A bi-criteria multiple-choice secretary problem
This article studies a Bi-criteria Multiple-choice Secretary Problem (BMSP) with full information. A sequence of candidates arrive one at a time, with a two-dimensional attribute vector revealed upon arrival. A decision maker needs to select a total number of η candidates to fill η job openings, based on the attribute vectors of candidates. The objective of the decision maker is to maximize the expected sum of attribute values of selected candidates for both dimensions of the attribute vector. An approach for generating Pareto-optimal policies for BMSP is proposed using the weighted sum method. Moreover, closed-form expressions for values of both objective functions under Pareto-optimal policies for BMSP are provided to help a decision maker in the policy planning stage. These analysis techniques can be applied directly to solve the more general class of multi-criteria multiple-choice Secretary Problems, provided the objective functions are in the form of accumulating a product-form reward for each selected candidate.