Stochastic optimization models for energy-resilient supply chains: mitigating cost shocks in Nigerian MSMEs using scientific machine learning

Abstract

Nigerian micro, small and medium-sized enterprises (MSMEs) absorb energy cost shocks with almost no financial buffer. This paper develops a stochastic optimization framework that links published national energy prices to enterprise investment decisions. Using twenty-nine months of official pump price data covering January 2024 to May 2026, we compare four candidate price processes by maximum likelihood estimation. A Merton jump-diffusion process is selected by the Akaike, corrected Akaike and Bayesian information criteria, and the jump term is supported by a boundary-aware parametric bootstrap, whereas mean reversion is not detected, so that for this sample price shocks appear largely permanent rather than temporary. The diffusive drift is statistically indistinguishable from zero, and the jump component accounts for essentially the whole of the estimated log-price drift of 0.373 per year. We embed the fitted process in a two-stage stochastic program with a mean and conditional value-at-risk objective and an energy-balance merit-order recourse, and we add two scientific machine learning components, namely a grey-box drift model and a deep recourse operator. Optimal solar and storage investment reduces the expected annual energy cost of a representative enterprise by 42.8 per cent and the conditional value-at-risk of its operating cost by 86.1 per cent. The shadow price of investment capital reaches about 2.67 naira per naira invested, which shows that, within the model, finance rather than technology or tariff policy is the binding constraint. The learned recourse operator reproduces expected cost to within about one per cent and conditional value-at-risk to within about two and a half per cent, while running about one hundred times faster.