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Data-Driven Stochastic Optimization with Application to Water Resources Management

Park, Jangho
http://orcid.org/0000-0002-9901-8555
http://rave.ohiolink.edu/etdc/view?acc_num=osu1555623442635498

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Industrial and Systems Engineering.
Data-driven methods have become paramount in science, engineering, and business with the advances in data collection and storage. This dissertation focuses on data-driven optimization of systems under uncertainty. It makes several methodological advances, examining what happens as more data is collected and applies them to water resources management problems. First, the dissertation examines sequential sampling procedures, where an optimization problem under uncertainty is solved with the current available data. If the obtained solution is "high-quality" with respect to a user-specified criterion, then, the procedure stops. Otherwise, more data is collected and the optimization and solution quality assessment steps are repeated until a desirable solution is obtained. Earlier work in this area mainly looked at using independent and identically distributed data. In this dissertation, we investigate the use of variance reduction techniques antithetic variates and Latin hypercube sampling within sequential sampling procedures both theoretically and numerically. Next, the dissertation studies a class of time-dynamic optimization problems under uncertainty, where there is limited data. In particular, the dissertation uses Multistage Distributionally Robust Optimization (MDRO) with phi-divergences to model such problems. The appeal of this modeling approach is that it acknowledges that the data contains prediction errors; so it considers all distributions sufficiently close to a nominal distribution and minimizes a worst-case expectation taken with respect to these distributions. The dissertation studies this modeling approach and devises an efficient decomposition-based solution method to solve the resulting MDROs. The dissertation then applies the MDRO modeling and solution techniques to solve a long-term water allocation problem. Decisions must be made in order to tackle possible future water shortages, and these decisions must take into account various uncertainties like demand, climate, population, and so forth. The dissertation incorporates various data and several statistical methods to estimate water demand and supply. Then, it uses the MDRO modeling approach to evaluate constructing decentralized water infrastructures in the area. Finally, the dissertation investigates the value of additional data in a distributionally robust model. Such notions have been used in decision analysis and stochastic programming since the 50s. We extend this notion to the DRO setting. The change in the optimal value due to a specific additional observation of a scenario is called the value of data (VoD). The average change in the VoD is called the price of data (PoD). If one's budget is larger than the PoD, it is worthwhile to collect additional data. Additional optimization problems should be solved to calculate the VoD and estimate the PoD. This is computationally expensive. Therefore, the dissertation provides ways to estimate VoD and PoD without solving any additional optimization problems and showcases how they can be used by decision makers to gain insight into their problems.
Guzin Bayraksan (Advisor)
King Yeung Lam (Committee Member)
Cathy Honghui Xia (Committee Member)
Industrial Engineering; Operations Research

Recommended Citations

Citations

  • Park, J. (2019). Data-Driven Stochastic Optimization with Application to Water Resources Management [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555623442635498

    APA Style (7th edition)

  • Park, Jangho. Data-Driven Stochastic Optimization with Application to Water Resources Management. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1555623442635498.

    MLA Style (8th edition)

  • Park, Jangho. "Data-Driven Stochastic Optimization with Application to Water Resources Management." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555623442635498

    Chicago Manual of Style (17th edition)

osu1555623442635498
516
© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.