zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Parallel machines scheduling to minimize job tardiness and machine deteriorating cost with deteriorating jobs. (English) Zbl 1193.90105
Summary: This paper studies the parallel machines bi-criteria scheduling problem (PMBSP) in a deteriorating system. Sequencing and scheduling problems (SSP) have seldom considered the two phenomena concurrently. This paper discusses the parallel machines scheduling problem with the effects of machine and job deterioration. By the machine deterioration effect, we mean that each machine deteriorates at a different rate. This deterioration is considered in terms of cost which depends on the production rate, the machine’s operating characteristics and the kind of work done by each machine. Moreover, job processing times are increasing functions of their starting times and follow a simple linear deterioration. The objective functions are minimizing total tardiness and machine deteriorating cost. The problem of total tardiness on identical parallel machines is NP-hard, thus the problem with machine deteriorating cost as an additional term is also NP-hard. We propose the LP-metric method to show the importance of our proposed multi-objective problem. A metaheuristic algorithm is developed to locate optimal or near optimal solutions based on a Tabu search mechanism. Numerical examples are presented to show the efficiency of this model.
90B35Scheduling theory, deterministic
90C60Abstract computational complexity for mathematical programming problems
90C11Mixed integer programming
90C29Multi-objective programming; goal programming
[1]Browne, S.; Yechiali, U.: Scheduling deteriorating jobs on a single processor, Oper. res. 38, 495-498 (1990) · Zbl 0703.90051 · doi:10.1287/opre.38.3.495
[2]Ruat, S.; Swami, S.; Gupta, N. D.: Scheduling a capacitated single machine with time deteriorating job values, Product. econ. 114, 769-780 (2008)
[3]Gawiejnowicz, S.; Kurc, W.; Pankowska, L.: Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences, Discrete appl. Math. 154, 2150-2166 (2006) · Zbl 1113.90059 · doi:10.1016/j.dam.2005.04.016
[4]Wang, J.: Single-machine scheduling problems with the effects of learning and deterioration, Omega 35, 397-402 (2007)
[5]Xu, D.; Sun, K.; Li, H.: Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan, Comput. oper. Res. 35, 1344-1349 (2008) · Zbl 1171.90411 · doi:10.1016/j.cor.2006.08.015
[6]Oron, D.: Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times, Comput. oper. Res. 35, 2071-2078 (2008) · Zbl 1139.90012 · doi:10.1016/j.cor.2006.10.010
[7]Wang, J.; Xia, Z.: Scheduling jobs under decreasing linear deterioration, Inform. pro. Lett. 94, 63-69 (2005) · Zbl 1182.68359 · doi:10.1016/j.ipl.2004.12.018
[8]Jeng, A.; Lin, B.: Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs, Comput. oper. Res. 32, 521-536 (2005) · Zbl 1077.90025 · doi:10.1016/j.cor.2003.08.001
[9]Chakravarty, A. K.; Balakrislman, N.: Job sequencing rules for minimizing the expected makespan in flexible machines, Eur. J. Oper. res. 96, 274-288 (1996) · Zbl 0917.90186 · doi:10.1016/S0377-2217(96)00070-7
[10]Lam, C. T.; Yeh, R. H.: Optimal maintenance policies for systems under various maintenance strategies, IEEE trans. Reliab., 31-92 (1993)
[11]Grall, A.; Berenguer, C.; Dieulle, L.: A condition-based maintenance policy for stochastically deteriorating systems, Reliab. eng. Syst. safe. 76, 167-180 (2002)
[12]Bilge, U.; Kirac, F.; Kurtulan, M.; Pekgun, P.: A tabu search algorithm for parallel machine total tardiness problem, Comput. oper. Res. 31, 397-414 (2004) · Zbl 1057.90516 · doi:10.1016/S0305-0548(02)00198-3
[13]Yi, Y.; Wang, D. W.: Soft computing for scheduling with batch set up times earliness – tardiness penalties on parallel machine, J. int. Man. 14, 311-322 (2003)
[14]Radhakrishnan, S.; Ventura, J.: Simulated annealing for parallel machine scheduling with earliness – tardiness penalties and sequence-dependent set-up times, Int. J. Prod. res. 38, 2233-2252 (2000) · Zbl 0973.90512 · doi:10.1080/00207540050028070
[15]Lee, C. Y.; Uzsoy, R.; Martin-Vega, L.: Efficient algorithms for scheduling semiconductor burn in operations, Oper. res. 40, 764-775 (1992) · Zbl 0759.90046 · doi:10.1287/opre.40.4.764
[16]Park, Y.; Kim, S.; Lee, Y.: Scheduling jobs on parallel machines applying neural network heuristic rules, Comput. ind. Eng. 38, 189-202 (2000)
[17]Cao, D.; Chen, M.; Wan, G.: Parallel machine selection and job scheduling to minimize machine cost and job tardiness, Comput. oper. Res. 32, 1995-2012 (2005) · Zbl 1068.90054 · doi:10.1016/j.cor.2004.01.001
[18]Pfund, M.; J., W. Fowler; Gadkari, A.; Chen, Y.: Scheduling jobs on parallel machines with setup times and ready times, Comput. ind. Eng. 54, 764-782 (2008)
[19]Lingo User’s Guide, LINDO Systems Inc., Chicago, 1999.
[20]Glover, F.; Laguna, M.: Tabu search, (1997)
[21]D. Sule, Industrial Scheduling, PWS Pub. Co., Boston, 1997.