Time indexed formulation of scheduling problems

• Main Author: Williams, David Niranian
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/5850

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.