Optimization under Uncertainty for Supply Chain and Logistics Management

Supply chains and logistics networks are complex, multi-actor systems in which decisions at every level—strategic, tactical, and operational—are affected by pervasive uncertainty. This thesis addresses three distinct problems arising in supply chain and logistics management under uncertainty, each tackled with a different combination of methodologies, reflecting the diverse nature of the problems considered. The problems are organized around two operational contexts in which uncertainty plays a central and mathematically challenging role. The first is the procurement and planning domain: effective purchase decisions require accounting for lead time variability, since delays in supplier deliveries directly translate into excess inventory costs or unmet demand. The second is traffic congestion under uncertain demand: road networks are the physical backbone of supply chains, and congestion inflates lead times, increases logistics costs, and introduces delivery variability that propagates upstream through the entire supply chain. Understanding and managing uncertainty in both domains is therefore essential for building resilient and cost-efficient supply chain operations. In particular, the first contribution concerns supplier selection and purchase planning under lead time uncertainty. A buyer must decide which suppliers to activate and how much to order in each period, before actual delivery delays are known, so as to minimize worst-case total costs—purchase prices, fixed ordering fees, inventory holding, and backlogging penalties. We model the problem as a two-stage robust optimization problem over a structured uncertainty set that captures both a budget on the total number of late deliveries and temporal correlations across consecutive orders from the same supplier. Two solution methods are proposed: an exact branch-and-cut algorithm based on a Benders-like reformulation, and a horizon-split heuristic for large instances. A comprehensive computational study reveals managerial insights on procurement strategies and the cost of robustness. The second contribution studies worst-case traffic congestion under demand uncertainty. We formulate a bilevel optimization model in which a traffic planner maximizes congestion by selecting the origin–destination demand vector, while travelers respond by routing themselves according to Wardrop equilibrium principles—either the user equilibrium or the system optimum. Three families of uncertainty sets are considered: budgeted, ellipsoidal, and hose. The bilevel problem is reformulated as a mixed-integer nonlinear program via KKT optimality conditions, and several strengthening techniques are developed. Computational experiments on the Sioux Falls network and SNDlib instances demonstrate the effectiveness of the approach and provide insights into the impact of different congestion measures and uncertainty models. The third contribution presents a complete, reproducible data pipeline for city-scale travel demand modelling, implemented in the MATSim agent-based simulation framework for the city of Barcelona. The pipeline synthesizes population, network, and multi-modal transport demand from open-access statistical data, and is calibrated and validated against observed mobility statistics. The resulting simulator serves as both an empirical foundation for the uncertainty sets used in the congestion model and a testbed for evaluating urban mobility and logistics interventions.