Heuristics for the stochastic dynamic task-resource allocation problem with retry opportunities

This paper deals with a stochastic multi-period task-resource allocation problem. A team of agents with a set of resources is to be deployed on a multi-period mission with the goal to successfully complete as many tasks as possible. The success probability of an agent assigned to a task depends on the resources available to the agent. Unsuccessful tasks can be tried again at later periods. While the problem can in principle be solved by dynamic programming, in practice this is computationally prohibitive except for tiny problem sizes. To be able to tackle also larger problems, we propose a construction heuristic that assigns agents and resources to tasks sequentially, based on the estimated marginal utility. Based on this heuristic, we furthermore propose various Approximate Dynamic Programming approaches and an Evolutionary Algorithm. All suggested approaches are empirically compared on a number of randomly generated problem instances. We show that the construction heuristic is very fast and provides good results. For even better results, at the expense of longer computational time, Approximate Dynamic Programming seems a suitable alternative.