Tractable Policies in Dynamic Robust Optimization

In many sequential decision problems, uncertainty is revealed over time and we need to make decisions in the face of uncertainty. This is a fundamental problem arising in many applications such as facility location, resource allocation and capacity planning under demand uncertainty. Robust optimization is an approach to model uncertainty where we optimize over the worst-case realization of parameters within an uncertainty set. While computing an optimal solution in dynamic robust optimization is usually intractable, affine policies (or linear decision rules) are widely used as an approximate solution approach. However, there is a stark contrast between the observed good empirical performance and the bad worst-case theoretical performance bounds. In the first part of this thesis, we address this stark contrast between theory and practice. In particular, we introduce a probabilistic approach in Chapter 2 to analyze the performance of affine policies on randomly generated instances and show they are near-optimal with high probability under reasonable assumptions. In Chapter 3, we study these policies under important models of uncertainty such as budget of uncertainty sets and intersection of budgeted sets and show that affine policies give an optimal approximation matching the hardness of approximation. In the second part of the thesis and based on our analysis of affine policies, we design new tractable policies for dynamic robust optimization. In particular, in Chapter 4, we present a tractable framework to design piecewise affine policies that can be computed efficiently and improve over affine policies for many instances. In Chapter 5, we introduce extended affine policies and threshold policies and show that their performance guarantees are significantly better than previous policies. Finally, in Chapter 6, we study piecewise static policies and their limitations for solving some classes of dynamic robust optimization problems

Maximum Load Assortment Optimization: Approximation Algorithms and Adaptivity Gaps

Motivated by modern-day applications such as Attended Home Delivery and Preference-based Group Scheduling, where decision makers wish to steer a large number of customers toward choosing the exact same alternative, we introduce a novel class of assortment optimization problems, referred to as Maximum Load Assortment Optimization. In such settings, given a universe of substitutable products, we are facing a stream of customers, each choosing between either selecting a product out of an offered assortment or opting to leave without making a selection. Assuming that these decisions are governed by the Multinomial Logit choice model, we define the random load of any underlying product as the total number of customers who select it. Our objective is to offer an assortment of products to each customer so that the expected maximum load across all products is maximized. We consider both static and dynamic formulations. In the static setting, a single offer set is carried throughout the entire process of customer arrivals, whereas in the dynamic setting, the decision maker offers a personalized assortment to each customer, based on the entire information available at that time. The main contribution of this paper resides in proposing efficient algorithmic approaches for computing near-optimal static and dynamic assortment policies. In particular, we develop a polynomial-time approximation scheme (PTAS) for the static formulation. Additionally, we demonstrate that an elegant policy utilizing weight-ordered assortments yields a 1/2- approximation. Concurrently, we prove that such policies are sufficiently strong to provide a 1/4-approximation with respect to the dynamic formulation, establishing a constant-factor bound on its adaptivity gap. Finally, we design an adaptive policy whose expected maximum load is within factor 1-\eps of optimal, admitting a quasi-polynomial time implementation

Matching Drivers to Riders: A Two-Stage Robust Approach

Matching demand (riders) to supply (drivers) efficiently is a fundamental problem for ride-hailing platforms who need to match the riders (almost) as soon as the request arrives with only partial knowledge about future ride requests. A myopic approach that computes an optimal matching for current requests ignoring future uncertainty can be highly sub-optimal. In this paper, we consider a two-stage robust optimization framework for this matching problem where future demand uncertainty is modeled using a set of demand scenarios (specified explicitly or implicitly). The goal is to match the current request to drivers (in the first stage) so that the cost of first stage matching and the worst-case cost over all scenarios for the second stage matching is minimized. We show that this two-stage robust matching is NP-hard under both explicit and implicit models of uncertainty. We present constant approximation algorithms for both models of uncertainty under different settings and show they improve significantly over standard greedy approaches

On the Optimality of Affine Policies for Budgeted Uncertainty Sets

We study the performance of affine policies for two-stage adjustable robust optimization problem under a budget of uncertainty set. This important class of uncertainty sets provides the flexibility to adjust the level of conservatism in terms of probabilistic bounds on constraint violations. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than $\Omega( \frac{\log n}{\log \log n})$ for budget of uncertainty sets where $n$ is the number of decision variables. We show that surprisingly affine policies provide the optimal approximation for this class of uncertainty sets that matches the hardness of approximation; thereby, further confirming the power of affine policies. We also present strong theoretical guarantees for affine policies when the uncertainty set is given by intersection of budget constraints. Furthermore, our analysis gives a significantly faster algorithm to compute near-optimal affine policies. This is joint work with Vineet Goyal.Non UBCUnreviewedAuthor affiliation: Columbia UniversityGraduat

Morocco’s First Biobank: Establishment, Ethical Issues, Biomedical Research Opportunities, and Challenges

Background. Biobanks are highly organized infrastructures that allow the storage of human biological specimens associated with donors’ personal and clinical data. These infrastructures play a key role in the development of translational medical research. In this context, we launched, in November 2015, the first biobank in Morocco (BRO Biobank) in order to promote biomedical research and provide opportunities to include Moroccan and North African ethnic groups in international biomedical studies. Here, we present the setup and the sample characteristics of BRO Biobank. Methods. Patients were recruited at several departments of two major health-care centers in the city of Oujda. Healthy donors were enrolled during blood donation campaigns all over Eastern Morocco. From each participant, personal, clinical, and biomedical data were collected, and several biospecimens were stored. Standard operating procedures have been established in accordance with international guidelines on human biobanks. Results. Between November 2015 and July 2020, 2446 participants were recruited into the BRO Biobank, of whom 2013 were healthy donors, and 433 were patients. For healthy donors, the median age was 35 years with a range between 18 and 65 years and the consanguinity rate was 28.96%. For patients, the median age was 11 years with a range between 1 day and 83 years. Among these patients, 55% had rare diseases (hemoglobinopathies, intellectual disabilities, disorders of sex differentiation, myopathies, etc.), 13% had lung cancer, 4% suffered from hematological neoplasms, 3% were from the kidney transplantation project, and 25% had unknown diagnoses. The BRO Biobank has collected 5092 biospecimens, including blood, white blood cells, plasma, serum, urine, frozen tissue, FFPE tissue, and nucleic acids. A sample quality control has been implemented and suggested that samples of the BRO Biobank are of high quality and therefore suitable for high-throughput nucleic acid analysis. Conclusions. The BRO Biobank is the largest sample collection in Morocco, and it is ready to provide samples to national and international research projects. Therefore, the BRO Biobank is a valuable resource for advancing translational medical research