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L-Shaped Bonus Algorithm with Application to Water Pollutant Trading

Yogendra Shastri, Agricultural and Biological Engineering, University of Illinois at Urbana Champaign / Vishwamitra Research Institute (CUSTOM), 1304 W. Pennsylvania avenue, Urbana, IL 61801 and Urmila Diwekar, Vishwamitra Research Institute, Center for Uncertain Systems: Tools for Optimization and Management, Vishwamitra Research Institute, Clarendon Hills, IL 60514.

Applications of optimization in the field of process systems engineering often involve dealing with

nonlinearity and uncertainty, necessitating the solution of stochastic nonlinear programming (SNLP) problems.

However, the existing algorithms to solve such problems suffer from various limitations. L-shaped BONUS

algorithm, an integration of BONUS algorithm and sampling based L-shaped method, has been recently proposed to

overcome some of these problems. It is shown to have desirable computational properties. This work further

investigates the properties of the algorithm by applying it to the environmental problem of pollutant

(nutrient) trading in Christina River Basin. Environmental concerns being heightened, pollution abatement

related decisions are important for the industries, making the efficient solution techniques invaluable. The

results confirm the computational efficiency of the L-shaped BONUS algorithm. Simultaneously, interesting

aspects of the environmental trading problem are also explored, pointing towards the scope of implementing

stochastic programming techniques for better decision making in the field of industrial ecology.