Table 2.

Summary of Parameter Regions.

Conditions			Region and the relationship of optimal decisions
Low demand variability $1<\frac{{\theta }_h}{{\theta }_l}⩽1+\sqrt{2}$	${\theta }_h/{\theta }_l<1+\sqrt{2}$ and $c<{\stackrel{\sim }{c}}^{\mathit{KB}}$		Region I $0<q_l^{\mathit{KB}}<q_h^{\mathit{KB}}=q_b^{\mathit{KB}}$
	${\theta }_h/{\theta }_l<1+\sqrt{2}$ and ${\stackrel{\sim }{c}}^{\mathit{KB}}<c⩽{\stackrel{\sim }{\stackrel{\sim }{c}}}^{\mathit{KB}}$		Region II $0<q_l^{\mathit{KB}}<q_b^{\mathit{KB}}<q_h^{\mathit{KB}}$
	${\theta }_h/{\theta }_l<(1+\sqrt{5})/2$ and ${\stackrel{\sim }{\stackrel{\sim }{c}}}^{\mathit{KB}}<c⩽{\stackrel{\sim }{\stackrel{\sim }{\stackrel{\sim }{c}}}}^{\mathit{KB}}$	${\theta }_h/{\theta }_l>(1+\sqrt{5})/2$ and ${\stackrel{\sim }{\stackrel{\sim }{c}}}^{\mathit{KB}}<c$	Region III $0<q_l^{\mathit{KB}}=q_b^{\mathit{KB}}<q_h^{\mathit{KB}}$	Region V $0=q_l^{\mathit{KB}}<q_h^{\mathit{KB}}=q_b^{\mathit{KB}}$
	${\theta }_h/{\theta }_l<(1+\sqrt{5})/2$ and ${\stackrel{\sim }{\stackrel{\sim }{\stackrel{\sim }{c}}}}^{\mathit{KB}}<c$		Region IV $0<q_b^{\mathit{KB}}<q_l^{\mathit{KB}}<q_h^{\mathit{KB}}$
High demand variability $\frac{{\theta }_h}{{\theta }_l}>1+\sqrt{2}$	$0<c$		Region V $0=q_l^{\mathit{KB}}<q_h^{\mathit{KB}}=q_b^{\mathit{KB}}$

Note:${\stackrel{\sim }{c}}^{\mathit{KB}}=\left\{\begin{array}{c}{c}^{\prime }if\text{0}<z⩽{\stackrel{\sim }{z}}^{\mathit{KB}}\\ \frac{{\theta }_h+{\theta }_l}{2\left(2+z\right){\theta }_h-2{\theta }_l}if{\stackrel{\sim }{z}}^{\mathit{KB}}<z<1\end{array}\right)$,${\stackrel{\sim }{\stackrel{\sim }{c}}}^{\mathit{KB}}=\left\{\begin{array}{c}{c}^{\prime }if\text{0}<z⩽{\stackrel{\sim }{z}}^{\mathit{KB}}\\ c^{″}if{\stackrel{\sim }{z}}^{\mathit{KB}}<z⩽{\stackrel{\sim }{\stackrel{\sim }{z}}}^{\mathit{KB}}\\ \frac{{\theta }_l}{2({\theta }_h-{\theta }_l)}if{\stackrel{\sim }{\stackrel{\sim }{z}}}^{\mathit{KB}}<z<1\end{array}\right)$,${\stackrel{\sim }{\stackrel{\sim }{\stackrel{\sim }{c}}}}^{\mathit{KB}}=\frac{z{\theta }_h+\left(2-z\right){\theta }_l}{z\left(3{\theta }_l-{\theta }_h\right)}$.