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A Study of Data-driven Models with Challenges Arising from OR Applications

Ren, Ke (2021) A Study of Data-driven Models with Challenges Arising from OR Applications. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Data-driven models have been widely adopted in solving operations research (OR) problems, especially those from real applications where the distributions of the random variables are unknown. Note that these models are mainly inspired by methods from statistics and machine learning communities. However, many features in the OR problems place additional challenges in formulating and modeling. These challenges make models that are directly borrowed from other communities less efficient or even invalid. In this dissertation, we examine four typical OR problems, where they face challenges arising from the small data, complex objective function, incomplete data, and nonstationary data, respectively.

The first problem is chance-constrained programming under a small-data regime. We propose one upper bound on the performance of the commonly used scenario approach. To address the poor performance implied by this upper bound, we propose a new model with better performance. This model demonstrates a clear physical interpretation and a simple linear/conic formulation. Moreover, it is shown to be equivalent to distributionally robust chance-constrained programming under a specific setting. The second problem is maximum weight cycle and chain packing with inhomogeneous edge existence uncertainty. We fill a major gap observed in prior studies by proposing the first scalable model to solve this problem. The proposed model is a mixed-integer linear program, which can be solved directly by a general-purpose integer programming solver. The third problem studied is distributionally robust optimization (DRO) with incomplete joint data. We develop a new DRO framework with incomplete data sets. It presents an integrated framework to jointly analyze missing data and stochastic decision-making, which enables us to derive theoretical guarantees on the performance of stochastic programming under incomplete data. Several kinds of ambiguity sets are also discussed. Finally, we examined an inventory problem with highly unpredictable nonstationary demand. The demand is considered nonstationary and assumed that future demand cannot be reliably predicted through historical features or data. Managers can only make decisions based on sequentially observed demand in an online fashion. We propose methods based on the idea of distinguishing the stochasticity/randomness and demand distribution changes among the sequentially observed demand.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Ren, Keker102@pitt.eduker102
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairBidkhori, Hodabidkhori@pitt.edu
Committee CoChairZeng, Bobzeng@pitt.edu
Committee MemberRajgopal, Jayantrajgopal@pitt.edu
Committee MemberShen, Zuo-Junmaxshen@berkeley.edu
Date: 3 September 2021
Date Type: Publication
Defense Date: 14 July 2021
Approval Date: 3 September 2021
Submission Date: 19 July 2021
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 165
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Industrial Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: data-driven decision-making, distributionally robust optimization, stochastic programming, machine learning
Date Deposited: 03 Sep 2021 18:23
Last Modified: 03 Sep 2021 18:23
URI: http://d-scholarship.pitt.edu/id/eprint/41450

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