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
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
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 consider a two-stage optimization problem with sparsity constraints, motivated by a common challenge in packaging logistics: minimizing the volume of transported air by optimizing the size and number of available packaging boxes, given the demand for order items. In the first stage, we select the optimal dimensions of the boxes, while in the second … Read more
We develop a unified framework for robust nonsmooth optimization problems with equilibrium constraints (UNMPEC). As a foundation, we study a robust nonsmooth nonlinear program with uncertainty in both the objective function and the inequality constraints (UNP). Using Clarke subdifferentials, we establish Karush–Kuhn–Tucker (KKT)–type necessary optimality conditions under an extended no–nonzero–abnormal–multiplier constraint qualification (ENNAMCQ). When the … Read more
Transportation network design, or the problem of optimizing infrastructure for a societal goal, subject to individual travelers optimizing their behavior for their own preferences arises frequently in many contexts. However, it is also an NP-hard problem due to the leader-follower or bi-level structure involving a follower objective that is different from yet significantly affects the … Read more
Large language models (LLMs) trained with reinforcement learning from human feed- back (RLHF) struggle with complex instructions that bundle multiple, potentially con- icting requirements. We introduce constraint decomposition, a framework that separates multi-objective instructions into orthogonal componentssemantic correctness, structural organization, format specications, and meta-level requirementsand optimizes each in- dependently before hierarchical combination. Our approach addresses … Read more
Benders’ decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be applied in a BD framework, one central technique has not been applied systematically in BD: symmetry handling. The main reason for this … Read more
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise linear approximations of the standard normal cumulative density function. We show that $O\left(\sqrt{\ln(1/\tau)/\tau} \right)$ pieces are sufficient to attain $\tau$-accuracy in the chance constraint. … Read more
This survey proposes a unifying conceptual framework and taxonomy that systematically integrates Machine Learning (ML) and Reinforcement Learning (RL) with classical paradigms for Constraint Satisfaction and Boolean Satisfiability solving. Unlike prior reviews that focus on individual applications, we organize the literature around solver architecture, linking each major phase—constraint propagation, heuristic decision-making, conflict analysis, and meta-level … Read more