Pareto optimization scheduling with two competing agents to minimize the number of tardy jobs and the maximum cost

Two-agent Pareto optimization scheduling.The number of tardy jobs and the maximum cost.Optimal and Pareto optimal schedules.Strongly polynomial-time algorithm. This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A-jobs and agent B wants to minimize the maximum cost of B-jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A-jobs under the restriction that the maximum cost of B-jobs is bounded is solved in polynomial time. This implies that the corresponding Pareto optimization scheduling problem can be solved in a weakly polynomial time. In this paper, by presenting a new algorithm for the constrained optimization problem, we provide a strongly polynomial-time algorithm for the corresponding Pareto optimization scheduling problem. Experimentation results show that the proposed algorithm for the considered problem is efficient.

[1]  Donatas Elvikis,et al.  Two-agent scheduling on uniform parallel machines with min-max criteria , 2012, Annals of Operations Research.

[2]  Joseph Y.-T. Leung,et al.  Competitive Two-Agent Scheduling and Its Applications , 2010, Oper. Res..

[3]  Jinjiang Yuan,et al.  Single machine preemptive scheduling with fixed jobs to minimize tardiness related criteria , 2005, Eur. J. Oper. Res..

[4]  T. C. Edwin Cheng,et al.  Multi-agent scheduling on a single machine with max-form criteria , 2008, Eur. J. Oper. Res..

[5]  Alessandro Agnetis,et al.  Scheduling Problems with Two Competing Agents , 2004, Oper. Res..

[6]  T. C. Edwin Cheng,et al.  A note on the complexity of the problem of two-agent scheduling on a single machine , 2006, J. Comb. Optim..

[7]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[8]  Weiping Shang,et al.  A note on the scheduling with two families of jobs , 2005, J. Sched..

[9]  Han Hoogeveen,et al.  Single-Machine Scheduling to Minimize a Function of Two or Three Maximum Cost Criteria , 1996, J. Algorithms.

[10]  T. C. Edwin Cheng,et al.  Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs , 2006, Theor. Comput. Sci..

[11]  Jonathan Cole Smith,et al.  A Multiple-Criterion Model for Machine Scheduling , 2003, J. Sched..

[12]  Jean-Charles Billaut,et al.  Solving a bicriteria scheduling problem on unrelated parallel machines occurring in the glass bottle industry , 2001, Eur. J. Oper. Res..

[13]  Jose M. Framiñan,et al.  A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems , 2014, Eur. J. Oper. Res..

[14]  T. C. Edwin Cheng,et al.  Bounded parallel-batching scheduling with two competing agents , 2012, Journal of Scheduling.

[15]  Alessandro Agnetis,et al.  A Lagrangian approach to single-machine scheduling problems with two competing agents , 2009, J. Sched..

[16]  Thuruthickara C. John.  Tradeoff solutions in single machine production scheduling for minimizing flow time and maximum penalty , 1989, Comput. Oper. Res..

[17]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[18]  Jinjiang Yuan,et al.  Unbounded parallel-batching scheduling with two competitive agents , 2012, J. Sched..

[19]  Han Hoogeveen,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[20]  Han Hoogeveen,et al.  Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time , 1994, Oper. Res. Lett..

[21]  Ameur Soukhal,et al.  Two-Agent Scheduling on an Unbounded Serial Batching Machine , 2012, ISCO.

[22]  Ludo Gelders,et al.  Solving a bicriterion scheduling problem , 1980 .