nI the permutation flow shop each machine processes the jobs ni the same order. For the F$2||$R $($two$-$machine flowshop problem where the objective si a regular measure$)$ there exists an optimal permutation schedule. In general, however the permutation schedule need not be

optimal. For the folowing instance of the F$4||$Cuax problem with n$=2$jobs, the processing times are given as folows: Machines $1234|$

Job$1414$ Job $21441$

$1.$Can the jobs have adifferent sequence on the first two machines? Why$/$Why not?

$\mathrm{.}2$ Construct wt o permutation schedules S$,$ and S$,$ and compute their makespan $($Cmax$).$

$\mathrm{.}3$Construct anon$-$permutation schedule Sy such that Cmax $($Ss$)$ si les htan Cmax $($Sy$)$ and Cmax $($S$>=).$