Using a pseudo-stochastic approach for multiple-parts scheduling on an unreliable machine

In this paper we follow previous "pseudo-stochastic" approaches that solve stochastic control problems by using deterministic optimal control methods. In a similar manner to the certainty equivalence principle, the suggested model maximizes a given profit function of the expected system outcome. However, unlike the certainty equivalence principle, we model the expected influences of all future events (including those that are expected beyond the planning horizon), as encapsulated by their density functions and not only by their mean values. The model is applied to the optimal scheduling of multiple part-types on a single machine that is subject to random failures and repairs. The objective of the scheduler is to maximize the profit function of the produced multiple-part mix. A numerical study is performed to evaluate the suggested pseudo-stochastic solutions under various conditions. These solutions are compared to a profit upper bound of the stochastic optimal control solutions.