We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible with probability at least $1{-}\alpha$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a modified high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent’s kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios under realistic execution. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and scales better with higher numbers of robots without compromising the solution quality across a variety of environments.

A centralized multiechelon, multiproduct supply chain network is presented in a multiperiod setting with products that show varying demand against price. An important consideration in such complex supply chains is to maintain system performance at high levels for varying demands that may be sensitive to product price. To examine the price-centric behavior of the customers, the concept of price elasticity of demand is addressed. The proposed approach includes many realistic features of typical supply chain systems such as production planning and scheduling, inventory management, transportation delay, transportation cost, and transportation limits. In addition, the proposed system can be extended to meet unsatisfied demand in future periods by backordering. Effects of the elasticity in price demand in production and inventory decisions are also examined. The supply chain model is formulated as a convex mixed-integer nonlinear programming problem. Reformulations are presented to make the problem tractable. The differential equations are reformulated as difference equations, and unbounded derivatives in the nonlinear objective function are handled with an approximation, with guaranteed bounds on the loss of optimality. The approach is illustrated on a multiechelon, multiproduct supply chain network.