We have K people, and B choices to allocate from for each person (imagine for eg one of B movies being given to each of K persons) - each person gets utility U_k_b (you know this number) for the k, b pair. There is a budget constraint C_b for every allocation such that number of people allocated to (movie) b can be only <= C_b. Sum of C_b > K (given). How would you find an optimal allocation?
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(I discovered that) This is a version of the assignment problem and can be solved using min cut - max flow methods.
piedpiper
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https://www.cs.yale.edu/homes/aspnes/pinewiki/MaxFlow.html - here is where i found it – piedpiper Oct 11 '21 at 12:53