Single-Machine Multiple-Recipe Predictive Maintenance

Abstract

This paper studies a multiple-recipe predictive maintenance problem with M/G/1 queueing eects. The server degrades according to a discrete-time Markov chain and we assume that the controller knows both the machine status and the current number of jobs in the system. The controller's objective is to minimize total discounted costs or long-run average costs which include preventative and corrective maintenance costs, holdings costs, and possibly production costs. An optimal policy determines both when to perform maintenance and which type of job to process. Since the policy takes into account the machine's degradation status, such control decisions are known as predictive maintenance policies. In the single-recipe case, we prove that the optimal policy is monotone in the machine status, but not in the number of jobs in the system. A similar monotonicity result holds in the two-recipe case. Finally, we provide computational results indicating that signicant savings can be realized when implementing a predictive maintenance policies instead of a traditional job-based threshold policy for PMs.

Integrated Maintenance Decision-Making and Product Sequencing in Flexible Manufacturing Systems

“…[10][11][12], the authors considered systems which produced only a single type of a product, which means that they did not consider the effects of producing different products on the degradation dynamics of the equipment and the overall decisionmaking system. Kazaz and Sloan [13] and Cai et al [14] tackle the maintenance and production planning problem in a singlestage multiple-product system. In these studies, at each decision epoch, the question of whether to maintain the machine or not is answered based on the current degradation state of the machine.…”

Joint Maintenance and Production Operations Decision Making in Flexible Manufacturing Systems

“…There have been some studies in the literature, such as the ones presented by Kazaz and Sloan [132] and Cai et al [133], that tackle the maintenance and production planning problem in a single-stage multiple-product system. In these studies at each decision epoch, the decision of whether to maintain the machine or not is given based on the current degradation state of the machine.…”

Dynamically scheduling and maintaining a flexible server

“…In particular, the majority of papers in the maintenance literature do not consider the effect that the amount of work in the system (i.e., the queue length) may have on optimal maintenance decisions; see for example, the surveys (McCall, 1965; Pierskalla & Voelker, 1976; Sherif & Smith, 1981; Valdez‐Flores & Feldman, 1989). Two papers where such effects are accounted for, via models that are very closely related to the one presented in Section 2, are Kaufman and Lewis (2007) and Cai et al (2013), which we describe in more detail below. Moreover, while previous work such as that of Andradóttir et al (2007) and Wu et al (2006, 2008) has accounted for server failures in the context of queueing models of flexible manufacturing systems, with the exception of Cai et al (2013), we are not aware of any other work in this area that combines scheduling with maintenance decisions.…”

“…Two papers where such effects are accounted for, via models that are very closely related to the one presented in Section 2, are Kaufman and Lewis (2007) and Cai et al (2013), which we describe in more detail below. Moreover, while previous work such as that of Andradóttir et al (2007) and Wu et al (2006, 2008) has accounted for server failures in the context of queueing models of flexible manufacturing systems, with the exception of Cai et al (2013), we are not aware of any other work in this area that combines scheduling with maintenance decisions. We note that there has been recent work on joint scheduling and maintenance in the contexts of deterministic scheduling (Grigoriu & Briskorn, 2017), developing metaheuristics (Celen & Djurdjanovic, 2015), and mixed‐integer programming that incorporates constraints specific to semiconductor manufacturing (Cai et al, 2012; Yao et al, 2004).…”

“…Cai et al (2013) consider an M / G /1 queueing model with at most two types of jobs, which is motivated by potential semiconductor manufacturing applications. In this model, the service and deterioration dynamics differ from those in Kaufman and Lewis (2007).…”