Crew Scheduling Problems to Optimality

**
Tallys H. Yunes ^{1}
tallys@acm.org
Arnaldo V. Moura
arnaldo@dcc.unicamp.br
Cid C. de Souza^{2}
cid@dcc.unicamp.br
**

Institute of Computing, University of Campinas

P.O. Box 6176, ZIP 13083-970

Campinas, SP, Brazil

In this article, we present a hybrid methodology for the
exact solution of large scale real world crew scheduling problems.
Our approach integrates mathematical programming and constraint
satisfaction techniques, taking advantage of their particular
abilities in modeling and solving specific parts of the problem.
An Integer Programming framework was responsible for guiding the
overall search process and for obtaining lower bounds on the
value of the optimal solution.
Complex constraints were easily expressed, in a declarative
way, using a Constraint Logic Programming language. Moreover, with
an effective constraint-based model, the huge space of feasible
solutions could be implicitly considered in a fairly efficient way.
Our code was tested on real problem instances arising from the
daily operation of an ordinary urban transit company that serves a
major metropolitan area with an excess of two million inhabitants.
Using a typical desktop PC, we were able find, in an acceptable
running time, an optimal solution to instances with more than 1.5
billion entries.

**Keywords**: Crew Scheduling, Constraint Programming,
Mathematical Programming, Hybrid Algorithms, Column Generation

- Introduction
- The Crew Scheduling Problem
- Pure Approaches
- A Hybrid Approach
- Conclusions and Future Work
- Bibliography
- About the Authors
- About this document ...