Abstract
In this paper, we introduce a new approach based on DC (Difference of Convex functions) Programming and DCA (DC Algorithm) for minimizing the maintenance cost involving flow-time and tardiness penalties. The main idea is to divide the horizon considered into H intervals and the problem is first formulated as a mixed integer linear problem (MILP). It is afterward reformulated in the form of a DC program by an exact penalty technique. Solution method based on DCA is investigated to solve the resulting problem. The efficiency of DCA is compared with the algorithm based on the new flow-time and tardiness rule (FTR) given in [8]. The computational results on several test problems show that the solutions provided by DCA are better.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Le Thi, H.A., Pham Dinh, T.: A Continuous approach for globally solving linearly constrained quadratic zero-one programming problem. Optimization 50(1-2), 93–120 (2001)
Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world non convex optimization problems. Annals of Operations Research 133, 23–46 (2005)
Le Thi, H.A., Pham Dinh, T., Le Dung, M.: Exact penalty ind.c. programming. Vietnam Journal of Mathematics 27(2), 169–178 (1999)
Rockafellar, R.T.: Convex analysis, 1st edn. Princeton University Press, Princeton (1970)
Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to d.c Programming: Theory, Algorithms and Applications. Acta Mathematica Vietnamica, dedicated to Professor Hoang Tuy on the occasion of his 70th birthday 22(1), 289–355 (1997)
Pham Dinh, T., Le Thi, H.A.: DC optimization algorihms for solving the trust region subproblem. SIAM J. Optimization 8, 476–505 (1997)
Le Thi, H.A., Pham Dinh, T.: A continuous approach for the concave cost supply problem via DC programming and DCA. Discrete Applied Mathematics 156, 325–338 (2008)
Adjallah, K.H., Adzakpa, K.P.: Minimizing maintenance cost involving flow-time and tardiness penalty with unequal release dates. Journal of Risk and Reliability, Part O 221(1), 57–66 (2007) (in press)
Adzakpa, K.P.: Maintenance of distributed systems: methods for real-time decision-making. PhD Thesis, University of Technology of Troyes, France (October 2004)
Burke, E.K., Smith, A.J.: Hybrid evolutionary techniques for the maintenance scheduling problem. IEEE 2000 Trans. on Power Systems 15(1), 122–128 (2000)
Derman, C., Lieberman, G.J., Ross, S.M.: On the optimal assignment of servers and a repairman. Journal of Applied Probability 17(2), 577–581 (1980)
Duron, C., Ould Louly, M.A., Proth, J.-M.: The one machine scheduling problem: Insertion of a job under the real-time constraint. European Journal of Operational Research 199, 695–701 (2009)
Gopalakrishnan, M., Mohan, S., He, Z.: A tabu search heuristic for preventive maintenance scheduling. Computers & Industrial Engineering 40(1-2), 149–160 (2001)
Lenstra, J., Kan, A.R., Brucker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343–362 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Quynh, T.D., An, L.T.H., Adjallah, K.H. (2010). DCA for Minimizing the Cost and Tardiness of Preventive Maintenance Tasks under Real-Time Allocation Constraint. In: Nguyen, N.T., Le, M.T., Świątek, J. (eds) Intelligent Information and Database Systems. ACIIDS 2010. Lecture Notes in Computer Science(), vol 5991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12101-2_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-12101-2_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12100-5
Online ISBN: 978-3-642-12101-2
eBook Packages: Computer ScienceComputer Science (R0)