Table 2 Overview of all implemented modeling approaches to considering equality, as well as the two extreme solutions and their corresponding theoretical parameter values, which we did not apply in practice

Cost-optimal

Equation 1 (LP)

–

–

Reference: cost-optimal solution without considering equality representing utilitarian extreme

\({c}^{\text{eq}}=0\)

\(d\to \infty\)

Equal

Equation 1 (LP)

K + 1

2 K + 1

Reference: solution with equal regional CPU as the egalitarian extreme

\({c}^{\text{eq}}\to \infty\)

\(d=0\)

Min var

Equation 1 + Eq. 16 (QP)

K + 1

K + 1

Co-minimization of the variance of regions’ CPU and total system costs

\({c}^{\text{eq}}\in [{10}^{9}, {10}^{12}]\)

Lim d

Equation 1 (LP)

K + 1

3 K + 1

Limit the deviation of regions’ CPU

\(d\in [0.05, 3]\)