Network flow approaches for an asset-task assignment problem with execution uncertainty

Abstract

We investigate the assignment of assets to tasks where each asset can potentially execute any of the tasks, but assets execute tasks with a probabilistic outcome of success. There is a cost associated with each possible assignment of an asset to a task, and if a task is not executed there is also a cost associated with the non-execution of the task. The objective is to make asset-task assignments to minimise the total expected cost. In [1], we showed that this is a nonlinear combinatorial optimisation problem and proposed a Random Neural Network (RNN) algorithm for its solution. In this paper we propose network flow algorithms which are based on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs.We introduce three different scheme for the estimation of the arc costs and we investigate their performance compared to RNN and greedy algorithms.