Title: Monotone Comparative Statics and Discrete Convexity
Speaker: Dr. Menglong Li
Decision Analytics and Operations, City University of Hong Kong
Time:2025年4月25日 上午10:00
Place:管理科研楼第二教室
Many operations management problems involve substitute structures, leading to parametric optimization models that maximize submodular objective functions. Deriving structural properties like monotone comparative statics of optimal solutions or submodularity preservation under optimization is crucial but challenging, as classical lattice programming results for supermodular objective maximization do not apply. Using M-natural-convexity from discrete convex analysis, we identify conditions for nonincreasing optimal solutions and submodularity preservation in parametric maximization models with submodular objectives and develop new M-natural-convexity properties. We introduce S-convexity with M-natural-convexity as a subclass, extending M-natural-convexity results to continuous S-convexity. We also show S-convex functions are a supermodular function subclass and present a new preservation property not found in M-natural-convexity. Our theoretical findings are applied to various operations models, including multi-product inventory, assemble-to-order, production control, portfolio contract, discrete choice, and random yield inventory models. Analyzing these models through M-natural-convexity and S-convexity simplifies and unifies complex literature proofs, facilitates monotone comparative statics analysis, and generalizes results.
Bio:
Prof. Menglong Li is an Assistant Professor of Decision Analytics and Operations in the College of Business, City University of Hong Kong. Before joining CityU, he was a postdoctoral associate of MIT Institute for Data, Systems, and Society. He received a PhD degree in Operations Research from the University of Illinois at Urbana-Champaign, an MS degree in Mathematics from the University of Pierre and Marie Curie and a BS degree in Mathematics from Tsinghua University. His research interests include inventory management, revenue management, (discrete) convex analysis, combinatorial optimization, approximation algorithms, and data-driven decision-making.