Minimizing the bicriteria of makespan and maximum tardiness with an upper bound on maximum tardiness

This paper studies the flowshop scheduling problem with a complex bicriteria objective function. A weighted sum of makespan and maximum tardiness subject to a maximum tardiness threshold value is to be optimized. This problem, with interesting potential applications in practice, has been sparsely studied in the literature. We propose global and local dominance relationships for the three-machine problem and a fast and effective genetic algorithm (GA) for the more general m-machine case. The proposed GA incorporates a novel three-phase fitness assignment mechanism specially targeted at dealing with populations in which both feasible as well as infeasible solutions might coexist. Comprehensive computational and statistical experiments show that the proposed GA outperforms the two most effective existing heuristics by a considerable margin in all scenarios. Furthermore, the proposed GA is also faster and able to find more feasible solutions. It should be noted that when the weight assigned to maximum tardiness is zero, then the problem is reduced to minimizing makespan subject to a maximum tardiness threshold value. Heuristics for both problems have been provided in the literature recently but they have not been compared. Another contribution of this paper is to compare these recent heuristics with each other.

[1]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[2]  Ali Allahverdi,et al.  A new heuristic for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness , 2004, Comput. Oper. Res..

[3]  Rubén Ruiz,et al.  A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem , 2008, INFORMS J. Comput..

[4]  Tarek Y. ElMekkawy,et al.  Bi-criteria scheduling of a flowshop manufacturing cell with sequence dependent setup times , 2007 .

[5]  R. A. Dudek,et al.  A Heuristic Algorithm for the n Job, m Machine Sequencing Problem , 1970 .

[6]  R. L. Daniels,et al.  Multiobjective flow-shop scheduling , 1990 .

[7]  Rubén Ruiz,et al.  Solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics , 2005, Eur. J. Oper. Res..

[8]  Jean-Charles Billaut,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[9]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[10]  Rainer Leisten,et al.  A heuristic for scheduling a permutation flowshop with makespan objective subject to maximum tardiness , 2006 .

[11]  Rubén Ruiz,et al.  Some effective heuristics for no-wait flowshops with setup times to minimize total completion time , 2007, Ann. Oper. Res..

[12]  W. Townsend Note---Sequencing n Jobs on m Machines to Minimise Maximum Tardiness: A Branch-and-Bound Solution , 1977 .

[13]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[14]  Chandrasekharan Rajendran,et al.  Scheduling in flowshops to minimize total tardiness of jobs , 2004 .

[15]  P. Lopez,et al.  Climbing depth-bounded discrepancy search for solving hybrid flow shop problems , 2007 .

[16]  Yeong-Dae Kim,et al.  Heuristics for Flowshop Scheduling Problems Minimizing Mean Tardiness , 1993 .

[17]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[18]  C. Rajendran,et al.  Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idletime or flowtime in the static permutation flowshop sequencing problem , 2003 .

[19]  Rubén Ruiz,et al.  TWO NEW ROBUST GENETIC ALGORITHMS FOR THE FLOWSHOP SCHEDULING PROBLEM , 2006 .

[20]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[21]  B. Michael Adams Design and Analysis of Experiments, Sixth Edition , 2005 .

[22]  Rubén Ruiz,et al.  No-wait flowshop with separate setup times to minimize maximum lateness , 2007 .

[23]  Jorge M. S. Valente Heuristics for the single machine scheduling problem with early and quadratic tardy penalties , 2007 .

[24]  Thomas Stützle,et al.  A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem , 2007, Eur. J. Oper. Res..

[25]  Rubén Ruiz,et al.  A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility , 2006, European Journal of Operational Research.

[26]  Rubén Ruiz,et al.  Minimising total tardiness in the m-machine flowshop problem: A review and evaluation of heuristics and metaheuristics , 2008, Comput. Oper. Res..

[27]  Jose M. Framiñan,et al.  A review and classification of heuristics for permutation flow-shop scheduling with makespan objective , 2004, J. Oper. Res. Soc..

[28]  Chris N. Potts,et al.  A decomposition algorithm for the single machine total tardiness problem , 1982, Oper. Res. Lett..

[29]  Bala Ram,et al.  Parameter setting in a bio-inspired model for dynamic flexible job shop scheduling with sequence-dependent setups , 2007 .

[30]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[31]  Xiaoyun Xu,et al.  Influencing factors of job waiting time variance on a single machine , 2007 .

[32]  Chandrasekharan Rajendran,et al.  A heuristic for scheduling in a flowshop with the bicriteria of makespan and maximum tardiness minimization , 1999 .

[33]  Jung Woo Jung,et al.  Flowshop-scheduling problems with makespan criterion: a review , 2005 .

[34]  Rubén Ruiz,et al.  A comprehensive review and evaluation of permutation flowshop heuristics to minimize flowtime , 2013, Comput. Oper. Res..