We consider multistage stochastic mixed-integer programs M-SMIPs, and show that these problems are asymptotically convex. That is, we show that the expected cost-to-go functions in the problem converge to convex functions as the variability of the random parameters in the model increases. To derive this result, we first propose a novel adapted Gomory relaxation for … Read more
Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
Facility location decisions are typically made before demand is fully known, yet most applied studies solve a single deterministic model using expected or nominal demand. This paper formulates and solves a capacitated facility location problem using a real academic benchmark instance, then extends it to a two-stage stochastic program in which facility-opening decisions are made … Read more
We develop a novel Dantzig-Wolfe (DW) decomposition algorithm for monotone two-stage stochastic mixed-integer programs (SMIPs). The key novelty in this algorithm is to relax the non-anticipativity constraints (NACs) in line with the monotonicity in the problem. We prove (i) that the relaxed restricted master problem (RMP) faster identifies dominated columns that cannot improve the RMP … Read more
We present an open-source software package that implements a provably convergent Benders-type decomposition algorithm for multistage stochastic integer programs. In addition to standard cut families, such as Benders, strengthened Benders, and Lagrangian cuts, the algorithm incorporates rectified linear unit (ReLU) cuts, which provide convergence guarantees for general mixed-integer state variables. However, the dual problems used … Read more
This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more
We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more
Dynamic dispatch networks in logistics and transportation require real-time, constraint-aware decision-making under stochastic demand. This paper bridges mathematical optimization, optimal control theory, and reinforcement learning by establishing non-asymptotic theoretical guarantees for learning-based optimal control in constrained stochastic dispatch systems. We formulate the problem as a constrained Markov decision process, enforce feasibility via a projection-based policy … Read more
In this paper, we address the Capacitated Vehicle Routing Problem with Stochastic Demands (CVRPSD), in which routes are planned a priori and recourse actions are performed to ensure demand fulfillment. These recourse actions are defined through policies and may include replenishment trips or demand backlogging subject to penalties. We develop the first family of pseudo-compact … Read more
Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing … Read more