Prospective Surveillance of Multivariate Spatial Disease Data

Surveillance systems are often focused on more than one disease within a predefined area. On those occasions when outbreaks of disease are likely to be correlated, the use of multivariate surveillance techniques integrating information from multiple diseases allows us to improve the sensitivity and timeliness of outbreak detection. In this paper, we present an extension of the surveillance conditional predictive ordinate to monitor multivariate spatial disease data. The proposed surveillance technique, which is defined for each small area and time period as the conditional predictive distribution of those counts of disease higher than expected given the data observed up to the previous time period, alerts us to both small areas of increased disease incidence and the diseases causing the alarm within each area. We investigate its performance within the framework of Bayesian hierarchical Poisson models using a simulation study. An application to diseases of the respiratory system in South Carolina is finally presented. Keywords: disease surveillance; multiple diseases; Shared component model; conditional predictive ordinate

A polyhedral approach to the Rural Postman Problem

[EN] In this paper we study the polyhedron associated with the Rural Postman Problem (RPP). Because the RPP is NP-hard, we cannot expect to find a complete description of the rural postman polyhedron of a general graph, but a partial knowledge of such a description frequently proves to be useful for both theoretical and computational purposes. We have tried to characterize the facial structure of this unbounded full-dimensional polyhedron. Sets of valid inequalities inducing facets have been studied as well as their use in a cutting-plane algorithm. The application of this algorithm to a set of RPP instances taken from the literature and two instances of larger size taken from a real world graph is described. All these instances were solved to optimality.Corberan, A.; Sanchís Llopis, JM. (1994). A polyhedral approach to the Rural Postman Problem. European Journal of Operational Research. 79(1):95-114. doi:10.1016/0377-2217(94)90398-0S9511479

A cutting plane algorithm for the general routing problem

The General Routing Problem (GRP) is the problem of finding a minimum cost route for a single vehicle, subject to the condition that the vehicle visits certain vertices and edges of a network. It contains the Rural Postman Problem, Chinese Postman Problem and Graphical Travelling Salesman Problem as special cases. We describe a cutting plane algorithm for the GRP based on facet-inducing inequalities and show that it is capable of providing very strong lower bounds and, in most cases, optimal solutions