Management Science and Engineering

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This is the collection for the University of Waterloo's Department of Management Science and Engineering.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

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Applications of stochastic modeling and data analytics techniques in healthcare decision making
(University of Waterloo, 2017-12-19) Dalgic, Ozden Onur; Erenay, Fatih Safa; Ozaltin, Osman
We present approaches utilizing aspects of data analytics and stochastic modeling techniques and applied to various areas in healthcare. In general, the thesis has composed of three major components. Firtsly, we propose a comparison analysis between two of the very well-known infectious disease modeling techniques to derive effective vaccine allocation strategies. This study, has emerged from the fact that individuals are prioritized based on their risk profiles when allocating limited vaccine stocks during an influenza pandemic. Computationally expensive but realistic agent-based simulations and fast but stylized compartmental models are typically used to derive effective vaccine allocation strategies. A detailed comparison of these two approaches, however, is often omitted. We derive age-specific vaccine allocation strategies to mitigate a pandemic influenza outbreak in Seattle by applying derivative-free optimization to an agent-based simulation and also to a compartmental model. We compare the strategies derived by these two approaches under various infection aggressiveness and vaccine coverage scenarios. We observe that both approaches primarily vaccinate school children, however they may allocate the remaining vaccines in different ways. The vaccine allocation strategies derived by using the agent-based simulation are associated with up to 70% decrease in total cost and 34% reduction in the number of infections compared to the strategies derived by the compartmental model. Nevertheless, the latter approach may still be competitive for very low and/or very high infection aggressiveness. Our results provide insights about the possible differences between the vaccine allocation strategies derived by using agent-based simulations and those derived by using compartmental models. Secondly, we introduce a novel and holistic scheme to capture the gradual amyotrophic lateral sclerosis progression based on the critical events referred as tollgates. Amyotrophic lateral sclerosis is neuro-degenerative and terminal disease. Patients with amyotrophic lateral sclerosis lose control of voluntary movements over time due to continuous degeneration of motor neurons. Using a comprehensive longitudinal dataset from Mayo Clinic’s ALS Clinic in Rochester, MN, we characterize the progression through tollgates at the body segment (e.g., arm, leg, speech, swallowing, breathing) and patient levels over time. We describe how the progression based on the followed tollgate pathways varies among patients and ultimately, how this type of progression characterization may be utilized for further studies. Kaplan-Meier analysis are conducted to derive the probability of passing each tollgate over time. We observe that, in each body segment, the majority of the patients have their abilities affected or worse (Level1) at the first visit. Especially, the proportion of patients at higher tollgate levels is larger for arm and leg segments compared to others. For each segment, we derive the over-time progression pathways of patients in terms of the reached tollgates. Tollgates towards later visits show a great diversity among patients who were at the same tollgate level at the first clinic visit. The proposed tollgate mechanism well captures the variability among patients and the history plays a role on when patients reach tollgates. We suggest that further and comprehensive studies should be conducted to observe the whole effect of the history in the future progression. Thirdly, based on the fact that many available databases may not have detailed medical records to derive the necessary data, we propose a classification-based approach to estimate the tollgate data using ALSFRS-R scores which are available in most databases. We observed that tollgates are significantly associated with the ALSFRS-R scores. Multiclass classification techniques are commonly used in such problem; however, traditional classification techniques are not applicable to the problem of finding the tollgates due to the constraint of that a patients’ tollgates under a specific segment for multiple visit should be non-decreasing over time. Therefore, we propose two approaches to achieve a multi-class estimation in a non-decreasing manner given a classification method. While the first approach fixes the class estimates of observation in a sequential manner, the second approach utilizes a mixed integer programming model to estimate all the classes of a patients’ observations. We used five different multi-class classification techniques to be employed by both of the above implementations. Thus, we investigate the performance of classification model employed under both approaches for each body segment.
Data-driven Structure Detection in Optimization: Decomposition, Hub Location, and Brain Connectivity
(University of Waterloo, 2018-07-13) Khaniyev, Taghi; Elhedhli, Samir; Erenay, Fatih Safa
Employing data-driven methods to efficiently solve practical and large optimization problems is a recent trend that focuses on identifying patterns and structures in the problem data to help with its solution. In this thesis, we investigate this approach as an alternative to tackle real life large scale optimization problems which are hard to solve via traditional optimization techniques. We look into three different levels on which data-driven approaches can be used for optimization problems. The first level is the highest level, namely, model structure. Certain classes of mixed-integer programs are known to be efficiently solvable by exploiting special structures embedded in their constraint matrices. One such structure is the bordered block diagonal (BBD) structure that lends itself to Dantzig-Wolfe reformulation (DWR) and branch-and-price. Given a BBD structure for the constraint matrix of a general MIP, several platforms (such as COIN/DIP, SCIP/GCG and SAS/ DECOMP) exist that can perform automatic DWR of the problem and solve the MIP using branch-and-price. The challenge of using branch-and-price as a general-purpose solver, however, lies in the requirement of the knowledge of a structure a priori. We propose a new algorithm to automatically detect BBD structures inherent in a matrix. We start by introducing a new measure of goodness to capture desired features in BBD structures such as minimal border size, block cohesion and granularity of the structure. The main building block of the proposed approach is the modularity-based community detection in lieu of traditional graph/hypergraph partitioning methods to alleviate one major drawback of the existing approaches in the literature: predefining the number of blocks. When tested on MIPLIB instances using the SAS/DECOMP framework, the proposed algorithm was found to identify structures that, on average, lead to significant improvements both in computation time and optimality gap compared to those detected by the state-of-the-art BBD detection techniques in the literature. The second level is problem type where problem-specific patterns/characteristics are to be detected and exploited. We investigate hub location problem (HLP) as an example. HLP models the problem of selecting a subset of nodes within a given network as hubs, which enjoy economies of scale, and allocating the remaining nodes to the selected hubs. The main challenge of using HLP in certain promising domains is the inability of current solution approaches to handle large instances (e.g., networks with more than 1000 nodes). In this work, we explore an important pattern in the optimal hub networks: spatial separability. We show that at the optimal solutions, nodes are typically partitioned into allocation clusters in such a way that convex hulls of these clusters are disjoint. We exploit this pattern and propose a new data-driven approach that uses the insights generated from the solution of a smaller problem - low resolution representation - to find high quality solutions for the large HLPs. The third and the lowest level is the instance level where the instance-specific data is explored for patterns that would help solution of large problem instances. To this end, we open up a new application of HLPs originating from human brain connectivity networks (BCN) by introducing the largest (with 998 nodes) and the first three-dimensional dataset in the literature so far. Experiments reveal that the HLP models can successfully reproduce similar results to those in the medical literature related to hub organisation of the brain. We conclude that with certain customizations and methods that allow tackling very large instances, HLP models can potentially become an important tool to further investigate the intricate nature of hub organisations in human brain.
Resource Allocation Models in Healthcare Decision Making
(University of Waterloo, 2017-08-31) Hiassat, Abdelhalim; Erenay, Fatih Safa; Ozaltin, Osman
We present models for allocating limited healthcare resources efficiently among target populations in order to maximize society's welfare and/or minimize the expected costs. In general, this thesis is composed of two major parts. Firstly, we formulate a novel uncapacitated fixed-charge location problem which considers the preferences of customers and the reliability of facilities simultaneously. A central planner selects facility locations from a set of candidate sites to minimize the total cost of opening facilities and providing service. Each customer has a strict preference order over a subset of the candidate sites, and uses her most preferred available facility. If that facility fails due to a disruptive event, the customer attends her next preferred available facility. This model bridges the gap between the location models that consider the preferences of customers and the ones that consider the reliability of facilities. It applies to many healthcare settings, such as preventive care clinics, senior centers, and disaster response centers. In such situations, patient (or customer) preferences vary significantly. Therefore, there could be a large number of subgroups within the population depending on their preferences of potential facility sites. In practice, solving problems with large numbers of population subgroups is very important to increase granularity when considering diverse preferences of several different customer types. We develop a Lagrangian branch-and-bound algorithm and a branch-and-cut algorithm. We also propose valid inequalities to tighten the LP relaxation of the model. Our numerical experiments show that the proposed solution algorithms are efficient, and can be applied to problems with extremely large numbers of customers. Secondly, we study the allocation of colorectal cancer (CRC) screening resources among individuals in a population. CRC can be early-detected, and even prevented, by undergoing periodic cancer screenings via colonoscopy. Current guidelines are based on existing medical evidence, and do not explicitly consider (i) all possible alternative screening policies, and (ii) the effect of limited capacity of colonoscopy screening on the economic feasibility of the screening program. We consider the problem of allocating limited colonoscopy capacity for CRC screening and surveillance to a population composed of patients of different risk groups based on risk factors including age, CRC history, etc. We develop a mixed integer program that maximizes the quality-adjusted life years for a given patient population considering the population's demographics, CRC progression dynamics, and relevant constraints on the system capacity and the screening program effectiveness. We show that the current guidelines are not always optimal. In general, when screening capacity is high, the optimal screening programs recommend higher screening rates than the current guidelines, and the optimal screening policies change with age and gender. This shows the significance of incorporating screening capacity into the decisions of optimal screening policies.
Use of Markov Decision Process Models in Preventive Medicine
(University of Waterloo, 2018-08-02) NEMUTLU, GIZEM SULTAN; Erenay, Fatih Safa
The biggest trade-off when proposing health care policies is about balancing the effectiveness and the practicality of the policies. The optimal policies providing benchmark performances can be driven through using operations research tools; however, they usually have complex structures that are necessary to sufficiently represent various aspects of the system being modeled. There are also policies either proposed in guidelines or followed in practice but they often vary with the system characteristics, i.e., preferences of the clinicians, available resources of the clinics, etc. Therefore, standardized, simple yet effective policies are needed for many healthcare applications, including preventive medicine. At this point, we study developing health care delivery policies that maximize the effect of the preventive interventions, while providing applicable policy structures that can be easily followed by health practitioners in practice. We focus on two applications of preventive medicine: childhood vaccine administration practices in developing countries; and colorectal cancer screening and surveillance. Vaccine administration practices in developing countries suffer from open-vial wastage. Doses remaining from opened vials are disposed at the end of a day, due to lack of appropriate cold storage conditions. We propose administering vaccines from different sizes of multi-dose vials to address the open-vial wastage problem. We utilize a Markov decision process model to maximize the expected total number of doses administered via reducing vaccine wastage. The model dynamically decides which size of a multi-dose vial to open next, and when to terminate vaccination service for the day, given the time remaining in the replenishment cycle and available vaccine stocks. We show that the optimal policies are of control-limit type. Using data for routine pediatric vaccines, we show that the proposed optimal policies could cost-effectively reduce open-vial wastage and significantly improve the covered vaccine demand. We also analyze the initial vaccine inventory composition that specifies how many vials of each size should be kept in stock. We show that the optimal policy for the right vaccine inventory composition may improve the expected vaccine demand covered up to target levels without early termination of vaccination service while realizing reasonably small or no additional cost. Although the number of system variables being tracked in our state space is manageable, the optimal policies still require significant effort to be adopted in practice. That is especially challenging in developing countries, where the resources, e.g., clinic staff, are limited. Therefore, we introduce simple vaccine administration policies that are developed with the guidance of the insights from our numerical and structural analyses. Our insights on the simple vaccine administration policies show that these policies can provide promising performance, in terms of costs and expected vaccine demand covered, compared to the optimal policies while requiring only a single system variable, i.e., time of a decision, to be monitored. Colonoscopy screening prevents, and early-detects colorectal cancer (CRC), one of the most common and deadliest cancers in the world. Considering that the risk of developing CRC significantly increases after age 50, and that the North American population is aging, the colonoscopy screening and follow-up policies employed by gastroenterologists play a vital role in the well-being of the population. Existing clinical guidelines recommend colonoscopy screening policies that are shown to be cost-effective in CRC prevention and early detection. Nevertheless, almost half the practitioners do not follow these guidelines, indicating controversy around the best CRC screening practices. Several studies analyze alternative CRC screening policies using simulation and mathematical models. Especially, dynamic alternative policies, derived by a stochastic dynamic programming approach, can significantly increase health outcome improvements due to CRC screening and follow-up. However, under dynamic policies, colonoscopy screening and surveillance intervals significantly vary in factors such as age, gender, and personal history, which are harder to implement for clinicians. Our study on this second application aims at deriving efficient and simpler-to-implement colonoscopy screening and follow-up policies, but that perform closely to the optimal policies. We employ a patient-level discrete-event simulation model, built and validated using real data, to mimic CRC progression in asymptomatic and higher-risk individuals. We estimate the expected life-years, age-based risk of having CRC, CRC mortality, costs associated with CRC screening, and the number of required colonoscopies for a large set of screening policies. We evaluate the performances of all relevant simpler-to-implement colonoscopy policies, including the periodic screening policies currently used by practitioners, and all feasible periodic policies with n-period switch times (for n=0,1,2). Our analysis identifies under the parameter settings under which alternative and simpler policies are sufficient to provide close-to-optimal performance. These results provide insights on the types of policies on which to focus in future studies, for researchers from both medical and operational research fields.

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Browsing Management Science and Engineering by Author "Erenay, Fatih Safa"