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Reverse osmosis (RO) has shown itself to be a viable technology for the treatment and minimization of industrial and domestic wastewater streams. The current research presents a deterministic branchand-bound global optimization-based algorithm for the solution of the reverse osmosis network (RON) synthesis problem. The mathematical programming model describes the RON through nonconvex mixedinteger nonlinear programs (MINLPs). A piecewise mixed-integer linear program (MILP) is derived based on the convex relaxation of the nonconvex terms present in the MINLP formulation to approximate the original nonconvex program and to obtain a valid lower bound on the global optimum. The MILP model is solved at every node in the branch-and-bound tree to verify the global optimality of the treatment network within a pre-specified gap tolerance. Several constraints are developed to simultaneously screen the treatment network alternatives during the search, tighten the variable bounds, and consequently accelerate algorithm convergence. Water desalination is considered as a case study to illustrate the global optimization of the RO network.

Production planning in the petrochemical industry requires a model that can account for the different interactions, needs, and features and provide at the same time suitable mathematical representation. In this work, a model with an environmental objective is presented. The system is formulated as a mixed-integer linear programming model where new value-added products are produced from the basic feedstock chemicals. From the superstructure of the technology alternatives, the optimal set of processes is selected with the objective function of sustainability. The quest for pollution prevention and increased pressure and demand for environmental considerations makes sustainability an important objective function. In this study, sustainability is quantified by a health index of the chemicals and increasing profit represented by processadded value. The model is applied to the case study of planning the development of the Kuwait petrochemical industry. Results give an optimal structure for the development and prove that simple indicators can represent sustainability, giving good results in selecting environmentally friendly processes and at the same time being profitable.

This paper considers the problem of reducing CO2 emissions from a power grid consisting of a variety of power-generating plants:  coal, natural gas, nuclear, hydroelectric, and alternative energy. The problem is formulated as a mixed integer linear program (MILP) and implemented in GAMS (General Algebraic Modeling System). Preprocessing and variable elimination strategies are used to reduce the size of the model. The model is applied to an existing Ontario Power Generation (OPG) fleet analyzed under three different operating modes:  (1) economic mode, (2) environmental mode, and (3) integrated mode. The integrated mode combines the objectives of both the economic and environmental modes through the use of an external pollution index as a conversion factor from pollution to cost. Two carbon dioxide mitigation options are considered in this study:  fuel balancing and fuel switching. In addition, four planning scenarios are studied:  (1) a base-load demand, (2) a 0.1% growth rate in demand, (3) a 0.5% growth rate in demand, and (4) a 1.0% growth rate in demand. A sensitivity analysis study is carried out to investigate the effect of parameter uncertainties such as uncertainties in natural gas price, coal price, and retrofit costs on the optimal solution. The optimization results show that fuel balancing can contribute to the reduction of the amount of CO2 emissions by up to 3%. Beyond 3% reductions, more stringent measures that include fuel switching and plant retrofitting have to be employed. The sensitivity analysis results indicate that fluctuations in gas price and retrofit costs can lead to similar fuel-switching considerations. The optimal carbon dioxide mitigation decisions are found, however, to be highly sensitive to coal price.

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