| Summary: | In this thesis, we study various approaches that could be used in finding
a lower bound for single and parallel machine scheduling problems. These
approaches are based on integer programming formulations involving binary
variables indexed by (i,t), where i denotes a job and t is a time period.
For the single machine case, we provide an approximation scheme and a Lagrangian
relaxation procedure both of which produce good lower bounds.
We also present a new column generation algorithm which solves the LP-relaxation
of time-indexed formulation using fewer columns than the standard
column generation procedure.
In chapter 3 we present a new integer programming formulation for the
movie scheduling problem, based on time indexed variables. This formulation
led us to investigate the general parallel machine scheduling problem, for
which we present a column generation procedure, which is an extension of
the work done by van den Akker for the single machine case.
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