  Attributes provide critical information about the alternatives that a
decision-maker is considering. When their magnitudes are uncertain, the
decision-maker may be unsure about which alternative is truly the best, so
measuring the attributes may help the decision-maker make a better decision.
This paper considers settings in which each measurement yields one sample of
one attribute for one alternative. When given a fixed number of samples to
collect, the decision-maker must determine which samples to obtain, make the
measurements, update prior beliefs about the attribute magnitudes, and then
select an alternative. This paper presents the sample allocation problem for
multiple attribute selection decisions and proposes two sequential, lookahead
procedures for the case in which discrete distributions are used to model the
uncertain attribute magnitudes. The two procedures are similar but reflect
different quality measures (and loss functions), which motivate different
decision rules: (1) select the alternative with the greatest expected utility
and (2) select the alternative that is most likely to be the truly best
alternative. We conducted a simulation study to evaluate the performance of the
sequential procedures and hybrid procedures that first allocate some samples
using a uniform allocation procedure and then use the sequential, lookahead
procedure. The results indicate that the hybrid procedures are effective;
allocating many (but not all) of the initial samples with the uniform
allocation procedure not only reduces overall computational effort but also
selects alternatives that have lower average opportunity cost and are more
often truly best.
