Stochastic optimisation model of oil refinery industry and uncertainty quantification in scenario tree of pricing and demand

Abstract

Uncertainties in oil prices and product demands affect oil refinery industry profits. The fluctuations in oil prices and unstable product demands result in disruptions at procurement, production, and inventory stages. This issue has increased awareness among managers and decision-makers to include uncertainty characteristics in refinery planning. Stochastic programming is an approach to optimising the profit of oil refineries under uncertainty. A crucial assumption for this approach is the use of scenario trees to characterise the probability distribution of the underlying stochastic process. However, there are limited studies on accurate forecast methods to generate scenario trees with low error. The existing stochastic programming approaches do not include uncertainty quantification of stochastic parameters with an accurate forecast model. Thus, this study has developed a framework to formulate uncertainty quantification of stochastic parameters in a stochastic programming model. In modelling oil price dynamics, information on whether the structural break exists is crucial due to the long memory property that might be camouflaged by the existence of the structural break. In this study, oil prices are modelled and forecasted based on the hurst value, and stochastic differential equations are explored to analyse the uncertainty of the time series. Meanwhile, the Holt-Winter method is adopted to describe the uncertainties of petroleum product demand with seasonal variation. The long memory analysis for the before-break and after-break series did not present similar results, which confirmed that the returns of oil prices did not possess true long memory during this period. The results indicate that Geometric Brownian Motion (GBM) and mean-reverting Ornstein-Uhlenbeck (OU) are accurate forecast models to represent future oil prices. It is found that the Holt-Winter seasonal method is an accurate model to represent future petroleum products demand as its mean absolute percentage error (MAPE) value is less than 10. The study obtained 64 scenarios for oil price uncertainty and 32 scenarios for product demand uncertainty as an effective scenario tree for the input of stochastic programming. This newly developed stochastic programming with uncertainty quantification gained 9% more profit than the stochastic programming based on expert judgment, amounting to approximately USD 269,000 per day (~USD 98 million per year). Thus by incorporating uncertainty quantification of stochastic parameters in stochastic programming, more profit could be gained compared to that using stochastic programming based on an expert judgement approach. This new method would also be able to capture more information in managing the supply and demand of petroleum products. The optimal process flow rate in the oil refinery and the amount of shortfall and surplus petroleum finish products in every possible scenario could be determined so the management could plan for future events. Future work for this study could apply more general techniques and reasonable estimates for the distribution of stochastic parameters. Matching the first four statistical moments such as mean, variance, skewness, and kurtosis that are sufficient to explain the characteristics of the uncertain parameters could also be considered.