Advanced scheduling Problem using constraint Programming techniques in SCM environment

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Advanced scheduling Problem using
constraintProgramming techniques in SCM
environment
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Introduction

• Consider preemptive and non-preemptive scheduling
  model
• One of the advanced scheduling problems by a
  constraint programming technique
• Propose a new GA considering simultaneously the
  prmp and non-prmp cases of the jobs activities
  under single machine job shop scheduling problem
• Propose the hybrid GAs with the Proposed GA and
  conventional sequencing rules.
• Experiment results show that the hybrid GA
  outperforms the proposed GA and other
  conventional sequencing rules.

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Background Information

• For the Preemptive case using constraint
  programming technique in job-shop scheduling
  problems
• Preemptive scheduling problem with finite
  capacity input buffer
• gt Hall, Posner, and Potts (1997)
• Preemptive scheduling problem with release times
  time windows in multi processor tasks.
• gt Bianco, Blazewicz and DellOlmo (1997)
• O(n4) algorithm for the preemptive scheduling of
  a single machine in order to minimize the number
  of late jobs.
• gt Baptiste (1999)
• Comparison of a time table algorithm with an
  edge-finding algorithm considering the concepts
  of a constraint programming technique.
• gt Pape and Baptiste (1994)

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Background Information

• For the GA considering preemptive case
• Using a GA for solveing the scheduling problem in
  the preemptive case under some resource
  limitations.
• gt Figielska (1997)
• Purposing the scheduling problem of preemptive
  jobs on unrelated parallel machines
• Presenting a two-stage heuristic integration the
  column generation tech. with a GA for the
  minimizing the makespan
• gt Figielska (1999)

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Constraint programming for preemptive and
non-preemptive cases
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Mathematical formlation
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Genetic algorithm for preemptive and
non-preemptive cases

• Gene representation
• Heuristic search
• if selecting randomly a job 3
• randomly generate an integer in 1, 11-1.
• if generating value is 5, the starting time 5,
  end time 8 (53), respectively.
• Job 3 is assigned,
• the feasible schedules of all the
  available jobs should be as follows,
• gt 0,5-1 and 8, 17-1 for job 1, 1,5-1 and
  8,11-1 for job 2
• If selecting randomly job 2, among the remainder
  (job1, job2)
• randomly generate an integer in 1,4 and 8,
  10
• If generating value is 4, the starting time 4,
  end time 5 (41)
• gt processing time of job 2 to change 4 into 3
• If regenerating the remainder process time 3 in
  feasible range 1,4-1 8,10
• If generating value is 8, the starting time 8,
  end time 11, respectively.
• Job 2 is assigned, last job can also be assigned
  as 0,4 and 12, 14

Job 1 0,412,14, job 2 4,58,11 job 3
5, 8
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Genetic algorithm for preemptive and
non-preemptive cases

• Crossover operation
• Use the swap crossover
• for the precedence constraints jobs and
  preempive case

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Genetic algorithm for preemptive and
non-preemptive cases

• Mutation operation
• Randomly setlect a job
• and randomly regenerate the
• allowable schdule of the job
• The in feasible schedules of other job
• should be checked
• If overlapped schedule is generated
• reshedule it to get its feasible schedule.

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Genetic algorithm for preemptive and
non-preemptive cases

• Evaluation

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Numerical example

• for the effective comparison of the
• proposed algorithm
• use two conventional rule(SPT EDD)
• HGA1 combine the proposed GA with
• SPT rule.
• HGA2 combine the proposed GA with
• EDD rule.
• generating the initial population of GA
• instead of random generation

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Conclusion

• Propose a new GA considered by the concepts of
  constraint programming techniques for solving
  single machine job-shop
• Proposed GA has used variable lengths for
  representing the chromosome of GA considering the
  preem and non-preem case
• We have used the two conventional sequencing
  rules(SPT and EDD rules) and also combine d the
  proposed GA with the rules.