Scheduling flexible maintenance activities subject to job-dependent machine deterioration

This paper considers single machine scheduling that integrates machine deterioration. The current maintenance state of the machine is determined by a maintenance level which drops by a certain, possibly job-dependent, amount while jobs are processed. A maintenance level of less than zero is associated with the machine’s breakdown and is therefore forbidden. Consequently, maintenance activities that raise the maintenance level again may become necessary and have to be scheduled additionally. In what follows, two general types of maintenance activities are distinguished. In the full maintenance case, maintenance activities are always executed until the machine has reached the maximum maintenance level. In contrast to this, the schedule in the partial maintenance case has to additionally determine the duration of maintenance activities. By combining both cases with regular objective functions such as minimization of maximum tardiness, minimization of the sum of completion times, or minimization of the number of tardy jobs, we obtain a new set of specific single-stage scheduling problems. Besides motivating and introducing these problems, we shall also analyze the computational complexity of general and specific cases.

[1]  Suh-Jenq Yang,et al.  Unrelated parallel-machine scheduling problems with multiple rate-modifying activities , 2013, Inf. Sci..

[2]  Vitaly A. Strusevich,et al.  Single machine scheduling with general positional deterioration and rate-modifying maintenance , 2012 .

[3]  D. Atkin.  OR scheduling algorithms. , 2000, Anesthesiology.

[4]  Edward G. Coffman,et al.  An Application of Bin-Packing to Multiprocessor Scheduling , 1978, SIAM J. Comput..

[5]  Eugene Levner,et al.  Fast approximation algorithm for job sequencing with deadlines , 1981, Discret. Appl. Math..

[6]  Jen-Shiang Chen,et al.  Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan , 2008, Eur. J. Oper. Res..

[7]  Hongxing Li,et al.  Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines , 2010 .

[8]  Hans Kellerer,et al.  Two linear approximation algorithms for the subset-sum problem , 2000, Eur. J. Oper. Res..

[9]  Dehua Xu,et al.  Scheduling jobs under increasing linear machine maintenance time , 2010, J. Sched..

[10]  Zhi-Long Chen.  Parallel Machine Scheduling with Time Dependent Processing Times , 1996, Discret. Appl. Math..

[11]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[12]  Bo Chen,et al.  Tighter bound for MULTIFIT scheduling on uniform processors , 1991, Discret. Appl. Math..

[13]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[14]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[15]  Gur Mosheiov,et al.  Scheduling a maintenance activity and due-window assignment on a single machine , 2009, Comput. Oper. Res..

[16]  M. Yue.  On the exact upper bound for the multifit processor scheduling algorithm , 1990 .

[17]  Suh-Jenq Yang,et al.  Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities , 2010 .

[18]  Vitaly A. Strusevich,et al.  Simple matching vs linear assignment in scheduling models with positional effects: A critical review , 2012, Eur. J. Oper. Res..

[19]  Bertrand M. T. Lin,et al.  A concise survey of scheduling with time-dependent processing times , 2004, Eur. J. Oper. Res..

[20]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[21]  Chuanli Zhao,et al.  Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan , 2010 .

[22]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[23]  Gur Mosheiov,et al.  Scheduling a maintenance activity and due-window assignment based on common flow allowance , 2012 .

[24]  Donald K. Friesen,et al.  Scheduling on same-speed processors with at most one downtime on each machine , 2010, Discret. Optim..

[25]  Dvir Shabtay,et al.  A survey of scheduling with controllable processing times , 2007, Discret. Appl. Math..

[26]  Suh-Jenq Yang.  Single-machine scheduling problems with both start-time dependent learning and position dependent aging effects under deteriorating maintenance consideration , 2010, Appl. Math. Comput..

[27]  Eric Sanlaville,et al.  Machine scheduling with availability constraints , 1998, Acta Informatica.

[28]  Dieter Jungnickel,et al.  Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem , 2000, Oper. Res. Lett..

[29]  Adam Janiak,et al.  Scheduling jobs under an aging effect , 2010, J. Oper. Res. Soc..

[30]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[31]  Adam Janiak,et al.  Single machine scheduling subject to deadlines and resource dependent processing times , 1996 .

[32]  Michael A. Langston,et al.  Bounds for Multifit Scheduling on Uniform Processors , 1983, SIAM J. Comput..

[33]  Suh-Jenq Yang,et al.  Computers and Mathematics with Applications Minimizing the Total Completion Time in Single-machine Scheduling with Aging/deteriorating Effects and Deteriorating Maintenance Activities , 2022 .

[34]  Christopher D. Geiger,et al.  A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration , 2010, Eur. J. Oper. Res..