We study the convex hull obtained after deleting prescribed vertices from the binary cube. The analysis separates three regimes according to the number of deleted vertices. When this number is fixed, both the original-space facet count and the linear extension complexity remain linear in the ambient dimension, up to constants depending only on the number … Read more
We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more
We consider mixed-integer linear-quadratic generalized Nash equilibrium problems, i.e., games in which each player solves a mixed-integer program subject to linear constraints in her own and rivals’ strategies as well as an objective which is quadratic in her own strategies and bilinear in her own and rivals’ strategies. For this class of games, we study … Read more
This paper proposes BPCOL+, an exact branch-and-price algorithm for the Graph Coloring Problem. The algorithm is both novel and highly effective, integrating enhanced pricing strategies within Zero-Suppressed Binary Decision Diagrams (ZDDs) to efficiently solve the pricing problem associated with the maximal-stable-set-based set-covering formulation. After computing upper and lower bounds at the root node using heuristic … Read more
This paper develops exact solution methods for the maximum mortality rate clique problem, which aims to identify a cluster of diseases in a comorbidity graph associated with the highest mortality rate among patients whose healthcare encounters are recorded in electronic health records. We establish the NP-hardness of the problem and propose two mixed-integer linear programming … Read more
We present a two-stage stochastic programming model for scheduling anesthesiologists to operating rooms under uncertainty in surgery durations. The proposed model takes a relief order to balance anesthesiologists’ workload as input and captures the trade-offs between anesthesiologist relief times, handoffs and under-staffing. To address the computational challenges of solving the proposed model, we derive supervalid … Read more
In this study, we explore how the domain of objective function values for challenging integer programs can be reduced and whether such a reduction can improve the solution process. Our work is motivated by binary search, a technique that efficiently narrows a search space by repeatedly halving it through feasibility checks. Building on this idea, … Read more
Lagrangian relaxation is a well-established technique for deriving strong bounds in single-objective discrete optimization. Its generalization to the multiobjective setting is not straightforward, as preserving the multiobjective structure leads to bound sets rather than scalar bounds. Recent studies show the existence of Lagrange multipliers that can yield tighter bound sets than those obtained from convex … Read more
The binary reflected Gray code orders the vertices of the unit hypercube along a Hamiltonian path in which consecutive vertices differ in exactly one coordinate. While Gray codes have been extensively studied from a combinatorial perspective, much less is known about the polyhedral structure of convex hulls of contiguous subpaths of this order. This paper … Read more