### Title: A two-stage stochastic programming optimisation for sugar-ethanol-electricity production from sugarcane: a case study of Mauritius

Addresses: Department of Mathematics, Faculty of Science, University of Mauritius, Réduit, Mauritius ' Department of Mathematics, Faculty of Science, University of Mauritius, Réduit, Mauritius ' Department of Mechanical and Production Engineering, Faculty of Engineering, University of Mauritius, Réduit, Mauritius ' Department of Mechanical and Production Engineering, Faculty of Engineering, University of Mauritius, Réduit, Mauritius

Abstract: Sugarcane is an economically essential plant from which juice is extracted to produce raw sugar and molasses. The raw sugar can further be refined while the molasses can be fermented to manufacture ethanol. Other than cane juice, bagasse is another by-product of sugarcane which can be used to generate electricity and as a raw material to manufacture paper and chemicals. In this paper, we present a two-stage stochastic programming model to quantify the optimal amount of sugar, ethanol and electricity to be made from sugarcane so as to minimise total production cost. The model developed is based on variation of prices of sugar, ethanol and electricity and energy required to produce them. We establish the boundedness, convexity and existence of solution of the model. The latter is then applied to data available for Mauritius and solved using a genetic algorithm approach. We estimate the optimal amount of sugar, ethanol and electricity to be produced up to the year 2027. Finally, we analyse three different scenarios, namely decrease in land under sugarcane, increase/decrease in price of sugar and increase/decrease in price of ethanol.

Keywords: stochastic modelling; optimisation; genetic algorithms; sugarcane; stochastic differential equations; Mauritius; stochastic programming; sugar refining; ethanol; electricity production; case study; bagasse; total production cost; biofuels; land use; prices.

International Journal of Mathematical Modelling and Numerical Optimisation, 2016 Vol.7 No.1, pp.20 - 32