Scheduling trainees at a hospital department using a branch-and-price approach.

Scheduling trainees (graduate students) is a complicated problem that has to be solved frequently in many hospital departments. We will describe a trainee scheduling problem encountered in practice (at the ophthalmology department of the university hospital Gasthuisberg, Leuven). In this problem a department has a certain number of trainees at its disposal, which assist specialists in their activities (surgery, consultation, etc.). For each trainee one has to schedule the activities in which (s)he will assist during a certain time horizon, usually one year. Typically, these kind of scheduling problems are characterized by both hard and soft constraints. The hard constraints consist of both work covering constraints and formation requirements, whereas the soft constraints include trainees' preferences and setup restrictions. In this paper we will describe an exact branch-and-price method to solve the problem to optimality.Branch-and-price; Constraint; Health care; Problems; Requirements; Scheduling; Staff scheduling; Time; University;

04261 Abstracts Collection -- Algorithmic Methods for Railway Optimization

From 20.06.04 to 25.06.04, the Dagstuhl Seminar 04261 ``Algorithmic Methods for Railway Optimization\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Multicommodity Flow Problems with Commodity Compatibility Relations

We present a class of Multicommodity Flow Problems with Commodity Compatibility Relations (MCFP-CCR), in which compatibility relations among commodities used at each node are required. This class of problems has application in the Train Unit Scheduling Problem (TUSP) [1, 2], where train units of different traction types may not be coupled with each other to serve the same train trip. Computational complexity issues are discussed and solution methods are proposed. Computational experiments using the proposed solution methods are reported

Reconstructing Polyatomic Structures from Discrete X-Rays: NP-Completeness Proof for Three Atoms

We address a discrete tomography problem that arises in the study of the atomic structure of crystal lattices. A polyatomic structure T can be defined as an integer lattice in dimension D>=2, whose points may be occupied by $c$ distinct types of atoms. To ``analyze'' T, we conduct ell measurements that we call_discrete X-rays_. A discrete X-ray in direction xi determines the number of atoms of each type on each line parallel to xi. Given ell such non-parallel X-rays, we wish to reconstruct T. The complexity of the problem for c=1 (one atom type) has been completely determined by Gardner, Gritzmann and Prangenberg, who proved that the problem is NP-complete for any dimension D>=2 and ell>=3 non-parallel X-rays, and that it can be solved in polynomial time otherwise. The NP-completeness result above clearly extends to any c>=2, and therefore when studying the polyatomic case we can assume that ell=2. As shown in another article by the same authors, this problem is also NP-complete for c>=6 atoms, even for dimension D=2 and axis-parallel X-rays. They conjecture that the problem remains NP-complete for c=3,4,5, although, as they point out, the proof idea does not seem to extend to c<=5. We resolve the conjecture by proving that the problem is indeed NP-complete for c>=3 in 2D, even for axis-parallel X-rays. Our construction relies heavily on some structure results for the realizations of 0-1 matrices with given row and column sums

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools