On greedy approximation algorithms for a class of two-stage stochastic assignment problems

Abstract

In this paper we consider the two-stage stochastic linear assignment (2SSLA) problem, which is a stochastic extension of the classical deterministic linear assignment problem. For each agent and job, the decision maker has to decide whether to make assignments now or to wait for the second stage. Assignments of agents and jobs, for which decisions are delayed to the second stage, are then completed based on the scenario realized. We discuss two greedy approximation algorithms from the literature and derive a simple necessary optimality condition that generalizes the key ideas behind both of these approaches. Subsequently, based on this result we design a new greedy approximation method. Theoretical observations and the results of computational experiments are also presented.