Stochastic Mixed-Integer Optimization of Dynamic Electricity Tariffs with Consumer Protection

Abstract

Day-ahead residential tariffs must be posted before demand is observed. Aggressive high prices can cut peaks in simulation, but they can also raise customer bills. This paper measures how much peak reduction is lost when a tariff design problem is required to keep revenue near a flat-tariff baseline and to limit bill increases. Using half-hourly data from 5,566 Low Carbon London households (167.8 million validated readings), we estimate quasi-experimental price response against the standard-tariff comparison group, form bootstrap demand scenarios, and solve stochastic mixed-integer programs with HiGHS. On all 73 eligible held-out test days, a segment-protected stochastic tariff reduces simulated peak demand by 2.29% on average (95% day-bootstrap CI [2.11, 2.48]), with revenue change -2.26% and mean worst-segment bill increase 2.48%. Removing the segment bill cap raises peak reduction only to 2.37%, while the worst segment bill increase rises to 6.81%: in this sample, substantial average protection costs little peak-shaving performance. The same schedules leave a household 95th-percentile bill increase of 8.61% (CVaR95 14.76%), so segment-average caps do not bound household tails. We report the full price-of-protection frontier under consistent household simulation and compare segment protection with a representative-household (tail-aware) variant: the latter cuts household p95 from 8.61% to 7.05% while changing mean peak reduction only from 2.29% to 2.28%. All optimized outcomes are model-based counterfactuals under an opt-in trial; wholesale costs are unavailable, so we do not optimize profit.

Preprint. Submitted to the 5th World Conference on Information Systems for Business Management (ISBM 2026), Bangkok, Thailand, 17-19 September 2026. Currently under peer review