Convex maximization arises in many applications but is generally NP-hard, even for low-rank objectives. This paper introduces a set of broadly applicable conditions that certify when such problems are polynomially solvable. Our main condition is a new property of the feasible set, which we term co-monotonicity. We show that this property holds for two important … Read more
This paper addresses an operational planning challenge in two-tier robotized sorting systems (T-RSS), an emerging alternative to traditional conveyor-based sorting in e-commerce delivery stations. Designed to be compact and space-efficient, T-RSS use an upper tier to sort parcels from loading stations to drop-off points, which connect to roll containers on a lower tier where parcels … Read more
When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For … Read more
Capacity Planning problems are a class of optimization problems used in diverse industries to improve resource allocation and make investment decisions. Solving real-world instances of these problems typically requires significant computational effort. To tackle this, we propose machine-learning-aided column generation methods for solving large-scale capacity planning problems. Our goal is to accelerate column generation by … Read more
This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more
This work addresses the Close-Enough Traveling Salesman Problem (CETSP), a variant of the classic traveling salesman problem in which we seek to visit neighborhoods of points in the plane (defined as disks) rather than specific points. We present two exact formulations for this problem based on second-order cone programming (SOCP), along with approximated mixed-integer linear … Read more
In this paper, we propose an extension of the classical weight reduction inequalities for the binary knapsack polytope for settings where the maximum-weight item in the associated pack is not unique. We derive sufficient conditions under which the extended inequalities are facet-defining and identify conditions under which they strictly dominate the original weight reduction inequalities. … Read more
In Tower Defense (TD) games, the objective is to defend a specific point on the game map from mobile units by constructing towers with offensive capabilities. In this work, we focus on Bloons Tower Defense (Bloons TD), one of the earliest and most prominent TD games. We show that the problem of finding tower configurations … Read more
In many retail industries, the retailer can choose the inventory location or fulfillment center (FC) that fulfills an order, yielding opportunities for inventory pooling and product selection expansion. However, fulfillment decisions are complex and must consider cost and speed, among various factors. With the unprecedented growth of the retail industry, companies must look for strategies … Read more
We study the Heilbronn triangle problem, which involves placing \(n\) points in the unit square such that the minimum area of any triangle formed by these points is maximized. A straightforward maximin formulation of this problem is highly non-linear and non-convex due to the existence of bilinear terms and absolute value equations. We propose two … Read more