Scheduling a deteriorating maintenance activity on a single machine

Dolgui

2011

J Sched

International audienceWe review the results on scheduling with due date assignment under such conditions on job processing as given precedence constraints, maintenance activity or various scenarios of processing time changing. The due date assignment and scheduling problems arise in production planning when the management is faced with setting realistic due dates for a number of jobs. Most research on scheduling with due date assignment is focused on optimal sequencing of independent jobs. However, it is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements and this can be modeled by imposing precedence constraints on the set of jobs. In classical deterministic scheduling models, the processing conditions, including job processing times, are usually viewed as given constants. In many real-life situations, however, the processing conditions may vary over time, thereby affecting actual durations of jobs. In the models with controllable processing times, the scheduler can speed up job execution times by allocating some additional resources to the jobs. In the models with deterioration or learning, the actual processing time can depend either on the position or on the start time of a job in the schedule. In scheduling with deterioration, the later a job starts, the longer it takes to process, while in scheduling with learning, the actual processing time of a job gets shorter, provided that the job is scheduled later. We consider also scheduling models with optional maintenance activity. In manufacturing processing, production scheduling with preventive maintenance planning is one of the most significant methods in preventing the machinery from failure or wear

Section: Maintenance Activitymentioning

confidence: 98%

Scheduling with due date assignment under special conditions on job processing

Gordon¹,

Dolgui

2011

J Sched

“…The duration of a maintenance period can either be a given constant or be dependent on its start time. The latter type of maintenance is introduced in [15] and [16]; see also [17] and [18] for more recent developments. With several maintenance periods in a schedule, the jobs are split into several groups, one group before the first maintenance and one after each maintenance period.…”

Section: Messagementioning

confidence: 99%

Combining time and position dependent effects on a single machine subject to rate-modifying activities

Rustogi

2014

Omega

Citation for this version held on GALA:Rustogi, Kabir and Strusevich, Vitaly (2014) Combining time and position dependent effects on a single machine subject to rate-modifying activities. London: Greenwich Academic Literature Archive. We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and timedependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, e.g., maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects, on one hand, and between the positional effects and the start-time dependent effects, on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

“…This type of maintenance has been introduced by Strusevich (2005, 2006), and in combination with positional deterioration has recently been studied by Mosheiov and Sidney (2010), Rustogi and Strusevich (2011) and Yang and Yang (2010).…”

Section: Preliminariesmentioning

confidence: 99%

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

Kellerer

Rustogi

2012

J Sched

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.