Engineering (Faculty of)

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Now showing 1 - 12 of 12

Condition-based Inspection and Maintenance of Medical Devices
(University of Waterloo, 2017-08-25) Wu, Haoran; He, Qi-Ming; Abouee Mehrizi, Hossein
Inspection and Maintenance of medical devices are essential for modern health services, but the low availability of devices or unnecessary maintenance can cause major problems. A proper maintenance program can signi cantly reduce operational costs and increase device availability. For any maintenance program, two questions arise: 1) What kinds of devices should be included? and 2) How and when should they be inspected and maintained? This thesis proposes methods to solve those two problems. For the rst question, numerous classi cation and prioritization models have been suggested to evaluate medical devices, but most are empirical scoring systems, which can not be widely used. To build a generalized scoring system, we propose a risk level classi cation model. More speci cally, we select three important risk factors (Equipment function, Location of use and Frequency of use), then use provided data to nd the relationship between risk factors and risk levels. Four di erent classi cation models (Linear regression, Logistic regression, Classi cation tree and Random forest) are used to analyze the problem, and all of them are effective. For the second question, some inspection and maintenance models have been developed and widely used to assure the performance of medical devices. However, those models are restricted to a few speci c kind of problems. In contrast, our model provides a more comprehensive response to current maintenance problems in the healthcare industry, by introducing a condition-based multi-component inspection and maintenance model. We rst present a parameter estimation method to predict the deterioration rate of a system. We use provided data and expectation-maximization algorithm to estimate the transition matrix of system conditions. Then, we use Markov decision processes to solve the decision model, which consists of two decisions: the next inspection time and whether to repair the devices. The inspection interval is non-periodic in our model, and this flexibility of non-periodic inspection model can avoid unnecessary inspections. We use relative value iteration to nd the optimal inspection and maintenance strategies and the long-run average cost. Changing the parameter of cost and the structure of the system clarified the influence of these parameters. Our model achieves lower minimal average costs for complex systems than previous periodic inspection models.
Control Mechanisms in Queueing Systems with Nonlinear Waiting Costs
(University of Waterloo, 2017-08-14) Ghareh Aghaji Zare, Ata; Abouee Mehrizi, Hossein
In many queueing systems, customers have been observed to exhibit strategic behavior. Each customer gains a value when receiving a product or getting served and suffers when incurring a delay. We consider a nonlinear waiting cost function to capture the sensitivity of customers toward delay. We investigate customers' behavior and system manager's strategy in two different settings: (1) customers are served in a service system, or (2) they receive a product in a supply chain. In the first model, we study an unobservable queueing system. We consider that customers are impatient, and are faced with decision problems whether to join a service system upon arrival, and whether to remain or renege at a later time. The goal is to address two important elements of queueing analysis and control: (1) customer characteristics and behavior, and (2) queueing control. The literature on customer strategic behavior in queues predominately focuses on the effects of waiting time and largely ignores the mixed risk attitude of customer behavior. Empirical studies have found that customers’ risk attitudes, their anticipated time, and their wait time affect their decision to join or abandon a queue. To explore this relationship, we analyze the mixed risk attitude together with a non-linear waiting cost function that includes the degree of risk aversion. Considering this behavior, we analyze individuals' joint balking and reneging strategy and characterize socially optimal strategy. To determine the optimal queue control policy from a revenue-maximizer perspective, which induces socially optimal behavior and eliminates customer externalities, we propose a joint entrance-fee/abandonment-threshold mechanism. We show that using a pricing policy without abandonment threshold is not sufficient to induce socially optimal behavior and in many cases results in a profit lower than the maximum social welfare the system can generate. Also, considering both customer characteristics and queue control policy, our findings suggest that customers with a moderate anticipation time provide higher expected revenue, acknowledging the importance of understanding customer behavior with respect to both wait time and risk attitude in the presence of anticipation time. In the second model, we consider a two-echelon production inventory system with a single manufacturer and a single distribution center (DC) where the manufacturer has a finite production capacity. There is a positive transportation time between the manufacturer and the DC. Each customer gains a value when receiving the product and suffers a waiting cost when incurring a delay. We assume that customers' waiting cost depends on their degree of impatience with respect to delay (delay sensitivity). We consider a nonlinear waiting cost function to show the degree of risk aversion (impatience intensity) of customers. We assume that customers follow the strategy p where they join the system and place an order with probability p. We analyze the inventory system with a base-stock policy in both the DC and the manufacturer. Since customers and supply chain holder are strategic, we study the Stackelberg equilibrium assuming that the DC acts as a Stackelberg leader and customers are the followers. We first obtain the total expected revenue and then derive the optimal base-stock level as well as the optimal price at the DC.
Data-Driven Analytics to Support Scheduling of Multi-Priority Multi-Class Patients with Wait Targets
(University of Waterloo, 2016-08-09) Jiang, Yangzi; Abouee Mehrizi, Hossein
The aim of dynamic scheduling is to efficiently assign available resources to the most suitable patients. The dynamic assignment of multi-class, multi-priority patients over time has long been a challenge, especially for scheduling in advance and under non-deterministic capacity. In this paper, we first conduct descriptive analytics on MRI data of over 3.7 million patient records from 74 hospitals. The dataset captures patients of four different priority levels, with different wait time targets, seeking treatment for one of ten classes of procedures, which have been scheduled over a period of 3 years. The goal is to serve 90% of patients within their wait time targets; however, under current practice, 67% of patients exceed their target wait times. We characterize the main factors affecting the waiting times and conduct predictive analytics to forecast the distribution of the daily patient arrivals, as well as the service capacity or number of procedures performed daily at each hospital. We then prescribe two simple and practical dynamic scheduling policies based on a balance between the First-In First-Out (FIFO) and strict priority policies; namely, weight accumulation and priority promotion. Under the weight accumulation policy, patients from different priority levels start with varying initial weights, which then accumulates as a linear function of their waiting time. Patients of higher weights are prioritized for treatment in each period. Under the priority promotion policy, a strict priority policy is applied to priority levels where patients are promoted to a higher priority level after waiting for a predetermined threshold of time. To evaluate the proposed policies, we design a simulation model that applies the proposed scheduling policies and evaluates them against two performance measures: 1) total exceeding time: the total number of days by which patients exceed their wait time target, and 2) overflow proportion: the percentage of patients within each priority group that exceed the wait time target. Using historical data, we show that, compared to the current practice, the proposed policies achieve a significant improvement in both performance measures. To investigate the value of information about the future demand, we schedule patients at different points of time from their day of arrival. The results show that hospitals can considerably enhance their wait time management by delaying patient scheduling.
Data-driven Models for Inferring the Patient Scheduling Policies via Inverse Reinforcement Learning
(University of Waterloo, 2024-01-23) Moradi, Parham; Abouee Mehrizi, Hossein
In this work, we study multi-class patient scheduling with stochastic daily patient arrivals. Different classes of patients are characterized by different service times, waiting cost parameters, and rejection cost parameters. Our primary objective is to infer the policy used by the decision-makers, who schedule patients over a finite time horizon, based on their historical decisions. To achieve this, we first develop a mathematical model that captures the complexities of patient scheduling and is representative of the problem that decision-makers may consider to scheduling patients. Then, we utilize the Riccati and Hamiltonian approaches to estimate the cost parameters that have influenced the scheduling decisions made by the decision-maker. The Riccati approach begins by estimating the expert's policy, which is then used to determine the cost parameters. Conversely, the Hamiltonian approach derives the cost parameters through the optimality conditions of a path trajectory without needing to estimate the expert's policy. Using a simulation model, we demonstrate the efficiency and robustness of the proposed methods. Furthermore, we apply Riccati and Hamiltonian approaches to MRI data from two hospitals to estimate the cost parameters used in their scheduling decisions. Utilizing the estimated cost parameters, we analyze the root causes of the observed outcomes and examine the impact of these underlying factors on the scheduling process. Finally, through counterfactual analysis, we propose two alternative scheduling policies that reduce the total cost, even with the original cost parameters used by the decision-makers.
Dynamic Robust Multi-Class Advance Patient Scheduling
(University of Waterloo, 2022-09-01) Khajeh Arzani, Hamidreza; Abouee Mehrizi, Hossein
In this work, we study an advance patient scheduling problem where patients of different classes have different service times and incur different waiting costs to the system. It is known in the literature that multi-class advance dynamic patient scheduling is a challenging problem due to the high variability in the daily arrival process of patients, as well as the high dimensionality of the problem. To overcome these challenges, we develop a novel dynamic optimization framework where the multi-class advance scheduling problem can be approximately decomposed to multiple single-stage stochastic programs. Furthermore, we develop a distributionally robust formulation and quantify uncertainty in arrivals by applying a risk-averse optimization approach. Exploiting patient-level offline data, we develop a data-driven algorithm to minimize the worst-case outcome that may happen due to the high variability in arrivals. We examine the performance of the proposed robust algorithm by leveraging the MRI data from hospitals in Ontario and show that the dynamic robust model outperforms the dynamic stochastic approach significantly. We also observe that the proposed robust model performs well compared to an offline policy, which is based on the full knowledge of the future arrivals.
The Impact of Information on the Performance of an M/M/1 Queueing System
(University of Waterloo, 2017-01-23) Nasiri, Mojgan; Abouee Mehrizi, Hossein
Reviews provided by previous customers contain information, which can be used by new customers. This research examines the impact of the user-generated reviews, on the performance of an M/M/1 queueing system. We assume that customers do not know the expected service time and they obtain this information by reading reviews. The results show that reading unbiased reviews can result in either a better or worse performance, depending on the parameters of the system. We also investigate the impact of the number of reviews each customer reads, on the diﬀerent performance measures. We observe that if each customer reads more reviews, it does not necessarily result in a system which is more similar to a system with full information. Moreover, even with a huge pool of reviews, it may either not converge to the system with full information or converges very slowly. Finally, we show that if reviews consist of the waiting time that customers experience in the system along with the number of people that they observe upon their arrival, the rate of convergence to the system with full information is much faster.
Reducing Conservatism in Pareto Robust Optimization
(University of Waterloo, 2022-06-09) Rahimi, Fahimeh; Mahmoudzadeh, Houra; Abouee Mehrizi, Hossein
Robust optimization (RO) is a sub-field of optimization theory with set-based uncertainty. A criticism of this field is that it determines optimal decisions for only the worst-case realizations of uncertainty. Several methods have been introduced to reduce this conservatism. However, non of these methods can guarantee the non-existence of another solution that improves the optimal solution for all non-worse-cases. Pareto robust optimization ensures that non-worse-case scenarios are accounted for and that the solution cannot be dominated for all scenarios. The problem with Pareto robust optimization (PRO) is that a Pareto robust optimal solution may be improved by another solution for a given subset of uncertainty. Also, Pareto robust optimal solutions are still conservative on the optimality for the worst-case scenario. In this thesis, first, we apply the concept of PRO to the Intensity Modulated Radiation Therapy (IMRT) problem. We will present a Pareto robust optimization model for four types of IMRT problems. Using several hypothetical breast cancer data sets, we show that PRO solutions decrease the side effects of overdosing while delivering the same dose that RO solutions deliver to the organs at risk. Next, we present methods to reduce the conservatism of PRO solutions. We present a method for generating alternative RO solutions for any linear robust optimization problem. We also demonstrate a method for determining if an RO solution is PRO. Then we determine the set of all PRO solutions using this method. We denote this set as the ``Pareto robust frontier" for any linear robust optimization problem. Afterward, we present a set of uncertainty realizations for which a given PRO solution is optimal. Using this approach, we compare all PRO solutions to determine the one that is optimal for the maximum number of realizations in a given set. We denote this solution as a ``superior" PRO solution for that set. At last, we introduce a method to generate a PRO solution while slightly violating the optimality of the optimal solution for the worst-case scenario. We define these solutions as ``light PRO" solutions. We illustrate the application of our approach to the IMRT problem for breast cancer. The numerical results present a significant impact of our method in reducing the side effects of radiation therapy.
Robust Multi-Class Multi-Period Scheduling of MRI Services with Wait Time Targets
(University of Waterloo, 2018-01-23) Mirahmadi Shalamzari, Akram; Mahmoudzadeh, Houra; Abouee Mehrizi, Hossein
In recent years, long wait times for healthcare services have become a challenge in most healthcare delivery systems in Canada. This issue becomes even more important when there are priorities in patients' treatment which means some of the patients need emergency treatment, while others can wait longer. One example of excessively long wait times in Canada is the MRI scans. These wait times are partially due to limited capacity and increased demand, but also due to sub-optimal scheduling policies. Patients are typically prioritized by the referring physician based on their health condition, and there is a wait time target for each priority level. The difficulty of scheduling increases due to uncertainty in patients' arrivals and service times. In this thesis, we develop a multi-priority robust optimization (RO) method to schedule patients for MRI services over a multi-period finite horizon. First, we present a deterministic mixed integer programming model which considers patient priorities, MRI capacity, and wait time targets for each priority level. We then investigate robust counterparts of the model by considering uncertainty in patients' arrivals and employing the notion of the budget of uncertainty. Finally, we apply the proposed robust model to a set of numerical examples and compare the results with those of the non-robust method. Moreover, sensitivity analysis is performed over capacity, penalty cost, service level, and budget of uncertainty. Our results demonstrate that the proposed robust approach provides solutions with higher service levels for each priority, and lower patients' wait time in realistic problem instances. The analysis also provides some insights on expanding capacity and choosing the budget of uncertainty as a trade-off between performance and conservatism.
A Robust Optimization Approach for Advance Scheduling in Health Care Systems with Demand Uncertainty: Policy Insights
(University of Waterloo, 2021-02-17) Niazi Shahraki, Nafise; Abouee Mehrizi, Hossein; Mahmoudzadeh, Houra
Patient wait times have increased significantly over the past few decades. According to the Canadian Institute for Health Information (CIHI), 40% of Canadians have experienced difficulties in receiving diagnostics tests. MRI wait times have increased by 26% from 2012 to 2016. The lengthy wait times for the health care systems are translated to economic losses and risks to the lives of Canadians. These inefficiencies in health care systems are an indication that health care infrastructure investment has not been able to keep pace with the increased demands. While building new health care infrastructure to create capacity may be the first solution that comes to mind, it is often not feasible due to budget limitations. Optimizing the use of the existing capacity is a more feasible and cost-effective solution to healthcare system inefficiencies. This research builds on previous literature and proposes a robust optimization method for a multi-priority multi-period advance scheduling problem with wait time target which is solved using a proposed adversarial-based algorithm. A sensitivity analysis is conducted to calibrate the model parameters. Several numerical examples are used to extract practical policy insights. The advantages of the robust model in comparison with the deterministic model are highlighted. It is shown that the robust modelling leads to policies that are easier to execute and are more suitable for policy planning purposes when compared to deterministic modelling.
Staff Scheduling During a Pandemic
(University of Waterloo, 2021-09-30) Aminoleslami, Arian; Abouee Mehrizi, Hossein
The year 2019 revealed that some of the policies which have shaped the core structure of many organizations in different industries for a long time, could result in an absolute failure in an unprecedented crisis like the COVID-19 pandemic. In the light of such changes, the interaction between the people is a determining factor to limit an outbreak among the staff members of an organization to prevent any disruption in the process of the service/product they provide. Thus, an effective staff scheduling policy can be the clincher to achieve this goal. In this work, we consider a staff scheduling problem with the goal of minimizing the expected number of staff replacements that happens as a result of getting infected during a pandemic. In this days-off scheduling problem, we discuss a two-stage optimization approach where we first, determine the optimal scheduling patterns for the staff members and next, we will assign them to different resources so that the interaction between the staff members is minimized. In the proposed mathematical formulation for the problem, we consider the characteristics of the disease and the situation of the public health at different stages of the pandemic such as the incubation period, the probability of getting infected on a working day versus a rest-day, and the availability of swab tests. We design a column generation algorithm to solve the optimization model which requires up to 70% less computational power compared to the traditional algorithms that solve the problem when all available patterns are generated. A simulation model is also designed to compare the effectiveness of our suggested policies with the traditional scheduling policies. We examine our findings using data from the Grand River Regional Cancer Centre (GRRCC), which is a comprehensive cancer treatment and research centre located in Kitchener, Ontario. Particularly, we worked closely with the Department of Medical Physics and Radiation Oncology who plans and delivers radiation therapy treatments to cancer patients and treats over 2000 new patients annually. Our results show that depending on the different stages of a pandemic, the proposed staff scheduling policies can lead up to 20% less full-time equivalent staff replacements which have a significant impact on the availability of the centre's resources as well as the patient flow in long-term.
Stochastic Perishable Inventory Systems: Dual-Balancing and Look-Ahead Approaches
(University of Waterloo, 2016-12-23) Diao, Yuhe; Abouee Mehrizi, Hossein
We study a single-item, multi-period, stochastic perishable inventory problem under both backlogging and lost-sales circumstances, with and without an order capacity constraint in each period. We first model the problem as a dynamic program and then develop two heuristics namely, Dual-Balancing (DB) and Look-Ahead (LA) policies, to approximate the optimal inventory level at the beginning of each period. To characterize the holding and backlog cost functions under the proposed polices, we introduce a truncated marginal holding cost for the marginal cost accounting scheme. Our numerical examples demonstrate that both DB and LA policies have a possible worst-case performance guarantee of two in perishable inventory systems under different assumptions, and the LA policy significantly outperforms the DB policy in most situations. We also analyze the target inventory level in each period (the inventory level at the beginning of each period) under different policies. We observe that the target inventory level under the LA policy is not larger than the optimal one in each period in systems without an order capacity constraint.
A Tractable Approach To Inverse Optimization Under Euclidean Norm
(University of Waterloo, 2023-09-11) Ebrahimkhani, Sara; Mahmoudzadeh, Houra; Abouee Mehrizi, Hossein
The conventional optimization assumes that the problem and its parameters are known, and it utilizes this information to determine the optimal solution. Inverse optimization works in reverse by determining different parameters of an optimization model such that a given dataset of observed decisions from the past becomes optimal for the model. The parameters imputed through inverse optimization can be in the objective function and/or the constraints of the model. When inferring the constraint parameters, the choice of objective for the inverse optimization problem can result in different inverse optimal solutions. However, it is unclear which solution provides the best fit to the data. In this study, a goodness-of-fit measure is first introduced to evaluate the fit between the model and data and determine the quality of the inferred feasible region based on the distances of data points from its boundary. Next, employing this measure as the objective function, a multi-point inverse optimization problem under the Euclidean norm is proposed to infer the feasible region of a linear optimization model. Given the nonlinear nature of the Euclidean norm, a relaxation technique using the non-smooth L1 penalty function is proposed for the inverse optimization problem. This reformulates the non-convex mixed-integer quadratically-constrained programming problem into a mixed-integer quadratic programming problem which is more tractable. Then, an exact heuristic method and a greedy heuristic method are introduced to alleviate the computational challenges of the problem. Finally, two application examples to illustrate the practicality and effectiveness of our proposed model and solution approach are presented. In the first application, our model determines the implicit criteria based on which a patient is identified as an outpatient without requiring hospital supervision. The second application focuses on improving the recommended diets by uncovering hidden preferences and suggesting meal plans based on individuals' past food choices.

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