Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

Abstract

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-product problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants.

A two-stage coupled algorithm for an integrated maintenance planning and flowshop scheduling problem with deteriorating machines

“…The above scheduling problems do not model any correlation between machine conditions and processing times, ignoring the effect of maintenance on machine deterioration and restoration processes (Rustogi and Strusevich 2012;Kellerer et al 2013). Lee and Leon (2001) were the first to introduce such maintenance considerations into the scheduling literature, initiating the study of the second category of problems.…”

“…The first addresses the limited availabilities of machines due to maintenance requirements (Ma et al 2010), and the second area models the effect of maintenance on processing times by considering maintenance as a ratemodifying activity (Lee and Leon 2001). However, there is no decision regarding planning maintenance since the time windows for maintenance are typically given [e.g., Kuo and Yang (2008), Mosheiov and Sidney (2010), Kellerer et al (2013)]. To address the interdependency between maintenance and scheduling decisions in highly coupled processes such as wafer fabrication (Yao et al 2004), in this paper, we consider a flowshop system with multiple machines over multiple time periods where maintenance concepts are modeled as defined in the maintenance research literature (McCall 1965;Cho and Parlar 1991;Dekker et al 1997;Wang 2002;Nicolai and Dekker 2008).…”

The symmetric quadratic knapsack problem: approximation and scheduling applications

“…The model that we discuss below is based on the paper by Kellerer et al (2011). A single machine is subject to a so-called cumulative deterioration.…”

“…Thus, the main issue in solving problem 1 |Cumu, M P(Φ)| C max , including its simpler version 1 |Cumu, M P(0)| C max , is to find an appropriate partition of the jobs into two groups. It is proved by Kellerer et al (2011) that both problems are NP-hard.…”

“…Finding such a partition N * 1 (0) and N * 2 (0) reduces to the subset-sum problem which admits a very fast FPTAS by Kellerer et al (2003) that requires no more than O(min n/ε, n + 1/ε 2 log (1/ε) ) time. The found sets N ε 1 and N ε 2 are such that Kellerer et al (2011) show that an FPTAS for the subset-sum problem can be converted into an FPTAS for problem 1 |Cumu, M P(0)| C max .…”