INE $317-$Multiple Criteria Decision Making

Hol$10,10$k $1$

$(3$questions$,100$pts$.$total$)$

Keeney and Raiffa $(1976)$discuss the assessment of a blood bank's multiattribute utility function. For simplicity, we assume that the blood bank must determine at the beginning of each week how many pints of blood should be ordered. Any blood left over at the end of the week spoils $($it is outdated$).$For the blood bank, two attributes of interest are as follows: Attribute $1$: Number of pints of blood by which ordered blood falls short of the week's demand $($the weekly shortage$).$The weekly shortage is known to be always between $0$and $10$pints$.$

Attribute $2$: Number of pints of blood that are outdated $($known to be always between $0$and $10$pints$).$Assume that attributes $1$and $2$are mutually utility independent $($mui$).$

Suppose the blood bank is indifferent between

Let x$1=$value of attribute $1,$and x$2=$value of attribute $2.$Also suppose that

u$1($x$1)=\mathrm{.}58$exp$(1-$x$110)-\mathrm{.}58$

and

u$2($x$2)=1-$x$22100$

a$.$Determine the blood bank's multiattribute utility function. $(20$pts$.)$

b$.$Suppose that each week there is a $0\mathrm{.}5$chance that the demand for blood will be $25$pints and a $0\mathrm{.}5$chance it will be $35$pints$.$ Would the blood bank be better off ordering $28$pints$,30$pints$,$ or $32$pints$?(10$pts$.)$