SINGLE MACHINE EARLY TARDY PROBLEM

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SINGLE MACHINE EARLY TARDY PROBLEM

• IE 573 PAPER PRESENTATION

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AGENDA

• Introduction
• Problem definition
• Analysis of Early/Tardy Problem
• Heuristics
• Computational Study
• Conclusion

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Introduction

• Early Tardy problem became popular with JIT.
• Tries to handle the tradeoff between meeting due
  dates and holding excessive inventory
• Paper by OW and MORTON is the first paper on
  general early/tardy problem

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Problem Definition

• No preemption, no idle time, all jobs are
  initially available
• NP-Complete
• Irregular objective function
• Thus, exact solution is very limited

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Analysis of the Problem

• Objective

Early Cost Rate
Tardy Cost Rate
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Analysis of the Problem

• Adjacency Condition
• Where i precedes j
• Theorem 1 Adjacency condition holds for all
  adjacent pairs in the optimal sequence
• This is a necessary but not sufficient condition
  for global optimality

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Analysis of the Problem

• Special Cases
• Lemma 1 WSPT sequence resulting with no early
  jobs is optimal.

Minimized with WSPT
All zero since there is no early jobs
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Analysis of the Problem

• Special Cases
• Lemma 2 WLPT sequence resulting with no tardy
  jobs is optimal.

All zeros since there is no tardy jobs
Minimized with WLPT
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Heuristics

• Tardiness Heuristics This heuristic suggested by
  Morton, Rachamadugu and Vepsaleinen
• i immediately precedes j in the optimal sequence
  if where

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Heuristics

• Tardiness Heuristics
• - Compute the priority of each job according to
  the formula at each iteration
• - At each iteration choose the job with the
  highest priority
• - A myopic heuristic

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Heuristics

• Tardiness Heuristics
• - Use k jobs to calculate priority of job i
• - With experimentation, the formula became

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Heuristics

• Early/Tardy Heuristics
• - Authors improved the tardiness heuristic
• - Theorem 1 is used to come up with
• - Then look ahead parameter k is added

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Heuristics

• Early/Tardy Heuristics
• - With experimentations made, priority function
  is developed into EXP-ET
• - In figure 4. By Lemmas rules give optimum in
  the extreme cases.

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Heuristics

• Beam-Search Method
• Figure 5 in page 184
• Beam search approach with two types of evaluation
  function
• - Priority evaluation
• - Cost evaluation

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Heuristics

• Filtered Beam Search with two evaluation
  functions
• - First filter by priority function
• - Then by cost function

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Computational Study

• Priority functions are tested with different
  input parameters and k values
• High job clashes increases k
• Beam search and filtered beam search was tested
• See Table 1

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Conclusion

• This is the first paper on general early/tardy
  problem
• The authors try to find good solutions for this
  NP-Complete problem
• The evaluation of these heurisic methods suggests
  that filtered beam search with EXP-ET is the best

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Thank you for your attentIon

• IE 573 PAPER PRESENTATION
• BY ERSIN KÖRPEOGLU