Risk-Aware Multi-Objective Optimization for AI Infrastructure Supply Allocation under Demand and Supplier Uncertainty

Suchuan Xing; Yihan Wang

doi:10.6911/

Authors

Suchuan Xing Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
Yihan Wang School of Engineering and Applied Science, The University of Pennsylvania, Philadelphia, PA 19104, USA

DOI:

https://doi.org/10.6911/

Keywords:

AI infrastructure, supply allocation, conditional value-at-risk, multi-objective optimization, stochastic programming, supply chain resilience, sustainable computing.

Abstract

Operators of AI infrastructure must commit accelerator procurement months before demand is known, from a supply base whose deliveries are themselves unreliable. Existing supply-allocation models optimize expected cost and treat service risk and environmental impact as constraints or afterthoughts, which hides the trade-off that actually drives capital decisions. This paper formulates AI-accelerator supply allocation as a two-stage risk-averse three-objective stochastic program that minimizes expected total cost, the conditional value-at-risk (CVaR) of the service-level shortfall, and expected carbon emissions, subject to minimum order quantities, all-units volume discounts, capital budgets and diversification limits, under jointly uncertain demand, fulfilment yield, correlated regional disruptions and lead-time slippage. Demand scenarios are generated from a moving-block bootstrap of a real two-month production GPU-cluster trace comprising 737,137 tasks. We solve the problem with RA-TGEA, a matheuristic that combines (i) an exact closed-form vectorized recourse evaluator, verified against linear programming to a maximum relative error of 1.9e-14, (ii) a direction-aware local search driven by an exact closed-form sub-gradient of the CVaR tail, and (iii) progressive scenario refinement with tail-preserving stratified reduction. On an exactly solvable instance, RA-TGEA attains 98.1% of the hypervolume of an epsilon-constraint MILP reference front while being roughly three orders of magnitude faster at producing a dense front. Against five state-of-the-art multi-objective evolutionary algorithms under an equal wall-clock budget, it improves hypervolume by 9.1% and 20.4% on the two larger instances (p = 0.014). Out of sample on 2,000 unseen scenarios, the risk-aware model reduces attainable tail shortfall by up to 36.1% relative to a deterministic expected-value plan at the same cost. A sensitivity study quantifies the price of resilience: halving the tail shortfall target from 0.10 to 0.05 costs 56 percentage points of additional expenditure.

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