Formulating a deterministic equivalent of stochastic programming in describing behaviour of oil prices and demand uncertainty

Abstract

Recently, the fluctuations of oil prices and unstable product demands resulting in disruption at procurement, production, and inventory stages have led to increased awareness among managers and decision-makers to include uncertainty in the refinery planning. Among the most prominent approach in handling optimization under uncertainty is stochastic programming. However, it is critical and challenging to construct a representation of random variables that describe the uncertainty behaviour. Thus, this study proposes the model and forecasting of oil prices and petroleum products demand under uncertainty to incorporate Hurst parameter values and structural break approach as input parameters to the stochastic programming. In modelling oil price, the 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. The Hurst parameter, connected to the fractional differencing parameter, was used to characterize the long memory process. The time series will be modelled and forecasted based on the Hurst value, and stochastic differential equations will be explored to analyze the uncertainty of oil prices. Meanwhile, the Holt-Winter method is adopted to describe the uncertainties of petroleum product demand. The result indicates that Geometric Brownian Motion (GBM) and mean-reverting Ornstein-Uhlenbeck (OU) are accurate forecast models to forecast future oil prices, and Holt-Winter seasonal method is an accurate model to forecast future petroleum products demand due to mean absolute percentage error (MAPE) value is less than 10. Thus, we conclude that the coherent probabilistic scenario can then be constructed with this stochastic model framework to formulate a deterministic equivalent of stochastic programming.