The Intersection problem for 2-(v; 5; 1) directed block designs

The intersection problem for a pair of 2-(v, 3, 1) directed designs and 2-(v, 4, 1) directed designs is solved by Fu in 1983 and by Mahmoodian and Soltankhah in 1996, respectively. In this paper we determine the intersection problem for 2-(v, 5, 1) directed designs.Comment: 17 pages. To appear in Discrete Mat

On the order three Brauer classes for cubic surfaces

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over \bbQ such that \Br(S)/\Br(\bbQ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.Comment: Extended introduction, discussion of the example of Cassels and Gu

Exact algorithms for the order picking problem

Order picking is the problem of collecting a set of products in a warehouse in a minimum amount of time. It is currently a major bottleneck in supply-chain because of its cost in time and labor force. This article presents two exact and effective algorithms for this problem. Firstly, a sparse formulation in mixed-integer programming is strengthened by preprocessing and valid inequalities. Secondly, a dynamic programming approach generalizing known algorithms for two or three cross-aisles is proposed and evaluated experimentally. Performances of these algorithms are reported and compared with the Traveling Salesman Problem (TSP) solver Concorde