In this paper we address the problem of visualizing the proportions and the similarities attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual, their areas reflect the proportions, and the closeness between … Read more
Emergency care necessitates adequate and timely treatment, which has unfortunately been compromised by crowding in many emergency departments (EDs). To address this issue, we study patient scheduling in EDs so that mandatory targets imposed on each patient’s door-to-provider time and length of stay can be collectively met with the largest probability. Exploiting patient flow data … Read more
The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received significant attention, both in theory and practice. This paper compares different methods for handling symmetries using a common implementation framework. We start by investigating the computation of symmetries and analyze the symmetries present … Read more
We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution … Read more
The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of the enumeration tree. State-of-the-art procedures base the selection of variables on their “LP gains”, which is the dual bound … Read more
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a “dual form” mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory … Read more
As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators’ toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that … Read more
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e., number of iterations needed, can theoretically be improved by scaling methods. We extend these results by an … Read more
A variety of formulations for the Travelling Salesman Problem as Mixed Integer Program have been proposed. They contain either non-binary variables or the number of constraints and variables is large. We want to give a new formulation that consists solely of binary variables; the number of variables and the number of constraints are of order … Read more
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems … Read more