-offs and patterns between the variables.
Fig. 4.6 Contour lines of WR1-WC1-iSE trade-offs and patterns along four C1 values
4 Sefficiency (Sustainable Efficiency)
C1 =
C
I
, R1 =
R
I
, C1 + R1 = 1
W C1 =
W dC
W d I
, W R1 =
W d R
W d I
, d = b, q, s
(4.14)
C1 is Consumption fraction, R1 is Return fraction, WC1 is desirable Consumption
fraction, and WR1 is desirable Return fraction. For example, if d = b, WC1 is
beneficial Consumption fraction. Applying Eq. (4.14) to Eq. (4.8), we get Eq. (4.15).
S E =
W C1 ∗ C1 + ic ∗ W R1 ∗ R1
1 − (1 − ic) ∗ W R1 ∗ R1
, ic = {0, 1}
(4.15)
Equation (4.15) and C1 + R1 = 1 form a 4D problem: C1 or R1, WC1, WR1 and
SE (for d = b, we should use the symbol SE b ). This is still difficult to visualize, but
keeping one of the variables constant, contour lines of iSE and cSE can be shown as
in Figs. 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16 and 4.17 (MatLab
(MathWorks 2018) was used, with special thanks to Rui M.S. Pereira). These figures
give trade-offs and patterns between the variables.
Fig. 4.6 Contour lines of WR1-WC1-iSE trade-offs and patterns along four C1 values