Table 2 . Features and performance of three models.

Optimal time

\(\frac{\left(1-b\right)\left(h-{\tau }_{0}\right)-\lambda (s{t}_{1}+c)}{\lambda (h-s)}\)

\(\frac{\lambda ({\omega }_{{\rm {l}}}-c-\left({s-\tau }_{0}\right){t}_{1})}{(1-\lambda )({s-\tau }_{0})}\)

\(\frac{{\lambda }^{2}{t}_{1}}{1-\lambda }\)

Optimal wholesale price

\(\frac{\lambda h\left(c+s{t}_{1}-{\tau }_{0}{t}_{1}\right)+\left(h-{\tau }_{0}\right)\left[{\tau }_{0}\left(1-b\right)+{bs}-h\right]-\lambda c{\tau }_{0}}{\lambda (h-s)}\)

–

–

Optimal price of PC

\(\frac{{b}^{2}({\tau }_{0}-h)}{\lambda (b-1)}\)

\(\frac{b}{b-1}({\omega }_{{\rm {l}}}+{\tau }_{0}{t}_{1}+\frac{\lambda ({h-\tau }_{0})({\omega }_{{\rm {l}}}-c-\left({s-\tau }_{0}\right){t}_{1})}{(1-\lambda )({s-\tau }_{0})})\)

\(\frac{b}{b-1}({\omega }_{{\rm {l}}}+{\lambda }^{2}h{t}_{1}-s{t}_{1}+\frac{{\omega }_{{\rm {l}}}-c}{1-\lambda })\)

Optimal amount of crashing cost shared

–

–

\(s-\frac{{\omega }_{\rm {{l}}}-c}{(1-\lambda ){t}_{1}}\)