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Robust optimization
Distributional robust optimization
Robust integer optimization
Robust combinatorial optimization
Robust machine and deep learning
Robust control problems
Organizers: Ahmadreza Marandi (TU Eindhoven) and Jannis Kurtz (University of Amsterdam)
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We study a robust contract design problem with deferred inspection, in which a principal allocates a scarce resource to an agent, observes the agent’s realized outcome ex post at negligible cost, and conditions transfers on this information through rewards. The principal faces ambiguity about the agent’s value distribution and seeks to maximize worst-case expected revenue subject to incentive compatibility and limited liability. In contrast to existing work on inspection mechanisms, which relies on common-prior assumptions, we adopt a distributionally robust approach based on moment information. Our main contribution is a clear characterization of the robust contract design problem with a single agent. When the ambiguity set is defined by the first moment, we identify a robustly optimal contract with a concave allocation rule and a linear payment rule. We further show that robustness does not uniquely pin down transfers: we construct a Pareto robustly optimal contract that preserves the same allocation while extracting maximal feasible payments from all types, yielding strictly higher expected revenue under non-worst-case distributions. We also derive structural results for multi-agent extensions. For ambiguity sets defined by the first N moments, we show that robust optimality requires aggregate payments to be lower bounded by a multi-dimensional polynomial of degree N. However, unlike the single-agent case, robust multi-agent mechanisms are substantially more complex: dominant-strategy incentive compatibility becomes necessary, simple monotone mechanisms are no longer tractable, and worst-case distributions may involve correlated types or degenerate to a Dirac distribution at the mean. These results highlight a sharp contrast between robust contract design and robust multi-agent mechanism design with inspection.
Bio:
Halil İbrahim Bayrak is a postdoctoral researcher in the Chair of Decision Sciences and Systems at the Technical University of Munich. His research sits at the intersection of robust optimization and mechanism design, with a focus on decision-making under uncertainty for allocation, inspection, and pricing. He develops tractable, implementable models, e.g., allocation, payment, and inspection policies, that remain reliable under limited data. He earned a PhD in Industrial Engineering from Bilkent University (2022) and was a visiting researcher at the University of Pennsylvania.
Abstract:
We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We model retailer demand as random variables with uncertain distributions belonging to a moment-based ambiguity set. We develop a distributionally robust optimization formulation that minimizes the worst-case expected cost over the ambiguity set, while ensuring service reliability through a distributionally robust chance constraint. Our main results are that we prove that the worst-case expected inventory cost is attained under a multi-point distribution, which can be identified a posteriori via linear programming, and that the distributionally robust chance constraint can be reformulated into equivalent deterministic forms. This yield a deterministic reformulation of the original problem. To solve it, we design a nested branch-and-price framework, in which the first level partitions retailers into clusters, and the second level concerns routing and replenishment decisions within each cluster. Computational experiments on both synthetic instances and real-world data from SAIC Volkswagen Automobile Co., Ltd. demonstrate the effectiveness and efficiency of the proposed approach.
Menglei Jia is an Associate Professor in the School of Maritime Economics and Management at Dalian Maritime University. She received her Ph.D. from the Antai College of Economics and Management, Shanghai Jiao Tong University, and was a visiting Ph.D. researcher in the Operations, Planning, Accounting and Control (OPAC) Group at Eindhoven University of Technology. Her research lies at the intersection of Operations Research, Machine Learning, and Data Science, with a focus on intelligent decision-making under uncertainty. She develops data-driven and optimization-based methodologies to address complex challenges in transportation and logistics systems.