Individual Assignment #$1$

$(5)$ A local authority has to decide on the location of a new waste$-$disposal facility and five sites are currently being considered: Inston Common, Jones Wood, Peterton, Red Beach and Treehome Valley. In order to help them choose between the sites, the managers involved in the decision arranged for a decision analyst to attend one of their meetings. He first got the managers to consider the factors which they thought were relevant to the decision and, after some debate, four factors were identified:

$($i$)$ The visual impact of the site on the local scenery $($for example, a site at Treehome Valley would be visible from a nearby beauty spot$).$

$($ii$)$ The ease with which waste could be transported to the site $($for example, Red Beach is only $2$ miles from the main town in the area and is close to a main highway, while Inston Common is in a remote spot and its use would lead to a major increase in the volume of transport using the minor roads in the area$).$

$($iii$)$ The risk that the use of the site would lead to contamination of the local environment $($e$.$g$.,$ because of leakages of chemicals into watercourses$).$

$($iv$)$ The cost of developing the site.

The decision analyst then asked the managers to assign scores to the sites to show how well they performed on each of the first three attributes. The scores they eventually agreed are shown below, together with the estimated cost of developing each site. Note that $0$ represents the worst and $100$ the best score on an attribute. In the case of risk, therefore, a score of $100$ means that a site is the least risky.

$\backslash$table$[[$Site$,$Benefit,Costs $($$ m$)],[\backslash$table$[[80\%$

Individual Assignment #$1$

$($c$)$ Assuming that mutual preference independence exists between the attributes, determine the value of aggregate benefits for each site.

$($d$)$ Plot the aggregate benefits and costs of each site on a graph and hence identify the sites which lie on the efficient frontier.

Benefits$($y$)$

$($e$)$ Although a weight of $80$ was finally agreed for visual impact, this was only after much debate and some managers still felt that a weight of $65$ should have been used while others thought that $95$ would have been more appropriate. Perform a sensitivity analysis on the weight assigned to visual impact to examine its effect on the aggregate benefits of the sites and interpret your results.