This paper proposes a mixed-integer nonlinear programming approach for joint scheduling of long-term maintenance decisions and short-term production for groups of complex machines with multiple interacting components. We introduce an abstract model where the production and the condition of machines are described by convex functions, allowing the model to be employed for various application areas … Read more
Mixed-Integer Linear Programming (MIP) is applicable to such a wide range of real-world decision problems that the competition for the best code to solve such problems has lead to tremendous progress over the last decades. While current solvers can solve some of the problems that seemed completely out-of-reach just 10 years ago, there are always … Read more
The decarbonization of short-haul air transport has gained increasing attention, with electric aircraft emerging as a promising alternative to conventional short-haul aviation. However, given the substantial investment anticipated for the necessary infrastructure, a strategic and globally coordinated selection of airports is imperative. The aim of this paper is to address this problem and determine the … Read more
In this paper, we address the problem of allocating and scheduling employees for work shifts in the pharmacy sector of a private hospital. To tackle this issue, we introduce the pharmacy staff scheduling problem (PSSP) in the literature. To solve the problem, we propose a mixed-integer programming formulation that considers various aspects, such as the … Read more
Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more
Antibiotic resistance, which is a serious healthcare issue, emerges due to uncontrolled and repeated antibiotic use that causes bacteria to mutate and develop resistance to antibiotics. The Antibiotics Time Machine Problem aims to come up with treatment plans that maximize the probability of reversing these mutations. Motivated by the severity of the problem, we develop … Read more
We study proximity (resp. integrality gap), that is, the distance (resp. difference) between the optimal solutions (resp. optimal values) of convex integer programs (IP) and the optimal solutions (resp. optimal values) of their continuous relaxations. We show that these values can be upper bounded in terms of the recession cone of the feasible region of … Read more
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are adversarially perturbed. Notably, most existing statistical studies on this variant focus on recovering the ground truth and verifying the robustness of classical algorithms when the … Read more
For equality-constrained linear mixed-integer programs (MIP) defined by rational data, it is known that the subadditive dual is a strong dual and that there exists an optimal solution of a particular form, termed generator subadditive function. Motivated by these results, we explore the connection between Lagrangian duality, subadditive duality and generator subadditive functions for general … Read more
Section 2 of the Voting Rights Act (VRA) prohibits voting practices that minimize or cancel out minority voting strength. While this section provides no clear framework for avoiding minority vote dilution and creating minority-majority districts, the Supreme Court proposed the Gingles test in the 1986 case Thornberg v Gingles. The Gingles test provides three conditions … Read more