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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, TĆ¢nia; PĆ³voa, 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.
- Designing integrated biorefineries supply chain: combining stochastic programming models with scenario reduction methodsPublication . Paulo, Helena; Cardoso, Teresa; Relvas, Susana; Barbosa-Povoa, AnaThis paper addresses the design and planning of integrated biorefineries supply chain under uncertainty. A two-stage stochastic mixed integer linear programming (MILP) model is proposed considering the presence of uncertainty in the residual lignocellulosic biomass availability and technology conversion factors. Nevertheless, when the scenario tree approach is applied to a large real world case study, it generates a computationally complex problem to solve. To address this challenge the present paper proposes the improvement of the scenario tree approach through the use of two scenario reduction methods. The results illustrate the impact of the uncertain parameters over the network configuration of a real case when compared with the deterministic solution. Both scenario reduction methods appear promising and should be further explored when solving large scenario trees problems.
- Assessment of financial risk in the design and scheduling of multipurpose plants under demand uncertaintyPublication . Vieira, Miguel; Paulo, Helena; Pinto-Varela, TĆ¢nia; Barbosa-PĆ³voa, 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 Īµ-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, TĆ¢nia; 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 Īµ-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.
- Supply chain optimization of residual forestry biomass for bioenergy production: the case study of PortugalPublication . Paulo, Helena; Azcue, Xavier; Barbosa-PĆ³voa, Ana P.; Relvas, SusanaWithin a large set of renewable energies being explored to tackle energy sourcing problems, bioenergy can represent an attractive solution if effectively managed. The supply chain design supported by mathematical programming can be used as a decision support tool to the successful bioenergy production systems establishment. This strategic decision problem is addressed in this paper where we intent to study the design of the residual forestry biomass to bioelectricity production in the Portuguese context. In order to contribute to attain better solutions a mixed integer linear programming (MILP) model is developed and applied in order to optimize the design and planning of the bioenergy supply chain. While minimizing the total supply chain cost the production energy facilities capacity and location are defined. The model also includes the optimal selection of biomass amounts and sources, the transportation modes selection, and links that must be established for biomass transportation and products delivers to markets. Results illustrate the positive contribution of the mathematical programming approach to achieve viable economic solutions. Sensitivity analysis on the most uncertain parameters was performed: biomass availability, transportation costs, fixed operating costs and investment costs. (C) 2015 Elsevier Ltd. All rights reserved.