The research, conducted by Ajay D. Sarange of Swami Ramanand Teerth Marathwada University and Kishor Y. Ingale of Netaji Subhashchandra Bose Arts, Commerce, and Science College in Nanded, India, is notable less for any single technique than for the disciplined way it connects every stage of a data-to-decision pipeline. Seventeen city-zone load series from Laayoune, Boujdour, Foum El Oued, and Marrakech were converted to a common unit, aggregated into four city-level series, and aligned on shared thirty-minute timestamps spanning a full year, from January 2023 to January 2024. The result is an experimental aggregate demand portfolio of nearly half a million observations that the authors stress is methodological rather than physical: the cities are not electrically interconnected, and no claim is made that a single retailer serves them all.

The forecasting stage is deliberately conservative. Three candidate models, a persistence forecast, a seasonal-naive forecast lagged by one day, and a Random Forest, were compared using only chronological training and validation splits, with no shuffling that could leak future information. The Random Forest, fed nothing but the previous twelve hours of half-hourly loads, won selection on validation error and was then asked to produce recursive 96-period forecasts, equivalent to 48-hour horizons, in which its own predictions feed back into subsequent steps. Crucially, the held-out test data were never touched during model choice or scenario construction. Interestingly, the seasonal-naive method later achieved lower test-period error than the selected Random Forest, an outcome the authors report candidly; the scheduling contribution, they emphasise, is not forecasting superiority but the disciplined treatment of uncertainty.

That uncertainty enters through a moving-block bootstrap applied to validation-period forecast residuals. Rather than resampling isolated errors, which would destroy the short-term correlation that matters for scheduling, the method draws contiguous blocks of residuals, 51 half-hours long in this configuration, and adds them to the point forecast to generate 10,000 plausible demand trajectories. A KMeans clustering procedure then compresses this vast pool into one hundred representative scenarios, each an actual generated trajectory selected as nearest to a cluster centroid rather than an averaged profile that would artificially smooth peaks. The authors deliberately compared averaged centroids against these representative selections, finding that representatives better preserved variance and extreme peaks, a detail that matters enormously when the whole point is to prepare for demand spikes.

The decision model itself is a two-stage stochastic programme, a classic operations-research structure with a modern twist. Before demand is known, the scheduler commits to day-ahead procurement, demand-response capacity, and reserve capacity. After a demand scenario materialises, recourse actions kick in: dispatching the committed demand response, deploying reserves, absorbing modelled unmet demand as a penalised slack, or dumping surplus. The mathematics enforces non-anticipativity, meaning first-stage decisions cannot secretly depend on which scenario later occurs. Three variants were compared under identical operational assumptions: a risk-neutral stochastic programme, a Conditional Value-at-Risk formulation that penalises the worst five percent of cost outcomes, and a study-specific formulation dubbed PMAD-SP, which adds a penalty on the maximum periodwise absolute deviation of scenario costs from their mean.

The headline result is striking. Evaluated on a separately generated common set of 10,000 scenarios that played no role in building any policy, the stochastic programme reduced expected normalised cost by 12.72 percent relative to the deterministic benchmark, and slashed the model’s penalised unmet-demand quantity by 87.42 percent. The mechanism is intuitive: the deterministic plan, anchored to one forecast path, committed no reserve capacity at all, leaving it dangerously exposed whenever demand exceeded the forecast. The stochastic plan paid slightly more for day-ahead procurement and for reserves, roughly 71 kilowatts of expected reserve commitment versus zero, but that insurance premium paid for itself many times over when reality diverged from the point forecast.

The risk-aware variants tell more nuanced stories. The CVaR formulation added about 18 percent more reserve commitment than the risk-neutral model and nudged empirical upper-tail cost down by just 0.54 percent, a modest gain the authors attribute to the finite resolution of the hundred-scenario planning tail. PMAD-SP went much further on insurance, boosting reserve commitment by 137 percent, and achieved its real objective: it cut the standard deviation of scenario-total costs by nearly 40 percent while leaving expected cost essentially unchanged. The authors are careful to position PMAD-SP as descriptive cost-dispersion regularisation rather than formal distributionally robust optimisation, since it optimises against a fixed empirical distribution rather than an ambiguity set of possible distributions.

Sensitivity analyses probe the framework’s robustness. Because three of the four cities record current in amperes rather than power, the conversion to kilowatts required assumed values for voltage and power factor; testing nine combinations across 220 to 240 volts and power factors of 0.80 to 1.00 showed the stochastic programme’s advantage persisting in every case, with cost reductions ranging from 12.57 to 12.89 percent. Seven consecutive non-overlapping 48-hour historical windows also saw the stochastic policy win every time, a perfect record confirmed by an exact sign test, though the authors insist this evidence is descriptive because the windows share fitted models, calibration residuals, and adjacent chronology. Formal decision-value calculations reinforce the picture: the value of the stochastic solution amounts to 10.44 percent of the recourse problem’s optimal cost, while perfect foresight would be worth a further 3.67 percent.

The study is equally forthright about its limits. The single-node portfolio carries no network constraints, power flows, storage, renewables, or weather covariates; the cost coefficients are normalised experimental values rather than Moroccan tariffs; and the unmet-demand variable is a penalty-sensitive optimisation slack, not a measure of real blackouts. Reducing the hundred representative scenarios still discards nearly 48 percent of raw periodwise variance, and the risk weights were manually chosen rather than calibrated. Yet the core lesson survives these caveats intact and carries real weight for the energy transition. As smart meters proliferate across Africa, Europe, and beyond, the gap between forecasting demand and scheduling under demand uncertainty is where money is won or lost. This work shows, with unusual methodological transparency, that treating uncertainty as a first-class citizen of the optimisation problem, rather than an afterthought appended to a forecast, changes what a rational retailer buys, reserves, and dispatches, and by amounts large enough to matter.

Subject of Research: Scenario-based stochastic programming for electricity demand scheduling using smart-meter data

Article Title: Scenario based stochastic programming for aggregate electricity demand scheduling using Moroccan smart meter data

Article References: Sarange, A. D., & Ingale, K. Y. (2026). Scenario based stochastic programming for aggregate electricity demand scheduling using Moroccan smart meter data. Discover Informatics, 1(1), Article 19. https://doi.org/10.1007/s44564-026-00021-2

Image Credits: AI Generated

DOI: 10.1007/s44564-026-00021-2

Keywords: stochastic programming, smart meters, load forecasting, electricity demand scheduling, scenario generation, Conditional Value-at-Risk, Random Forest, Morocco, energy management, two-stage optimization, demand response, bootstrap