An Optimization-Based Framework for Process Planning under Uncertainty with Risk Management

In the current challenging and volatile political and economic environment, the process industry is exposed to a high degree of uncertainty that renders the production planning task to be a risky and complex optimization problem requiring high computational expense. This work proposes a computationally-tractable optimization-based framework for risk management in midterm process planning under uncertainty. We employ stochastic programming to account for the uncertainty in which a scenario-based approach is used to approximate the underlying probability distribution of the uncertain parameters. The problem is formulated as a recourse based two-stage stochastic program that incorporates a mean-risk structure in the objective function. Two risk measures are applied, namely Value-at-Risk (VaR) and Conditional Value-at Risk (CVaR). However, since a large number of scenarios are often required to capture the stochasticity of the problem, the model suffers from the curse of dimensionality. To circumvent this problem, we propose a computational procedure with a relatively low computational burden that involves the following two major steps. First, a linear programming (LP) approximation of the risk-inclined version of the planning model is solved for a number of randomly generated scenarios. Subsequently, the VaR parameters of the model are simulated and incorporated into a mean CVaR stochastic LP approximation of the risk-averse version of the planning model. The proposed approach is implemented on a petroleum refinery planning case study with satisfactory results that demonstrate how solutions with relatively affordable computational expense can be attained in a risk-averse model in the face of uncertainty. Future work will mainly involve extending the approach to a multiobjective formulation as well as for mixed-integer optimization problems.