An investigation on a two-agent single-machine scheduling problem with unequal release dates

This paper addresses a two-agent scheduling problem on a single machine with arbitrary release dates, where the objective is to minimize the tardiness of one agent, while keeping the lateness of the other agent below or at a fixed level Q. A mixed integer programming model is first presented for its optimal solution, admittedly not to be practical or useful in the most cases, but theoretically interesting since it models the problem. Thus, as an alternative, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is provided to derive the optimal solution and a marriage in honey-bees optimization algorithm (MBO) is developed to derive the near-optimal solutions for the problem. Computational results are also presented to evaluate the performance of the proposed algorithms.

[1]  Qing Lu,et al.  On decomposition of the total tardiness problem , 1995, Oper. Res. Lett..

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

[3]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[4]  F. D. Croce,et al.  The two-machine total completion time flow shop problem , 1996 .

[5]  A. Kan.  Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .

[6]  G. Rand.  Sequencing and Scheduling: An Introduction to the Mathematics of the Job-Shop , 1982 .

[7]  Christos Koulamas,et al.  The single-machine total tardiness scheduling problem: Review and extensions , 2010, Eur. J. Oper. Res..

[8]  C. Chu,et al.  Some new efficient methods to solve the n/1/ri/ϵTi scheduling problem , 1992 .

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

[10]  Lixin Tang,et al.  Two-agent group scheduling with deteriorating jobs on a single machine , 2010 .

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

[12]  Vincent T'Kindt,et al.  Coupling Genetic Local Search and Recovering Beam Search algorithms for minimizing the total completion time in the single machine scheduling problem subject to release dates , 2012, Comput. Oper. Res..

[13]  Mouloud Koudil,et al.  Using artificial bees to solve partitioning and scheduling problems in codesign , 2007, Appl. Math. Comput..

[14]  Hussein A. Abbass,et al.  MBO: marriage in honey bees optimization-a Haplometrosis polygynous swarming approach , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

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

[16]  Manoj Kumar Tiwari,et al.  Swarm Intelligence, Focus on Ant and Particle Swarm Optimization , 2007 .

[17]  Xianpeng Wang,et al.  A hybrid metaheuristic for the prize-collecting single machine scheduling problem with sequence-dependent setup times , 2010, Comput. Oper. Res..

[18]  Ceyda Oguz,et al.  A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine , 2012, Comput. Oper. Res..

[19]  Wen-Chiung Lee,et al.  A two-machine flowshop problem with two agents , 2011, Comput. Oper. Res..

[20]  E. Lawler.  A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness , 1977 .

[21]  Alessandro Agnetis,et al.  Multi-agent single machine scheduling , 2007, Ann. Oper. Res..

[22]  Gur Mosheiov,et al.  Scheduling problems with two competing agents to minimize minmax and minsum earliness measures , 2010, Eur. J. Oper. Res..

[23]  Joseph Y.-T. Leung,et al.  Scheduling two agents with controllable processing times , 2010, Eur. J. Oper. Res..

[24]  Colin R. Reeves,et al.  Heuristics for scheduling a single machine subject to unequal job release times , 1995 .

[25]  Ling-Huey Su,et al.  Minimizing total tardiness on a single machine with unequal release dates , 2008, Eur. J. Oper. Res..

[26]  Wlodzimierz Szwarc,et al.  Solution of the single machine total tardiness problem , 1999 .

[27]  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..

[28]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

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

[30]  P. Liu,et al.  Two-agent single-machine scheduling problems under increasing linear deterioration , 2011 .

[31]  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..

[32]  Byung-Cheon Choi,et al.  Approximation algorithms for multi-agent scheduling to minimize total weighted completion time , 2009, Inf. Process. Lett..

[33]  Mouloud Koudil,et al.  Using Bees to Solve a Data-Mining Problem Expressed as a Max-Sat One , 2005, IWINAC.

[34]  Wen-Chiung Lee,et al.  Branch-and-bound and simulated annealing algorithms for a two-agent scheduling problem , 2010, Expert Syst. Appl..

[35]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[36]  Hamilton Emmons,et al.  One-Machine Sequencing to Minimize Certain Functions of Job Tardiness , 1969, Oper. Res..

[37]  Philippe Baptiste,et al.  A Branch-and-Bound procedure to minimize total tardiness on one machine with arbitrary release dates , 2004, Eur. J. Oper. Res..

[38]  Der-Chiang Li,et al.  Solving a two-agent single-machine scheduling problem considering learning effect , 2012, Comput. Oper. Res..

[39]  Marshall L. Fisher,et al.  A dual algorithm for the one-machine scheduling problem , 1976, Math. Program..

[40]  C. Chu.  A branch-and-bound algorithm to minimize total tardiness with different release dates , 1992 .

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