Approximate policy iteration for dynamic resource-constrained project scheduling

We study non-preemptive scheduling problems where heterogeneous projects stochastically arrive over time. The projects include precedence-constrained tasks that require multiple resources. Incomplete projects are held in queues. When a queue is full, an arriving project must be rejected. The goal is to choose which tasks to start in each time-slot to maximize the infinite-horizon discounted expected profit. We provide a weakly coupled Markov decision process (MDP) formulation and apply a simulation-based approximate policy iteration method. Extensive numerical results are presented.