$1\mathrm{.}1$ Choosing a computer ${?}^1$

You are going to enter next year the Master cycle of

your business school and you need to buy a new

computer.

Your academic needs are mostly office$-$related, but

you also wish to use your computer for multimedia

tasks $($photo$,$ video and audio editing, among other

things$)$

After doing some research, and with the help of

reviews published in technical journals as well as

opinions collected, you have selected a short$-$list of

four computer models.

The characteristics considered are price, ease$-$of$-$use

$($measured by the size of the screen$)$ and multimedia

use. For this last item, a score ranging from $1$ to $5$ was

assigned to each machine, using the following scale:

The description of the selected computers,

according to these criteria, is given in the table

below:

You wish to:

minimize the price,

maximize ease$-$of$-$use $($largest possible screen

size$),$ and:

Maximize suitability for multimedia use

$($highest rating$)$

Establish a table presenting the utilities of

the $4$ alternatives considered, for each of the

three objectives: price, screen size and

multimedia use.

You will use the following acceptable ranges

for the attributes:

Price: you accept to pay a price between

$350$ and $850$

Screen: between $13$ and $18$ inches

MM suitability rating: $1$ to $5$

Using these ranges, the worst value of the

attribute corresponds to the utility level $0$

and the best to the utility level $1.$ Between

these two extremes, the utility varies

proportionally to the attribute's value.

At first, you do not feel able to assign a well$-$

defined importance score to each criterion.

You only know that the most important thing for

you is the price, then the ease of use $($measured

by the screen size$)$ and finally the multimedia

use.

Your objectives are therefore as follows, in order

of decreasing importance:

Minimize the price,

Maximize ease of use $($largest possible screen

size$)$

Maximize suitability for multimedia use

$($highest rating$).$

Use the SMARTER method to evaluate the weight

of each objective in the overall utility function.

Show your calculation table.

Calculate, using these weights, the overall utility

of each computer. Briefly explain the calculation.

Show these global utilities What is your

conclusion?

You consider now that the objective weights are

proportional to the following "importance

scores":

Compute again the objective weights and the

global utility of each computer. Do these new

elements modify your choice?