28+JOB_SHOP_SCHEDULING_USING_THEORY_OF_CONSTRAINTS

28+JOB_SHOP_SCHEDULING_USING_THEORY_OF_CONSTRAINTS -...

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JOB SHOP SCHEDULING  USING THEORY OF  CONSTRAINTS
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JOB SHOP SCHEDULING    The philosophy here is to apply the TOC principles to a job  shop  environment.  This  involves  determining  the  bottleneck  machine, exploiting the bottleneck machine, and subordinating  the  other  machines  to  the  needs  of  the  bottleneck.  In  flow  shop environment the way we practiced the TOC was using a  Drum-Buffer-Rope  (DBR)  technique.  In  that,  the  material  is  released to the first station with enough frequency to keep the  bottleneck machine busy all the time with the least amount of  WIP.  The  bottleneck  machine  paced  the  speed  (drumbeat).  The rope was the timing of the release of material to the first  machine, and the buffer corresponds to safety stock in front of  the bottleneck machine. 
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JOB SHOP SCHEDULING       The  machines  before  the  bottleneck(including  the  bottleneck)  were  scheduled  by  a  pull  mechanism  and  the  machines following the bottleneck were scheduled by using  a push mechanism.           In  job  shop  scheduling,  a  set  of  jobs  with  processing  times  on  each  machine  and  due  dates  are  given.  The  purpose is to schedule the order of jobs on each machine  to  optimize  a  suitable  objective  (e.g.,  minimize  the  maximum     tardiness).
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   Let P be the matrix representing the processing times of  each  job  on  each  machine.  Therefore,  pij  represents  the  processing  time  of  job  i  on  machine  j.  Similarly  let  Q  represent  the  routing  matrix  indicating  the  order  in  which  the jobs travel between the machines in their routing. The  entry,  qij,  represents  the  operation  number  of  job  i  on  machine j. For example, qij = 4 indicates    that job i visits machine j on its fourth operation. Also let Z  be the matrix of machine indices where z il  represents the  index  of  the  machine  for  job  i  in  its  l th  operation.  For  example consider the following data given for a scheduling  problem    called Quick Closures.
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scheduling.    m = number of machines    n = number of jobs    Step 1. Finding the Bottleneck Machine    Use rough-cut capacity utilization calculations by using      CUj =  j = 1, …, m     Choose  machine  b,  with  CUb  =  maxj  {CUj}  as  the  bottleneck  machine.  This    is  our  first  guess  on  the  bottleneck machine. = n
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28+JOB_SHOP_SCHEDULING_USING_THEORY_OF_CONSTRAINTS -...

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