A solution of the lot sizing problem as a stochastic resource contention game

We present a new way to solve the “lot sizing” problem viewed as a stochastic non-cooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem with no constraints on the distributional characteristics of the random processes in the system. We then use Infinitesimal Perturbation Analysis (IPA) methods and derive an on-line gradient-based algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective and observe that, uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results.