Optimal Policies for the Sequential Stochastic Threshold Assignment Problem

Abstract

The Stochastic Sequential Threshold Assignment Problem (SSTAP) addresses the optimal assignment of arriving tasks (jobs) to available resources (workers) to maximize a reward function which consists of indicator functions that incorporate threshold constraints. We present an optimal assignment policy for SSTAP, independent of the probability distribution of the job values and of the number of arriving jobs. We show through an example that this type of reward function can model aviation security problems. We analyze the performance limitations of systems that use the SSTAP optimal assignment policy. Finally, we study the multiple levels SSTAP and the SSTAP with uncertainties in workers performance rates.