A university library5 must cut annual subscription expenses sj to some or all scientific journals j = 1,

c, 40 to absorb a $5000 per year budget cut. One consideration will be the sum of published counts cj of the number of times other journals cite papers in journal j, which is a measure of how seminal a journal is to research. Another is the sum of usefulness ratings rj11 = low to 10 = high2 solicited from university faculty. Finally, the library wants to consider the sum of ratings aj of the relative availability 11 = low to 8 = high2 in nearby libraries, believing that journals readily available elsewhere need not be retained.

(a) Formulate a multiobjective ILP to choose journals to drop.

(b) Convert your multiobjective model to a goal program with targets at most C for total citations, at most R for total faculty ratings, and at least A for total availability ratings. Weight all goals equally.