DMP87 - Scheduling, Timetabling and Routing
Weekly Notes
Lecture 17, Fall 2008

Lecture April 7

We finished treating the case of Train Timetabling (sec. 11.4 of the text book).

We then discussed Workforce Scheduling:

• General classification (Slides)

• Crew Scheduling (section 12.6 textbook)

• Subgradient method (blackboard or references below)

• Employee Timetabling: shift scheduling, $(k,m)$-cyclic staffing (and extensions thereof) (sections 12.3, 12.4, 12.5)

• Solution method for IP with constraint matrix that has circular 1's property for rows (section 12.4)

• Nurse scheduling (Slides or Hooker's book, see bibliography)

Next Time, Wednesday 14:00 - 15:45 in room U25.

We will treat Vehicle Routing Problems. Material Chapter 1 and first part of Chapter 5 from the book by Toth and Vigo. Photocopies available from the Blackboard.

Annotated Bibliography on Workforce Scheduling

The list of references below is not included in the exam syllabus (pensum). It is only meant at those who want to deepen and enlarge the knowledge on the subject treated in the lecture.

• L. A. Wolsey (1998), Integer programming. John Wiley & Sons, New York, USA.

  Pages 37-52 explains totally unimodular and 167-183 the subgradient method

• Marshall L. Fisher. The Lagrangian Relaxation Method for Solving Integer Programming Problems, Management Science, Vol. 27, No. 1 (Jan., 1981), pp. 1-18

  Another reference where the subgradient method is explained.

• Slides from a course by Jakob Krarup og David Pisinger at DIKU.

  Another reference where the subgradient method is explained and exemplified.

• Bartholdi III, John J., Orlin, James B., Ratliff, H. Donald. Cyclic Scheduling via Integer Programs with Circular Ones. Operations Research. 1980 Vol. 28 Issue 5, p1074.

  Treats the employee cases discussed at the lecture and solved by means of IP.

• John N. Hooker, Integrated methods for optimization, Serie: International series in operations research & management science, Springer, New York, 2007, 486 pp.

  Treats the nurse scheduling case solved by CP. The book is also interesting for the integrated view of mathematical programming, constraint programming and heuristic methods for solving combinatorial optimization problems.

• Staff Scheduling and Rostering: Theory and Applications., Special Issue of Annals of Operations Research. Volumes 128-129, 2004

  Special Issue, contains several articles on different cases in workforce scheduling

• PATAT (Practice and Theory of Automated Timetabling) International Conference Series.

  Series of conferences where works on timetabling are presented.

• A. Meisels, A. Schaerf, Modeling and Solving Employee Timetabling Problems. Annals of Mathematics and Artificial Intelligence. 39(1-2): 41-59 (2003)

  An example of assignment of employees to shifts considering availabilities and skills conducted by local search.

• N. Musliu, A. Schaerf, W. Slany (2004) Local search for shift design. European Journal of Operational Research Volume 153, Issue 1, Pages 51-64

  An example of Shift scheduling solved by local search.