Conditional Value at Risk (CVaR) as a risk measure to support industrial plant design and scheduling decisions under demand uncertainty

Most decisions related to industrial plant design and scheduling, that strongly influences the the financial performance of a company, are taken in a complex environment under uncertainty. Mathematical modelling has been used to solve those problems considering stochastic programming, provinding an expected objective value which does not allow control over critical probability outcomes. Therefore, the risk assessment can integrate the trade-offs between the given objective and the risk profile of the decision maker. Conditional Value at Risk (CVaR) has demonstrated to be an effective risk metric, though its application in the problems in study is sparse and the influence of the stochastic parameters is often not fully characterized. To address this problem, a two stage stochastic Miexd Integer Linear Programming model that considers the design and scheduling of a multipurpose batch plant is used. A bi-objective optimization approach maximizes the profite while minimizing the risk using the e-constraint method. The generated Pareto curve is a valuable tool to support the decision-making process, with information about the different possible solutions in terms of profit and respective risk profiles under demand uncertainty. The CVaR dependence of the nature of the stochastic parameters through different scenarios trees is also explored.