American Institute of Mathematical Sciences

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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

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 & 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.  Google Scholar

[2]

S. Gawiejnowicz, Time-Dependent Scheduling, EATC Monograph in Theoretical Computer Science, Springer, 2008.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[7]

C.-Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[2]

S. Gawiejnowicz, Time-Dependent Scheduling, EATC Monograph in Theoretical Computer Science, Springer, 2008.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[7]

C.-Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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