Browsing by Author "Perez-Salazar, Sebastian"

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    Applications of Mixed Integer Programming to Cloud Computing: Modeling and Computation
    (2024-05-10) Alfant, Rachael M; Perez-Salazar, Sebastian; Schaefer, Andrew J
    Demand for computing capacity in the cloud is generally not easily forecast; however, sub-optimal pricing and mis-allocation of cloud computing resources both have negative consequences for users and providers of cloud computing. This thesis approaches pricing and capacity allocation in cloud computing through the lens of stochastic mixed integer programming (SMIP), which provides a particularly useful framework for solving large, complex decision-making problems under uncertainty. Often, the uncertainty inherent to SMIPs manifests in the right-hand side (demand) vector. Thus, it is important to have a framework by which to assess a mixed integer programming (MIP) model’s quality over unknown or stochastic right-hand sides. As such, this thesis explores both theoretical and practical applications of SMIPs and MIPs with unknown right-hand sides. In particular, this thesis develops theoretical evaluative metrics for MIPs over multiple right-hand sides via gap functions, presents several stochastic optimization approaches to optimal pricing in the cloud, and formulates waste-minimizing (revenue-maximizing) SMIP models that optimize capacity allocation in the cloud.
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    Stochastic Scheduling: Strategies for Abandonment Management
    (2024-06-23) Xu, Yihua; Perez-Salazar, Sebastian
    Motivated by applications where impatience is pervasive and resources are limited, we study a job scheduling model where jobs may depart at an unknown point in time. Initially, we have access to a single server and n jobs with known non-negative values. These jobs also have unknown stochastic service and departure times with known distributional information, which we assume to be independent. When the server is free, we can run a job that has neither been run nor departed and collect its value. This occupies the server for an unknown amount of time, and we aim to design a policy that maximizes the expected total value obtained from jobs run on the server. Natural formulations of this problem suffer from the curse of dimensionality. Furthermore we show that even when the service and departure times are deterministic, our problem is NP-hard to solve. Hence, we focus on policies that can provide high expected reward compared to the optimal value. We demonstrate a polynomial-time Linear Program (LP) based approximation algorithm with guaranteed performance under mild assumptions on service times. Our methodology is flexible, allowing additional constraints to be incorporated. We develop efficient approximation algorithms with provable guarantees for extensions like job release times, deadlines, and knapsack constraints. We further extend our analysis to the setting where all jobs have independent and identically distributed (i.i.d.) service times. In this case, we show that the greedy policy that always runs the highest-valued job whenever the server is free guarantees a factor of 1/2 compared to the optimal expected value. We evaluate our LP-based policies and the greedy policy empirically on synthetic and real datasets.