In this paper, we propose an approximate policy iteration (API) algorithm for asemiconductor fab-level decision making problem. This problem is formulated as adiscounted cost Markov Decision Process (MDP), and we have applied exact policy iterationto solve a simple example in prior work. However, the overwhelmingcomputational requirements of exact policy iteration prevent its application forlarger problems. Approximate policy iteration overcomes this obstacle by approximating thecost-to-go using function approximation. Numerical simulation on the same example showsthat the proposed API algorithm leads to a policy with cost close to that of the optimalpolicy.