Optimal Policies for the Sequential Stochastic Threshold Assignment Problem

TL;DR

This paper introduces an optimal assignment policy for the stochastic sequential threshold assignment problem, applicable regardless of job value distributions, with implications for aviation security and performance analysis.

Contribution

It presents a distribution-independent optimal policy for SSTAP and extends analysis to multiple levels and uncertain worker performance scenarios.

Findings

Optimal policy is independent of job value distribution.

Application demonstrated in aviation security modeling.

Performance limitations of SSTAP systems analyzed.

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.