Relaxed joint chance constraints with surrogate tail bounds

Many applications in power systems, supply chains, and transportation involve uncertain outcomes and optimisation decisions over multiple time periods while requiring high reliability. Joint chance constraints (JCC) enforce strict reliability but are overly conservative, while single chance constraints (SCC) offer flexibility at the cost of performance. We propose a relaxed JCC formulation that allows a controlled number of period violations for most scenarios, balancing reliability and flexibility while capturing inter-temporal correlations. Under finite support, we derive an exact deterministic reformulation and a tractable surrogate using tail bounds. Experiments on wind data from the European Meteorological (EMHIRES) dataset show that the relaxed JCC formulation delivers significant objective improvement without compromising reliability, with the surrogate delivering substantial computational gains.

Arjun Ramachandra is an Assistant Professor in the Decision Sciences area at the Indian Institute of Management (IIM) Bangalore. His research focuses on optimisation under uncertainty, spanning distributionally robust optimisation, chance constrained optimisation, correlation gap analysis, and data-driven tail risk estimation, with an emphasis on deriving tractable optimisation formulations and performance guarantees for complex decision problems. He holds a joint PhD in Operations Research the Singapore University of Technology and Design and National University of Singapore, along with an integrated master’s degree in mathematics and computing from the Indian Institute of Technology (IIT) Kharagpur. Outside work, he enjoys writing, music, meditation, and spending time with family.

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