Dynamic scheduling of manufacturing systems with setups and random disruptions

Abstract

Manufacturing systems are often composed of machines that can produce a variety of items but that most undergo time-consuming (and possibly costly) setups when switching between product types. Scheduling these setups efficiently can have important economic effects on the performance of the plant and involves a tradeoff between throughput, inventory, and operating costs. In addition, the schedule must be robust to random disruptions such as failures or raw material shortages, which are common in production environments. In this thesis, we study policies that address the setup scheduling problem dynamically, in response to current conditions in the system. A new heuristic, called the Hedging Zone Policy (HZP), is introduced and developed. It is a dynamic-sequence policy that always produces the current part type at its maximum production rate until a fixed base stock level is reached. Then, before switching setups, the policy might produce the current part type at its demand rate for some additional time. When selecting changeovers, the HZP implements two types of decision rules. If the difference between base stock and surplus level is small for all part types, the item with the largest weighted difference is selected. Otherwise, the policy uses a fixed priority ranking to select between items that are far from their base stock value. In order to demonstrate the benefits of our policy, we also adapt and implement several other heuristics that have been proposed in the literature for related models. The policies are first analyzed in a purely deterministic setting. The stability of the HZP is addressed and it is shown that a poor selection of its parameters leads to a condition in which some low-priority parts are ignored, resulting in an unstable system. Using Lyapunov's direct method, we obtain an easy-to-evaluate and not-too-conservative condition that ensures production of all part types with bounded surplus. We then compare, through a series of extensive numerical experiments with three-part-type systems, the deterministic performance of the policies in both make-to-order and make-to-stock settings. We show that the HZP outperforms other policies within its class in both cases, a fact that is mainly attributed to its priority-based decisions. When compared to the approximate optimal cost of the problem, our policy performs very well in the make-to-order case, while the simplicity of its base stock structure makes it less competitive in the deterministic make-to-stock problem. The results are then leveraged for the study of a stochastic model, where we consider the effect of random disruptions in the form of machine failures. We prove that our model converges to a fluid limit under an appropriate scaling. This fact allows us to employ our deterministic stability conditions to verify the stochastic (rate) stability of the failure-prone system. We also extend our previous numerical experiments by characterizing the performance of the policies in the stochastic setting. The results show that the HZP still outperforms other policies in the same class. Furthermore, we find that except for cases where failures occur much less or much more frequently than changeovers, the HZP outperforms a fixed-sequence policy that is designed to track a pre-determined, near-optimal deterministic schedule.