Question $4.$ Read the article A Preference Ranking Organisation Method $($Brans and

Vincke, $1985).$ For the delivery provider selection problem described in Question $3$ of

Homework $1,$ apply the PROMETHEE I method for the $5$ Nondominated Alter$-$

natives, namely $1,2,4,5,$ and $8,$ for four criteria cost, quality, delivery time and $C{O}_2$

emission. Use the weight vector $(w_c,w_q,w_d,w_{c{o}_2})$ where

$w_c=0\mathrm{.}135$

$w_q=0\mathrm{.}192$

$w_d=0\mathrm{.}547$

$w_{c{o}_2}=0\mathrm{.}126$

Question $3.$ Assume you are to select a new delivery provider for your com$-$

pany among a list of given ones. The management wants you to pay attention

to four criteria among many others: expected average costs per product unit,

service quality $($the higher the quality, the less likely the products are to have

defects when they reach the customers$),$ expected order delivery time given

in days, and average carbon emissions $($amount of $C{O}_2$ emitted per kilometer

$k\frac{g}{k}m)$ reported by the delivery firm. The list of $8$ delivery contract offers

is given in the table below.