Scheduling and control problems are traditionally solved sequentially. However, integration of both problems can result in a better overall performance. A main challenge in the integration is the solution to the derived mixed-integer dynamic optimization (MIDO) problem. To overcome the challenge, we present a novel integration method, which simultaneously determines the PI controller design and the scheduling decisions. The method decomposes the MIDO problem. The dynamic optimization for each transition can be solved independently offline. A set of controller candidates are generated and stored. Then the integrated problem is transformed into a mixed-integer nonlinear fractional programming problem of scheduling with controller selection. This problem can be efficiently solved to the global optimaity by the Dinkelbach's algorithm.
In this paper, a bi-criterion, multi-period, stochastic mixed-integer linear programming model is proposed to address the optimal design and planning of hydrocarbon biorefinery supply chains under supply and demand uncertainties. The model accounts for diverse conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk which is measured by conditional value-at-risk and downside risk. The model determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multi-cut L-shaped decomposition approach is implemented to circumvent the computational burden of solving large scale problems. The proposed modeling framework and algorithm are illustrated through two case studies of hydrocarbon biorefinery supply chain for the State of Illinois.
Solar energy is one of the most promising renewable energy alternatives for the replacement of traditional fossil fuels. CdTe photovoltaics (PVs) are thin-film solar cells that have the highest market share among all thin-film technologies. Previous LCA studies of CdTe PVs were based on the data from countries that have similar level of industrialization and strict environmental policies. Thus, to date, no LCA results have explored impacts of dramatic geographic diversity on environmental performance of CdTe PVs. Furthermore, few LCAs for CdTe PVs have taken uncertainty, which is an often overlooked but important aspect, into consideration. In this paper, we apply a "Cradle to Gate" LCA to two scenarios in China and the U.S. respectively and calculate the corresponding energy payback time and life cycle environmental impacts. Then, an uncertainty analysis is undertaken through Monte Carlo simulation. Both deterministic and uncertainty-based results indicate that geographic diversity can drastically change performance of CdTe PVs on environmental sustainability. However, this diversity of production locations has no correlation with other uncertain parameters. Results of uncertainty analysis indicate the influence of each parameter and provide guidance for future optimization of CdTe technology. Finally, comparison between CdTe and other PV technologies is displayed and discussed.
In this paper, a bi-criterion, multi-period, stochastic mixed-integer linear programming model is proposed to address the optimal design and planning of hydrocarbon biorefinery supply chains under supply and demand uncertainties. The model accounts for diverse conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk which is measured by conditional value-at-risk and downside risk. The model determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multi-cut L-shaped decomposition approach is implemented to circumvent the computational burden of solving large scale problems. The proposed modeling framework and algorithm are illustrated through two case studies of hydrocarbon biorefinery supply chain for the State of Illinois.
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