An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs

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July 2016, 12(3): 811-817. doi: 10.3934/jimo.2016.12.811

An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs

Imed Kacem ^1, and Eugene Levner ^2,

1.	LCOMS EA 7306, Université de Lorraine, 57000 Metz, France
2.	School of Economics, Ashkelon Academic College, Ashkelon, 78211, Israel

Received August 2013 Revised March 2014 Published September 2015

Abstract
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In this paper, we re-visit the problem of scheduling a set of proportional deteriorating non-resumable jobs on a single machine subject to maintenance. The maintenance has to be started prior to a given deadline. The jobs as well as the maintenance are to be scheduled so that to minimize the total completion time. For this problem we propose a new dynamic programming algorithm and a faster fully polynomial time approximation scheme improving a recent result by Luo and Chen [JIMO (2012), 8:2, 271-283].

Keywords: total completion time, maintenance activities, approximation scheme., deteriorating jobs, Scheduling.

Mathematics Subject Classification: Primary: 90B35; Secondary: 90C5.

Citation: Imed Kacem, Eugene Levner. An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs. Journal of Industrial and Management Optimization, 2016, 12 (3) : 811-817. doi: 10.3934/jimo.2016.12.811

References:

[1]	S. Gawiejnowicz, Scheduling deteriorating jobs subject to job or machine availability constraints, European Journal of Operational Research, 180 (2007), 472-478. doi: 10.1016/j.ejor.2006.04.021.
[2]	S. Gawiejnowicz, Time-Dependent Scheduling, EATC Monograph in Theoretical Computer Science, Springer, 2008.
[3]	S. Gawiejnowicz and A. Kononov, Complexity and approximability of scheduling resumable proportionally deteriorating jobs, European Journal of Operational Research, 200 (2010), 305-308. doi: 10.1016/j.ejor.2008.12.014.
[4]	G. Gens and E. Levner, Fast approximation algorithm for job sequencing with deadlines, Discrete Applied Mathematics, 3 (1981), 313-318. doi: 10.1016/0166-218X(81)90008-1.
[5]	M. Ji, Y. He and T. C. E. Cheng, Scheduling linear deteriorating jobs with an availability constraint on a single machine, Theoretical Computer Science, 362 (2006), 115-126. doi: 10.1016/j.tcs.2006.06.006.
[6]	H. Kellerer, K. Rustogi and V. A. Strusevich, Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance, Journal of Scheduling, 16 (2013), 675-683. doi: 10.1007/s10951-012-0287-8.
[7]	C.-Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.
[8]	W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283. doi: 10.3934/jimo.2012.8.271.
[9]	K. M. Ocetkiewicz, A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem, European Journal of Operational Research, 203 (2010), 316-320. doi: 10.1016/j.ejor.2009.07.025.
[10]	G. J. Woeginger, When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)?, INFORMS Journal on Computing, 12 (2000), 57-74. doi: 10.1287/ijoc.12.1.57.11901.
[11]	C.-C. Wu and W.-C. Lee, Scheduling linear deteriorating jobs to minimize makespan with an unavailability constraint on a single machine, Information Processing Letters, 87 (2003), 89-93. doi: 10.1016/S0020-0190(03)00262-X.

show all references

References:

[1]	S. Gawiejnowicz, Scheduling deteriorating jobs subject to job or machine availability constraints, European Journal of Operational Research, 180 (2007), 472-478. doi: 10.1016/j.ejor.2006.04.021.
[2]	S. Gawiejnowicz, Time-Dependent Scheduling, EATC Monograph in Theoretical Computer Science, Springer, 2008.
[3]	S. Gawiejnowicz and A. Kononov, Complexity and approximability of scheduling resumable proportionally deteriorating jobs, European Journal of Operational Research, 200 (2010), 305-308. doi: 10.1016/j.ejor.2008.12.014.
[4]	G. Gens and E. Levner, Fast approximation algorithm for job sequencing with deadlines, Discrete Applied Mathematics, 3 (1981), 313-318. doi: 10.1016/0166-218X(81)90008-1.
[5]	M. Ji, Y. He and T. C. E. Cheng, Scheduling linear deteriorating jobs with an availability constraint on a single machine, Theoretical Computer Science, 362 (2006), 115-126. doi: 10.1016/j.tcs.2006.06.006.
[6]	H. Kellerer, K. Rustogi and V. A. Strusevich, Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance, Journal of Scheduling, 16 (2013), 675-683. doi: 10.1007/s10951-012-0287-8.
[7]	C.-Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.
[8]	W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283. doi: 10.3934/jimo.2012.8.271.
[9]	K. M. Ocetkiewicz, A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem, European Journal of Operational Research, 203 (2010), 316-320. doi: 10.1016/j.ejor.2009.07.025.
[10]	G. J. Woeginger, When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)?, INFORMS Journal on Computing, 12 (2000), 57-74. doi: 10.1287/ijoc.12.1.57.11901.
[11]	C.-C. Wu and W.-C. Lee, Scheduling linear deteriorating jobs to minimize makespan with an unavailability constraint on a single machine, Information Processing Letters, 87 (2003), 89-93. doi: 10.1016/S0020-0190(03)00262-X.

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