x_{\imath} = \min_{i \in \{ 1,\ldots,m \}} 
\bar{b}_i / \bar{a}_{\jmath^k,i},   
\hspace{0.1in}  \mbox{subject to}  
\hspace{0.1in} \bar{a}_{\jmath^k,i}>0.
\label{outVar}\end{aligned}$$ The corresponding step-size is given by $$\begin{aligned}
\min_{i \in  \{ 1,\ldots,m \}} 
\bar{b}_i / \bar{a}_{\jmath^k,i},  
\hspace{0.1in} \mbox{subject to}
\hspace{0.1in}  \bar{a}_{\jmath^k,i}>0  .
\label{stepsize}\end{aligned}$$

As we pointed out above, our strategy is to select, in a deterministic way, two entering variables from the set of non-basic variables that will reduce the objective function. According to some extensive computational experience, for example [@ps14], Dantzig’s rule is the most efficient on average among all popular pivot rules (even though Dantzig’s rule needs exponentially many pivots to find the optimal solution for Klee-Minty cubes in the worst case), therefore, we select the first entering variable $x_{\jmath_1^k}$ using Dantzig’s rule: $${\jmath_1^k} :=\{ {\jmath_1^k} ~|~ \bar{c}_{\jmath_1^k} 
= \min_{j^k \in N^k} \bar{\c}_{j^k}  \}.
\label{enteringVar}$$ Kitahara and Mizuno [@km13] showed that the number of iterations in existing pivot rules is significantly affected by the minimum values of all the positive elements of primal basic feasible solutions. Carefully studying Klee-Minty cube and its variants [@greenberg97; @km11; @ibrahima13] indicates that the other entering variable should be determined by taking the variable among all $j^k \in N^k$ with $\bar{c}_{j^k}<0$ such that a particular $\jmath_2^k$ will maximize 