DMP87 - Scheduling, Timetabling and Routing
Weekly Notes
Lecture 7, Fall 2008

Lecture February 18

We treated the following topics:

• MIP formulation for the $1\vert\vert\sum w_j T_j$ problem that last lecture we solved approximately with local search.

• The resource constrained project scheduling problem (RCPSP). Generalized precedence constraints (slides and chalk).

• Overview of Software for CP (slides).

• CP Modelling Techniques: propagators, global constraints, symmetry breaking, reification (slides).

• Practical exercise: implementation of an RCPSP model in MiniZinc language (data in the lecture notes; job shop and open shop examples on the G12 project page; the file globals.mzn for the list of global constraints; the solution model).

The next lecture we treat dispatching rules and single machine models. Reading material are section C.2 and C.3 (pp. 414 - 420) of the text book and the photocopies available from the Document section of the Black Board.

Literature

To learn more about Constraint Programming a good starting point are the slides by Marco Kuhlmann and Guido Tack for their course at the Saarland University or the slides by Christian Schulte for an introductory lecture at ITU.

The following books and articles are also good for an introduction:

• Apt, K. R. (2003).
  Principles of Constraint Programming.
  Cambridge University Press. (in arrive at IMADA's Library).

• Schulte, C. and Carlsson, M. (2006).
  Finite Domain Constraint Programming Systems.
  Handbook of constraint programming.
  In Rossi, F., van Beek, P., and Walsh, T., editors, Handbook of Constraint Programming, Elsevier. (treats constraint propagators).

Non-mandatory Assignments

Exercise 1

Formulate the RCPSP, treated in the practical exercise in class, as a time-indexed integer program. Compare your formulation with the one given in Section 4.6 of the text book. Does the linear relaxation produce an integer solution?

Exercise 2

Show how single machine scheduling, parallel machine scheduling and shop scheduling can be modeled by the RCPSP model.

Exercise 3

Implement the RCPSP model that we developed for MiniZinc at the lecture for the Gecode/J interface. In order to understand how to implement the model in java you may consult the following documentation, in this order:

• The tutorial by Marco Kuhlmann and Guido Tack

• The walk-through available explaining the n-Queens standard example included in Gecode/J.

• The examples in the directory examples of the Gecode/J archive.