May 16, 2024
Journal Article

Approximating a linear multiplicative objective in watershed management optimization


Implementing management practices in a cost-ecient manner is critical for regional efforts to reduce the amount of pollutants entering Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes the resulting pollutant load|as simulated in a widely used regulatory watershed model|subject to budgetary and environmental constraints. We formulate this problem exactly as a nonlinear program with a linear multiplicative objective function, and approximately as a linear program with an exponential number of variables. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear program to handle its large number of variables. We demonstrate through examples and computational tests that the linear program and its restrictions approximate the problem well in practice, despite their poor approximation properties in the worst case. This study demonstrates that carefully crafted approximations can be a useful approach for tackling linear multiplicative programs that arise from watershed management optimization and other similar settings.

Published: May 16, 2024


Boddiford A., D.E. Kaufman, D.E. Skipper, and N. Uhan. 2023. Approximating a linear multiplicative objective in watershed management optimization. European Journal of Operational Research 305, no. 2:547-561. PNNL-SA-163149. doi:10.1016/j.ejor.2022.06.006

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