Question $3[20$ points$]$: A manager of a plastic manufacturing facility is not sure what material handling equipment he should use in the production line. If you know that he needs to move materials in large quantities and with different sizes and weights, and that movement can be done in batches. An industrial engineer proposed using AHP to help the manager examine which material handling equipment they should use for their manufacturing needs. This engineer collected the following tables for you.

Table $1.$ Weights of the different selection criteria

$\backslash$table$[[,$Capital Cost,O&M ${?}^{+},$Lifetime,Flexibility$],[$Capital Cost,$1,\frac{1}{2},3,5],[$O&M$,2,1,2,7],[$Lifetime$,\frac{1}{3},\frac{1}{2},1,3],[$Flexibility$,\frac{1}{5},\frac{1}{7},\frac{1}{3},1]]$

Operations & Maintenance

Table $2.$ Relative rank for each of the MHE vs selection criteria

$\backslash$table$[[,$Capital cost,$\backslash$table$[[$Operations and$],[$maintenance cost$]],$Lifetime,Flexibility$],[$Conveyer belt,$6,6,6,2],[$Forklift$,2,3,8,7],[$Dolly$/$cart$,9,9,4,9],[$Automated guided vehicle,$5,6,5,5]]$

$($a$)$ Develop a complete AHP method and show all calculations and final results.

$($b$)$ Prepare the required tables for alternatives $($MHE$)$ vs$.$ selection criteria

$($c$)$ What MHE do you recommend for this facility

$($d$)$ List pros and cons of the first $2$ alternatives $($MHE$)$ you recommend to this manufacturing facility