This thesis consists of three projects, centered around the aim to better model real-world systems under uncertainty, specifically, under stochastic disruptions, using optimization. A stochastic disruption is a type of infrequent event in which the timing and the magnitude are random. We introduce the concept of stochastic disruptions and a stochastic optimization model is proposed for such problems with a finite time horizon. We further develop the idea of a stochastic disruption for a specific example, a project crashing problem under a single disruption. When a disruption occurs, the duration of an activity, which has not yet started, can change. Both the magnitude of the change of an activity's duration and the timing of the disruption can be random. We formulate a stochastic mixed integer program (SMIP) with mixed integer recourse. This SMIP can be computationally challenging to solve using existing techniques. We propose an adaptive branch-and-cut algorithm to solve the SMIP and evaluate the computational performance of our approach. Next, we consider an application in electric power systems in which a disruption can occur due to uncertain demand or uncertain availability of renewable energy resources. We propose a robust optimization model for the alternating current optimal power flow (ACOPF) problem, considering a two-stage model in which potential disruptions occur on a 10-15 minute timescale. We use an uncertainty set to model a disruption in the context of robust optimization. Based on a recently developed convex relaxation for the ACOPF problem, we construct a robust convex optimization problem with recourse. We develop an enhanced cutting-plane algorithm to solve this problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound and an acceptable solution for the non-convex robust ACOPF problem. Finally, we consider a syringe exchange program (SEP) in which a client's behavior is stochastic. Using data from one program in Chicago over ten years, we study the behavior of its clients, focusing on the temporal process governing their visits to service locations and their demographics. The frequency of using the SEP services may be affected by stochastic disruptions such as the client relocating or participating in a treatment program. We construct a phase-type distribution to characterize unobservable changes in a client's status, and we use an affine relationship between model parameters and features of an individual client. The phase-type distribution governs inter-arrival times between reoccurring visits of each client to SEP sites and is informed by characteristics of a client including age, gender, ethnicity, drug-use habits and more. The inter-arrival time model is a sub-model in a simulation model that we construct for the larger system, which allows us to provide a personalized prediction regarding the client's time-to-return to a service location so that better intervention decisions can be made.

Creator

• Yang, Haoxiang

DOI

• https://doi.org/10.21985/n2-mpky-je38

Subject

• Operations research

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:14795
• etdadmin_upload_684485

Keyword

• Syringe exchange program
• Stochastic disruption
• Robust optimization
• Stochastic programming
• Optimal power flow

Date created

• 2019-01-01

Resource type

• Dissertation

Rights statement

• In Copyright