arXiv subjects

Karmel S. Shehadeh

Publications and source records attributed to Karmel S. Shehadeh.

12 recordsLinked to original sources

arXiv2025

Can LLMs Support Medical Knowledge Imputation? An Evaluation-Based Perspective

Medical knowledge graphs (KGs) are essential for clinical decision support and biomedical research, yet they often exhibit incompleteness due to knowledge gaps and structural limitations in medical coding systems. This issue is particularly evident in treatment mapping, where coding systems such as ICD, Mondo, and ATC lack comprehensive coverage, resulting in missing or inconsistent associations between diseases and their potential treatments. To address this issue, we have explored the use of Large Language Models (LLMs) for imputing missing treatment relationships. Although LLMs offer promising capabilities in knowledge augmentation, their application in medical knowledge imputation presents significant risks, including factual inaccuracies, hallucinated associations, and instability between and within LLMs. In this study, we systematically evaluate LLM-driven treatment mapping, assessing its reliability through benchmark comparisons. Our findings highlight critical limitations, including inconsistencies with established clinical guidelines and potential risks to patient safety. This study serves as a cautionary guide for researchers and practitioners, underscoring the importance of critical evaluation and hybrid approaches when leveraging LLMs to enhance treatment mappings on medical knowledge graphs.

cs.CL↗

arXiv2025

A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures

We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss their properties, and derive an axiomatic characterization for such measures. Then, we introduce the class of convex fairness measures, discuss their properties, and derive an equivalent dual representation of these measures as a robustified order-based fairness measure over their dual sets. Importantly, this dual representation renders a unified mathematical expression and an alternative geometric characterization for convex fairness measures through their dual sets. Moreover, it allows us to develop a unified framework for optimization problems with a convex fairness measure objective or constraint, including unified reformulations and solution methods. In addition, we provide stability results that quantify the impact of employing different convex fairness measures on the optimal value and solution of the resulting fairness-promoting optimization problem. Finally, we present numerical results demonstrating the computational efficiency of our unified framework over traditional ones and illustrating our stability results.

math.OC↗

arXiv2025

On the Trade-Off Between Distributional Belief and Ambiguity: Conservatism, Finite-Sample Guarantees, and Asymptotic Properties

We propose and analyze a new data-driven trade-off (TRO) approach for modeling uncertainty that serves as a middle ground between the optimistic approach, which adopts a distributional belief, and the pessimistic distributionally robust optimization approach, which hedges against distributional ambiguity. We equip the TRO model with a TRO ambiguity set characterized by a size parameter controlling the level of optimism and a shape parameter representing distributional ambiguity. We first show that constructing the TRO ambiguity set using a general star-shaped shape parameter with the empirical distribution as its star center is necessary and sufficient to guarantee the hierarchical structure of the sequence of TRO ambiguity sets. Then, we analyze the properties of the TRO model, including quantifying conservatism, quantifying bias and generalization error, and establishing asymptotic properties. Specifically, we show that the TRO model could generate a spectrum of decisions, ranging from optimistic to conservative decisions. Additionally, we show that it could produce an unbiased estimator of the true optimal value. Furthermore, we establish the almost-sure convergence of the optimal value and the set of optimal solutions of the TRO model to their true counterparts. We exemplify our theoretical results using an inventory control problem and a portfolio optimization problem.

math.OC↗

arXiv2024

Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

We propose combined allocation, assignment, sequencing, and scheduling problems under uncertainty involving multiple operation rooms (ORs), anesthesiologists, and surgeries, as well as methodologies for solving such problems. Specifically, given sets of ORs, regular anesthesiologists, on-call anesthesiologists, and surgeries, our methodologies solve the following decision-making problems simultaneously: (1) an allocation problem that decides which ORs to open and which on-call anesthesiologists to call in, (2) an assignment problem that assigns an OR and an anesthesiologist to each surgery, and (3) a sequencing and scheduling problem that determines the order of surgeries and their scheduled start times in each OR. To address uncertainty of each surgery's duration, we propose and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models with both risk-neutral and risk-averse objectives. We obtain near-optimal solutions of our SP models using sample average approximation and propose a computationally efficient column-and-constraint generation method to solve our DRO models. In addition, we derive symmetry-breaking constraints that improve the models' solvability. Using real-world, publicly available surgery data and a case study from a health system in New York, we conduct extensive computational experiments comparing the proposed methodologies empirically and theoretically, demonstrating where significant performance improvements can be gained. Additionally, we derive several managerial insights relevant to practice.

math.OC↗

arXiv2022

An inexact column-and-constraint generation method to solve two-stage robust optimization problems

We propose a new inexact column-and-constraint generation (i-C&CG) method to solve two-stage robust optimization problems. The method allows solutions to the master problems to be inexact, which is desirable when solving large-scale and/or challenging problems. It is equipped with a backtracking routine that controls the trade-off between bound improvement and inexactness. Importantly, this routine allows us to derive theoretical finite convergence guarantees for our i-C&CG method. Numerical experiments demonstrate computational advantages of our i-C&CG method over state-of-the-art column-and-constraint generation methods.

math.OC↗

arXiv2022

Stochastic Optimization Models for Location and Inventory Prepositioning of Disaster Relief Supplies

We consider the problem of preparing for a disaster season by determining where to open warehouses and how much relief item inventory to preposition in each. Then, after each disaster, prepositioned items are distributed to demand nodes during the post-disaster phase, and additional items are procured and distributed as needed. There is often uncertainty in the disaster level, affected areas locations, the demand for relief items, the usable fraction of prepositioned items post-disaster, procurement quantity, and arc capacity. To address uncertainty, we propose and analyze two-stage stochastic programming (SP) and distributionally robust optimization (DRO) models, assuming known and unknown (ambiguous) uncertainty distributions. The first and second stages correspond to pre- and post-disaster phases, respectively. We also propose a model that minimizes the trade-off between considering distributional ambiguity and following distributional belief. We obtain near-optimal solutions of our SP model using sample average approximation and propose a computationally efficient decomposition algorithm to solve our DRO models. We conduct extensive experiments using a hurricane season and an earthquake as case studies to investigate these approaches' computational and operational performance.

math.OC↗

arXiv2022

Integrated Home Care Staffing and Capacity Planning: Stochastic Optimization Approaches

We propose stochastic optimization methodologies for a staffing and capacity planning problem arising from home care practice. Specifically, we consider the perspective of a home care agency that must decide the number of caregivers to hire (staffing) and the allocation of hired caregivers to different types of services (capacity planning) in each day within a specified planning horizon. The objective is to minimize the total cost associated with staffing (i.e., employment), capacity allocation, over-staffing, and under-staffing. We propose two-stage stochastic programming (SP) and distributionally robust optimization (DRO) approaches to model and solve this problem considering two types of decision-makers, namely an everything in advance decision-maker (EA) and a flexible adjustment decision-maker (FA). In the EA models, we determine the staffing and capacity allocation decisions in the first stage before observing the demand. In the FA models, we decide the staffing decisions in the first stage. Then, we determine the capacity allocation decisions based on demand realizations in the second stage. We derive equivalent mixed-integer linear programming (MILP) reformulations of the proposed nonlinear DRO model for the EA decision-maker that can be implemented and efficiently solved using off-the-shelf optimization software. We propose a computationally efficient column-and-constraint generation algorithm with valid inequalities to solve the proposed DRO model for the FA decision-maker. Finally, we conduct extensive numerical experiments comparing the operational and computational performance of the proposed approaches and discuss insights and implications for home care staffing and capacity planning.

math.OC↗

arXiv2022

Data-Driven Distributionally Robust Surgery Planning in Flexible Operating Rooms Over a Wasserstein Ambiguity

We study elective surgery planning in flexible operating rooms (ORs) where emergency patients are accommodated in the existing elective surgery schedule. Specifically, elective surgeries can be scheduled weeks or months in advance. In contrast, an emergency surgery arrives randomly and must be performed on the day of arrival. Probability distributions of the actual durations of elective and emergency surgeries are unknown, and only a possibly small set of historical realizations may be available. To address distributional uncertainty, we first construct an ambiguity set that encompasses all possible distributions of surgery durations within a 1-Wasserstein distance from the empirical distribution. We then define a distributionally robust surgery assignment (DSA) problem to determine optimal elective surgery assignment decisions to available surgical blocks in multiple ORs, considering the capacity needed for emergency cases. The objective is to minimize the total cost consisting of the fixed cost related to scheduling or rejecting elective surgery plus the maximum expected cost associated with OR overtime and idle time over all distributions defined in the ambiguity set. Using the DSA model's structural properties, we derive an equivalent mixed-integer linear programming (MILP) reformulation that can be implemented and solved efficiently using off-the-shelf optimization software. In addition, we extend the proposed model to determine the number of ORs needed to serve the two competing surgery classes and derive a MILP reformulation of this extension. We conduct extensive numerical experiments based on real-world surgery data, demonstrating our proposed model's computational efficiency and superior out-of-sample operational performance over two state-of-the-art approaches. In addition, we derive insights into surgery scheduling in flexible ORs.

math.OC↗

arXiv2022

Distributionally Robust Optimization Approaches for a Stochastic Mobile Facility Fleet Sizing, Routing, and Scheduling Problem

We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models. Specifically, given a set of MFs, a planning horizon, and a service region, our models aim to find the number of MFs to use (i.e., fleet size) within the planning horizon and a route and schedule for each MF in the fleet. The objective is to minimize the fixed cost of establishing the MF fleet plus a risk measure (expectation or mean conditional value-at-risk) of the operational cost over all demand distributions defined by an ambiguity set. In the first model, we use an ambiguity set based on the demand's mean, support, and mean absolute deviation. In the second model, we use an ambiguity set that incorporates all distributions within a 1-Wasserstein distance from a reference distribution. To solve the proposed DRO models, we propose a decomposition-based algorithm. In addition, we derive valid lower bound inequalities that efficiently strengthen the master problem in the decomposition algorithm, thus improving convergence. We also derive two families of symmetry-breaking constraints that improve the solvability of the proposed models. Finally, we present extensive computational experiments comparing the operational and computational performance of the proposed models and a stochastic programming model, demonstrating where significant performance improvements could be gained and derive insights into the MFRSP.

math.OC↗

arXiv2021

Equity in Stochastic Healthcare Facility Location

We consider issues of equity in stochastic facility location models for healthcare applications. We explore how uncertainty exacerbates inequity and examine several equity measures that can be used for stochastic healthcare location modeling. We analyze the limited literature on this subject and highlight areas of opportunity for developing tractable, reliable, and data-driven approaches that might be applicable within and outside healthcare operations. Our primary focus is on exploring various ways to model uncertainty, equity, and facility location, including modeling aspects (e.g., tractability and accuracy) and outcomes (e.g., equity/fairness/access performance metrics vs. traditional metrics like cost and service levels).

stat.AP↗

arXiv2021

Stochastic Optimization Models for a Home Service Routing and Appointment Scheduling Problem with Random Travel and Service Times

We study a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator's route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers' waiting time, and the operator's travel time, idle time, and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to solve the problem, assuming a known and unknown service and travel time distribution, respectively. We consider two popular types of ambiguity sets for the DRO models, namely, the mean-support and 1-Wasserstein ambiguity set. We derive equivalent mixed-integer linear programming (MILP) reformulations of both DRO models that can be implemented and efficiently solved using off-the-shelf optimization software, thereby enabling practitioners to use these models. In an extensive numerical experiment, we investigate the proposed models computational and operational performance, demonstrating where significant performance improvements can be gained with each proposed model and derive insights into the problem.

math.OC↗

arXiv2021

Fleet Sizing and Allocation for On-demand Last-Mile Transportation Systems

The last-mile problem refers to the provision of travel service from the nearest public transportation node to home or other destination. Last-Mile Transportation Systems (LMTS), which have recently emerged, provide on-demand shared transportation. In this paper, we investigate the fleet sizing and allocation problem for the on-demand LMTS. Specifically, we consider the perspective of a last-mile service provider who wants to determine the number of servicing vehicles to allocate to multiple last-mile service regions in a particular city. In each service region, passengers demanding last-mile services arrive in batches, and allocated vehicles deliver passengers to their final destinations. The passenger demand (i.e., the size of each batch of passengers) is random and hard to predict in advance, especially with limited data during the planning process. The quality of fleet allocation decisions is a function of vehicle fixed cost plus a weighted sum of passenger's waiting time before boarding a vehicle and in-vehicle riding time. We propose and analyze two models-a stochastic programming model and a distributionally robust optimization model-to solve the problem, assuming a known and unknown distribution of the demand, respectively. We conduct extensive numerical experiments to evaluate the models and discuss insights and implications into the optimal fleet sizing and allocation for the on-demand LMTS under demand uncertainty.

math.OC↗