Column Generation

PROGRAM

Academic Program

Each day is divided into a morning and an afternoon session. At the end of some sessions, we reserve a 15-minute period for some participants to present the problem they are currently working on, to stimulate a discussion.

You'll find a tentative program below. We more or less cover some of the material in the recent Branch-and-Price book. A series of beamer slides (with around a thousand clicks) will also be available.

  9:00-12:00 13:30-17:00
Monday
(Marco)
Dantzig-Wolfe Reformulation
  • Cutting Stock Problem
  • Basic LP and ILP knowledge
  • Column Generation Algorithm
  • Examples & Applications
Dantzig-Wolfe Reformulation
  • DW for LPs (Convexification)
  • DW for ILPs (Convexification & Discretization)
  • Multiple Subproblems and Aggregation
  • Examples & Applications
Tuesday
(Guy)
Vehicle Routing and Crew Scheduling Problems
  • Vehicle routing problem with time windows
  • Compact and extended formulations
  • Labeling algorithm for the subproblem
  • Subproblem relaxations
  • Branching and cutting
Shortest Path Problem with Resource Constraints
  • Labeling algorithm
  • SPPRC with simultaneous pickups and deliveries
  • SPPRC with pickups and deliveries
  • SPPRC for crew pairing
  • SPPRC for electric vehicle routing
Wednesday
(Jacques)
Dual point of view
  • Row generation and the alternative master problem
  • Lagrangean relaxation
  • Dantzig-Wolfe reformulation vs. Lagrangian relaxation
  • How helpful can the dual information be?
Dual point of view
  • Stabilized column generation
  • Generalized assignment problem
  • Capacitated p- median problem
  • Dual guided pivot rules for LPs
Thursday
(Marco & Jacques)
Branch-Price-and-Cut
  • Integrality test
  • Time constrained shortest path problem
  • Cutting planes in the original and master variables
  • Branching on the original and master variables
  • Ryan-Foster rule
Practical session with SCIP
Friday
(G & M & J & Roberto & Emiliano)
Good to Know
  • Heuristics and accelerating strategies
  • Various advanced topics
More to Know
  • Column generation & machine learning
  • Examples & Applications
  • Questions and answers

GERAD      FRQNT      le cnam      MOS