Proceedings of the 2019 Winter Simulation Conference
N. Mustafee, K.-H.G. Bae, S. Lazarova-Molnar, M. Rabe, C. Szabo, P. Haas, and Y.-J. Son, eds.
A NUMERICAL STUDY ON THE STRUCTURE OF OPTIMAL PREVENTIVE
MAINTENANCE POLICIES IN PROTOTYPE TANDEM QUEUES
Taehyung Kim
James R. Morrison
Department of Industrial and System Engineering
Korea Advanced Institute of Science and Technology
291 Daehak-ro, Yuseong-gu
Daejeon, 34141, SOUTH KOREA
ABSTRACT
While high levels of automation in modern manufacturing systems increase the reliability of production,
tool failure and preventive maintenance (PM) events remain a significant source of production variability.
It is well known for production systems, such as the M/G/1 queue, that optimal PM policies possess a
threshold structure. Much less is known for networks of queues. Here we consider the prototypical tandem
queue consisting of two exponential servers in series subject to health deterioration leading to failure and
repair. We model the PM decision problem as a Markov decision process (MDP) with a discounted infinite-
horizon cost. We conduct numerical studies to assess the structure of optimal policies. Simulation is used
to assess the value of the optimal PM policy relative to the use of a PM policy derived by considering each
queue in isolation. Our simulation studies demonstrate that the mean cycle time and discounted operating
costs are 10% superior.
1 INTRODUCTION
1.1 Overview
While high levels of automation in modern manufacturing systems increase the reliability of production,
tool failure and preventive maintenance (PM) events remain a significant source of production variability.
It is well known for production systems, such as the M/G/1 queue, under certain assumptions and subject
to tool failures, repairs, and PMs, that optimal PM policies possess a threshold structure. Much less is
known for queues in tandem, or more generally, networks of queues. Here we consider the prototypical
tandem queue consisting of two exponential servers in series subject to deterioration in health, failure, and
repair and numerically explore the structure of optimal policies in this system.
1.2 Literature Review
Much of the research on PM policies has concentrated on non-production systems or has taken an isolated
view of the production equipment. When production systems are considered, there are two general
categories of work: production systems that build into an inventory and queueing systems. We will briefly
discuss equipment, inventory, and queueing systems next, with an eye toward motivating our work.
PMs are essential for efficient machine operation and much work has been devoted to the study of PM
policies, c.f. (Sim and Endrenyi 1988; Nicolai and Dekker 2008; Moghaddan and Usher 2011). Applications
include manufacturing equipment (cf. Laggoune et al. (2009)), windmills (cf. Krishna (2012)), and trucks
(cf. Barde et al. (2016)). Often, a PM policy to maximize the mean availability is sought. Alternately, the
cost of maintaining the machine may be pursued by considering failure costs, repair costs, and maintenance
costs. Recent examples in this vein of work include Barde et al. (2016) and Barde et al. (2019) which focus
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