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- Conditional Value at Risk (CVaR) as a risk measure to support industrial plant design and scheduling decisions under demand uncertaintyPublication . Vieira, Miguel; Paulo, Helena; Pinto-Varela, Tânia; Póvoa, Ana BarbosaMost 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.
- Assessment of financial risk in the design and scheduling of multipurpose plants under demand uncertaintyPublication . Vieira, Miguel; Paulo, Helena; Pinto-Varela, Tânia; Barbosa-Póvoa, Ana PaulaIndustrial companies are seeking for highly flexible strategic and operational solutions to face the requirements of current dynamic markets. The aim of this work is to provide a decision support assessment for the design and scheduling of a multipurpose plant under demand uncertainty, allowing the assessment of alternative risk profile solutions. A general two-stage mixed-integer linear programming (MILP) model is proposed with the goal to maximise the annualised profit of the plant operation under a set of scenarios while minimising the associated financial risk. Considering the long-term investment perspective, the Conditional Value at Risk (CVaR) measure is used to evaluate the likelihood that a specific loss or gain will exceed a certain value at risk. A bi-objective model is formulated using the augmented ε-constraint method to generate an approximation to the Pareto-optimal curve, illustrating the trade-offs between plant profit (with the corresponding design and scheduling decisions) and the associated financial risk. Addressing a set of propositions regarding a case-study, the conclusions highlight the advantages of the risk measure integration in support of the decision-making process, discussing the managerial insights in the assessment of diverse financial outcomes for the solution optimisation.
- Risk assessment for the design and scheduling optimization of periodic multipurpose batch plants under demand uncertaintyPublication . Vieira, Miguel; Paulo, Helena; Vilard, Corentin; Pinto-Varela, Tânia; Povoa, AnaThe aim of the present work is to provide an integrated decision support approach for the design and scheduling of multipurpose batch plants under demand uncertainty allowing the assessment of alternative risk profile solutions. Based on two-stage mixed integer linear programming (MILP) model, the goal is to maximize the annualized profit of the plant operation under a set of scenarios while minimizing the associated financial risk, evaluated by the Conditional Value at Risk (CVaR) using the augmented ε-constraint method. Considering a literature example, the conclusions highlight the advantages of the proposed approach for the decision-support in industrial plant design and scheduling solutions by considering the explicit risk measure assessment towards expected financial outcomes.