High Multiplicity Scheduling Problems

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High Multiplicity Scheduling Problems

• Alexander Grigoriev
• PhD-thesis
• Maastricht University
• 20/11/2003

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Outline

• Scheduling
• High multiplicity
• Research motivation and applications
• High multiplicity vs. Classic scheduling
• Approaches and results

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Scheduling Problems
Allocation of the resource to tasks over time
L
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Multiplicity High Multiplicity

• Multiplicity (40 hrs a week)
• Teaching 8 hrs
• SCM (Joris) 6 hrs
• Treewidth (Stan) 8 hrs
• Tarification (Anton) 6 hrs
• Defense and Workshop 8 hrs
• Miscellaneous 4 hrs.
• High Multiplicity (2080 hrs a year)
• Teaching 416 hrs
• Treewidth 770 hrs
• Scheduling 386 hrs
• Vacation 220 hrs
• Conferences 80 hrs
• Miscellaneous 208 hrs.

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Applications
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High Multiplicity vs. Classic Scheduling
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Research Questions

• Problem recognition and complexity determination
• Structural properties of solutions
• Algorithms for high multiplicity problems
• Approaches for output description.

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Results (Ch.2) Problems, algorithms, and outputs

• Notions on algorithms and problems
• Polynomial time algorithm
• Polynomial delay
• Incremental polynomial time
• Polynomial total time
• Pseudo-polynomial time
• Notions on outputs
• Job-oriented description
• Time-oriented description
• Sequence oriented description

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Results (Ch.3) Traveling Salesman
Structural result given an optimal tour of
multiplicity n, find an optimal tour for a
multiplicity larger than n (see Chapter 3)
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Results (Ch.4) Periodic Maintenance
Algorithm from Chapter 4 solves the problem to
optimality

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Results (Ch.5) Basic Scheduling

• Modification of existing exactand approximation
  algorithms for high multiplicity scheduling
  problems
• Effective output construction
• Complexity status determination
• New algorithms for cyclic scheduling problems

• 1rm1Cmax
• 1rm1,p1Cmax
• 1rm1,s1Cmax
• 1rm2,p1Cmax
• 1ddcCmax
• 1rm0Lmax
• 1rm1,p1Lmax
• 1rm1,s1Lmax
• 1rm2,p1Lmax
• 1ddcLmax
• 1rm,p1Lmax

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Results (Ch.6) Project Scheduling
start
finish
In Chapter 6 we show (by construction of an
example) that even the trivial problems may
become difficult when the input is short
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Further research

• High Multiplicity in non-scheduling
  combinatorialoptimization problems
• Complexity classification for the hard high
  multiplicityproblems
• Development of algorithmic techniques for high
  multiplicity problems and utilization of
  thesetechniques in single multiplicity problems