Mixed integer multi-objective

In this paper, we extend the work of [10] by simultaneously considering minimization of the total utility consumption, maximization of operational flexibility to source-stream temperatures, and even minimum number of matches as multiple design objectives. The flexible HEN synthesis problem is thus formulated as the one of multi-objective mixed-integer linear programming (MO-MILP). This formulation also assumes that the feasible region in the space of uncertain input parameters is convex, so that the optimal solution can thus be explored on the basis of the vertices... 

A product will thus be designed by considering molecular composition and conformation for its end-use value as well as process options for minimal by-products and wastes. This sort of integrated product and process design may require the formulation and analysis of multi-objective nonlinear mixed integer systems of very large scale and complexity. 

Multi-objective linear programming (MOLP) Multi-objective stochastic integer linear programming Interactive MOLP Mixed 0-1 MOLP... 

The economic objective, Fi, is measured by the total CLSC cost, including total material purchasing cost (PC), total installation cost (BC), total production cost (MC), total capacity expansion cost (CEC), total transportation cost (TC), and total disposal cost (DC). The environmental objective, F2, is measured by the total carbon (CO2) emission, including total production carbon emission (PCOE), total installation carbon emission (BCOE), and total transportation carbon emission (TCOE) in all the CLSC. For a MCSCD problem, we also need to consider material supply constraints, flow conservation constraints, capacity expansion and limitation constraints, and transportation constraints. Consequently, the MCSCD problem may be formulated as a multi-objective mixed integer programming model. 

Based on the given probabilities of success for each potential product, the problem is then to find the optimal product portfolio and investment decisions together with detailed production and sales plans so as to maximise the eNPV. The eNPV is simply the summation of all scenario NPVs, weighted by their associated probabilities. The derivation of the objective function is similar to the one in Papageorgiou et al. (2001). The overall problem is formulated as a two-stage, multi-scenario mixed integer linear programming (MILP) model. 

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