Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions
RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 2, pp. 125-147.

This paper deals with the parallel-machine scheduling problem with the aim of minimizing the total (weighted) tardiness under the assumption of different release dates. This problem has been proven to be NP-hard. We introduce some new lower and upper bounds based on different approaches. We propose a branch-and-bound algorithm to solve the weighted and unweighted total tardiness. Computational experiments were performed on a large set of instances and the obtained results showed that our algorithms are efficient.

DOI : 10.1051/ro/2012010
Classification : 90B35, 68M20, 90C57
Mots-clés : scheduling, weighted tardiness, parallel machines, branch-and-boun 
@article{RO_2012__46_2_125_0,
     author = {Kacem, Imed and Souayah, Nizar and Haouari, Mohamed},
     title = {Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {125--147},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {2},
     year = {2012},
     doi = {10.1051/ro/2012010},
     mrnumber = {2955461},
     zbl = {1248.90049},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2012010/}
}
TY  - JOUR
AU  - Kacem, Imed
AU  - Souayah, Nizar
AU  - Haouari, Mohamed
TI  - Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2012
SP  - 125
EP  - 147
VL  - 46
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2012010/
DO  - 10.1051/ro/2012010
LA  - en
ID  - RO_2012__46_2_125_0
ER  - 
%0 Journal Article
%A Kacem, Imed
%A Souayah, Nizar
%A Haouari, Mohamed
%T Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2012
%P 125-147
%V 46
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2012010/
%R 10.1051/ro/2012010
%G en
%F RO_2012__46_2_125_0
Kacem, Imed; Souayah, Nizar; Haouari, Mohamed. Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 2, pp. 125-147. doi : 10.1051/ro/2012010. http://www.numdam.org/articles/10.1051/ro/2012010/

[1] B. Alidaee and D. Rosa, Scheduling parallel machines to minimize total weighted and unweighted tardness. Comput. Oper. Res. 24 (1979) 75-788. | MR | Zbl

[2] E.J. Anderson and J.C. Nyirenda, Two new rules to minimize tardiness in a job shop. Int. J. Prod. Res. 28 (1990) 2277-2292.

[3] M. Azizoglu and O. Kirka, Tardiness minimization on parallel machines. Int. J. Prod. Econ. 55 (1998) 163-168.

[4] P. Baptiste and C. Le Pape, Scheduling a single machine to minimize a regular objective function under setup constraints. Discrete Optim. 2 (2005) 83-99. | MR | Zbl

[5] P. Baptiste, C. Carlier and J. Antoine, A branch, bound procedure to minimze total tardiness on one machine with arbitrary release dates. Eur. J. Oper. Res. 158 (2004) 595-608. | MR | Zbl

[6] P. Baptiste, A. Jouglet and D. Savourey, Lower bounds for parallel machine scheduling problems. Int. J. Oper. Res. 3 (2008) 643-664. | MR | Zbl

[7] S.J. Chen and L. Lin, Reducing total tardiness cost in manufacturing cell scheduling by a multi-factor priority rule. Int. J. Prod. Res. 37 (1999) 2939-2956. | Zbl

[8] C. Chu, A branch and bound algorithm to minimise total flow time with unequal release dates. Nav. Res. Logist. 39 (1992) 859-875. | MR | Zbl

[9] C. Chu, A branch and bound algorithm to minimize total tardiness with release dates. Nav. Res. Logist. 39 (1992) 265-283. | MR | Zbl

[10] S.E. Elmaghraby and S.H. Park, Scheduling jobs on a number of identical machines. AIIE Trans. 6 (1974) 1-13. | MR

[11] H. Emmons, One machine sequencing to minimize certain functions of job tardiness. Oper. Res. 17 (1969) 701-715. | MR | Zbl

[12] C. Koulamas, Polynomially solvable total tardiness problem : review and extensions. Int. J. Manage. Sci. 25 (1997) 235-239. | Zbl

[13] Y.H. Lee and M. Pinedo, Scheduling jobs on parallel machines with sequence-dependent times. Eur. J. Oper. Res. 100 (1997) 464-474. | Zbl

[14] G. Mosheiov and D. Oron, A note on the SPT heuristic for solving scheduling problems with generalized due dates. Comput. Oper. Res. 31 (2004) 645-655. | Zbl

[15] R. Nessah and C. Chu, An efficient branch and bound algorithm for the problem Pm | rj | ∑ Cj. Submitted manuscript.

[16] C.N. Potts and L.N. Van Wassenhove, A branch and bound algorithm for the total weighted tardiness problem. Oper. Res. 33 (1985) 363-377. | Zbl

[17] A.H.G. Rinnooy Kan, Machine sequencing problem : classification, complexity and computaion. Nijhoff, The Hague (1976).

[18] S.-O. Shim and Y.-D. Kim, Scheduling on parallel identical machines to minimize total tardiness. Eur. J. Oper. Res. 177 (2007) 135-146. | MR | Zbl

[19] H.D. Sherali and O. Ulular, Conjugate gradient methods using quasi-Newton updates with inexact line searches. J. Math. Anal. Appl. 150 (1990) 359-377. | MR | Zbl

[20] N. Souayah, I. Kacem, M. Haouari and C. Chu Scheduling on parallel identical machines to minimise the total weighted tardiness. Int. J. Adv. Oper. Manage. 1 (2009) 30-69.

[21] L.-H. Su and C.-J. Chen, Minimizing totla tardiness on a single machine with unequal release dates. Eur. J. Oper. Res. 186 (2008) 496-503. | MR | Zbl

[22] Z.J. Tian, C.T. Ng and T.C.E. Cheng, On the single machine total tardiness problem. Eur. J. Oper. Res. 165 (2005) 843-846. | MR | Zbl

[23] F. Yalaoui and C. Chu, Parallel machines scheduling to minimize total tardiness. Int. J. Prod. Econ. 76 (2002) 265-279.

[24] F. Yalaoui and C. Chu, New exact method to solve the Pm | rj | ∑ Cj schedule problem. Int. J. Prod. Econ. 100 (2005) 168-179.

Cité par Sources :