Robust Linear Programming and Its Application to Water and Environmental Decision-Making under Uncertainty

Yang Zhou,Bo Yang,Jingcheng Han,Yuefei Huang

doi:10.3390/su11010033

Abstract

In this study, we introduce a robust linear programming approach for water and environmental decision-making under uncertainty. This approach is of significant practical utility to decision makers for obtaining reliable and robust management decisions that are “immune” to the uncertainty attributable to data perturbations. The immunization guarantees that the chosen robust management plan will be implementable with no violation of the mandatory constraints of the problem being studied—i.e., natural resource supply constraint, environmental carrying capacity constraint, environmental pollution control constraint, etc.—and that the actual value of the objective will be no worse than the given estimation if the perturbations of data fall within the specified uncertainty set. A simplified example in regional water quality management is provided to help water and environmental practitioners to better understand how to implement robust linear programming from the perspective of application, as well as to illustrate the significance and necessity of implementing robust optimization techniques in real-world practices. Robust optimization is a growing research field that requires more interdisciplinary research efforts and engagements from water and environmental practitioners. Both may benefit from the advances of management science.

Highlights

Scarcity of freshwater has become a continuing worldwide problem as population increases, urbanization advances and climate changes
We introduced a robust linear programming approach for water and environmental decision-making under uncertainty
This approach is of significant practical utility to decision makers for obtaining reliable and robust management decisions that are “immune” to the uncertainty attributable to data perturbations

Summary

Introduction

Scarcity of freshwater has become a continuing worldwide problem as population increases, urbanization advances and climate changes. Multiple types of uncertain information, including interval number, fuzzy set and probability distribution, can be translated into model parameters effectively through different mathematical techniques [30–35] Most of these efforts have limited practical values due to the limitation on providing reliable and robust managerial support under uncertainty. A semi-hypothetical example in water quality management is provided to illustrate the applicability of the robust linear programming approach and the vulnerability of the nominal optimal solutions in practice. The data of this example is mainly based on government reports and the numerical example has been simplified for the purpose of illustration. This example may help water and environmental practitioners to better understand the significance and necessity of implementing robust optimization techniques in real-world practices

Methodology

Case Study

Result

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Conclusions