Candidate to Job Allocation Problem with a Lexicographic Objective

Allocation of candidates to jobs is required in a situation where each candidate can only be allocated to certain jobs, and every job's "length" decreases as more candidates are allocated to it. The objective is to minimize the "ranked length vector," which is derived by arranging the job-lengths in nonincreasing order, in the lexicographic sense. Necessary and sufficient conditions for optimality are derived, and an algorithm for obtaining optimal allocations is presented, along with computational experience.