In mathematical optimization, we want to find the best possible solution for a decision-making problem. Curiously, these problems are harder to solve if they have discrete decisions. Imagine that you would like to buy chocolate: you can buy no chocolate or one chocolate bar, but typically you cannot buy just half of a bar. Now … Read more
To meet sustainability goals and regulatory requirements, transit agencies worldwide are planning partial and complete transitions to electric bus fleets. This paper presents the first comprehensive and computationally efficient multi-period optimization framework integrating the key planning decisions necessary to support such electrification initiatives. Our model, formulated as a two-stage integer program with integer subproblems, jointly … Read more
In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more
Given a set of train routes with route costs and a set of compatible route pairs with pairing costs, the Train Single-Routing Selection Problem (TSRSP) seeks to assign one route to each train, minimizing the total cost while ensuring pairwise compatibility among the selected routes. This problem is of significant practical relevance in rail traffic … Read more
This study addresses the problem of minimizing the weighted completion time variance (WCTV) in single-machine scheduling. Unlike the unweighted version, which has been extensively studied, the weighted variant introduces unique challenges due to the absence of theoretical properties that could guide the design of efficient algorithms. We propose a mathematical programming framework based on a … Read more
We propose a novel facial reduction algorithm tailored to semidefinite programming relaxations of combinatorial optimization problems with quadratic objective functions. Our method leverages the specific structure of these relaxations, particularly the availability of feasible solutions that can often be generated efficiently in practice. By incorporating such solutions into the facial reduction process, we substantially simplify … 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
Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our algorithm has an approximation ratio of at most the sparsity constant with high probability, if called enough times. Under a … Read more
Implied-integer detection is a well-known presolving technique that is used by many Mixed-Integer Linear Programming solvers. Informally, a variable is said to be implied integer if its integrality is enforced implicitly by integrality of other variables and the constraints of a problem. In this work we formalize the definition of implied integrality by taking a … Read more
This paper presents scalable algorithms for computing pure Nash equilibria (PNEs) in large-scale integer programming games (IPGs), where existing exact methods typically handle only small numbers of players. Motivated by a county-level aquatic invasive species (AIS) prevention problem with 84 decision makers, we develop and analyze random-restart best-response dynamics (RR-BRD), a randomized search framework for … Read more