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We study the scheduling of production in a multi-item, failure-prone machine with setup times, with the objective of minimising long-run average inventory and backlog costs. We make two contributions to this problem, which has received significantly less attention compared to the standard stochastic economic lot scheduling problem (with random demand and production times). First, we adapt and implement a variety of existing scheduling policies and compare their performance through a set of numerical experiments spanning a wide range of operating conditions. This analysis allows us to identify important shortcomings of the policies, including their poor performance when items have widely different priorities (as dictated by the product of their cost and production rate parameters). Second, we leverage these insights to develop and analyse a new, easy-to-implement policy. This policy tightly controls the surplus of the highest-priority items using fixed base-stock levels and, for all other items, it determines their run lengths dynamically in such a way that long production runs become decreasingly likely with decreasing item priority. Our experiments show that our new policy greatly outperforms the benchmarking policies over a large and important set of operating regimes, comprising high-utilisation systems where the machine cycles through all items at a frequency comparable to or greater than the frequency of failure events.

Dynamic scheduling in make-to-stock production systems with setup times and random breakdowns: performance analysis and improved policies