The optimum method ASSUMING honest voting is each professor provides his utility for each office (in some common units like dollars) and the max-utility permutation is chosen. If N professors N offices this is NxN matrix of utilities as input.
And no, this is not NP-hard, it is polynomial time, in fact it is the "maximum weighted bipartite matching problem" also called the "assignment problem" and efficiently soluble by e.g, the "Hungarian method." However... in practice we could not rely on honest voting nor on assessment of utilities in common units. If the "utilities" were, in fact, dollar values which actually had to be paid by the professors out of their salary or something, then that'd force a certain amount of honesty upon them (since they'd have to pay, they could not submit a bid for a gazillion trillion dollars) and the Hungarian algorithm would also garner the max money for the university, both of which would be good. Voting would however be pretty painful, need to price every single office. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
