This study addresses the critical yet under researched area of supported evacuation for vulnerable populations during wildfires, such as hospital patients and long term care residents, by developing a two stage stochastic optimization model that optimizes facility location, fleet sizing, and vehicle routing under strict time windows. To overcome the problem NP hard complexity, the authors propose an innovative solution methodology leveraging Logic Based Benders Decomposition, featuring Combinatorial Benders Cuts and logic based inequalities. Extensive numerical experiments and real world data from a community wildfire drill in Roxborough Park, Colorado, demonstrate that the proposed approach yields high quality solutions, significantly improving shelter placement, vehicle utilization, and overall evacuation efficiency compared to alternative policies.

This paper addresses the inherent bias-variance limitations of approximate dynamic programming (ADP) in highdimensional stochastic control problems by introducing an Adaptive Piecewise Affine Approximate Optimal Policy (PW-AOP) through a novel Fitted Value Iteration algorithm. While traditional global affine approximations suffer from severe approximation bias when confronting non-linear system dynamics (e.g., congestion bottlenecks or threshold penalties), our method dynamically constructs a localized, separable piecewise affine value function. We depart from standard Monte Carlo trajectory evaluations by utilizing exact one-step look-ahead Bellman targets, effectively eliminating estimation variance caused by transition noise. Furthermore, the algorithm incorporates Dynamic State Relevance Weighting, which involves blending a strictly positive geometric prior with empirical policy visitation frequencies, to actively align the training distribution with the operational policy, thereby taming the concentrability coefficient. By evaluating Weighted Bellman Residuals (WBR), our approach automatically discovers and allocates partitioning breakpoints to regions of the state space exhibiting large WBRs due to critical non-linearities. We establish rigorous finite-time performance bounds for this methodology, proving that it systematically breaks the representational bottleneck of global affine architectures while strictly regulating the pseudo-dimension to prevent estimation error explosion. Across diverse and complex domains, including controllable queueing networks, battery management systems, and multi-priority patient scheduling, we conduct numerical experiments to demonstrate that our adaptive framework yields strictly superior control policies and tighter value function approximations, all while preserving the computational efficiency and structural interpretability of linear programming-based ADP.

This paper studies the appointment scheduling problem where heterogeneous appointments (jobs) are processed by multiple providers (machines). Our goal is to optimize provider utilization and appointment wait time under uncertainties (processing time, punctuality, and no-show). We propose a learning-based algorithm combining deep learning and partial mixed integer programming. Specifically, we develop a convolutional neural network that captures uncertainties and estimates associated costs. It is trained on synthetically generated data and then integrated into the deterministic model’s objective. Under nondeterministic conditions, our approach performs well, showing an average improvement of over 157% on the largest instance compared with a heuristic. Through simulation, we compare deterministic and nondeterministic solutions: deterministic solutions yield about 16% higher utilization rewards, whereas nondeterministic solutions reduce wait time and overtime penalties by around 80% and 82%, respectively (99% confidence). Our results also show that a more flexible unpunctuality management policy reduces appointment wait time and machine overtime but increases job tardiness because it often necessitates serving jobs out of order, potentially encouraging further unpunctuality. History: This paper’s review was handled by special issue editor Xiaocheng Li for the Virtual Special Issue on GenAI etc. for Business Analytics. Funding: Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), [Grant RGPIN-2020-04301]. Data Ethics & Reproducibility Note: The appendix and code capsule are available in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2025.0090 ).

This study examines a patient scheduling problem with multiple appointment types and priority levels, where certain appointments must precede others and lead times play a crucial role. Although both factors significantly influence the quality of care—particularly when specialist assessments depend on timely diagnostic tests—they have been largely overlooked in existing healthcare scheduling models. To address this gap, we propose a dynamic scheduling model that explicitly incorporates appointment dependencies, lead times, and patient heterogeneity across multiple priority levels. The model reflects the real-world complexities of coordinating diagnostic and consult appointments in time-sensitive clinical settings. Using Approximate Dynamic Programming techniques, we develop an Approximate Optimal Policy (AOP) that efficiently allocates clinical resources, minimizes patient wait times, and ensures the availability of test results prior to consult appointments. We further derive a closed-form solution for the optimal approximation parameters, supported by a mathematical proof, which offers significant computational advantages. We evaluate the performance of the proposed AOP through simulation and compare it against a set of benchmark policies, including heuristics adapted from existing scheduling logic and current clinical practice. The solution is applied to a case study created based on data from a Stroke Prevention Clinic (SPC), where the complexity of care protocols and high demand present substantial scheduling challenges. The results demonstrate that the AOP consistently outperforms all benchmarks in terms of reducing wait times, ensuring timely diagnostic completion before consults, and meeting wait-time targets. We also introduce a practical, easy-to-implement heuristic called (MSP), which is derived from the AOP and designed for operational use. While simpler in structure, MSP performs comparably well and is well-suited for adoption in real healthcare settings due to its interpretability and minimal computational requirements. Finally, although the proposed approach is demonstrated in the context of an SPC, it has broader applicability to other areas such as cancer care, kidney transplant scheduling, and other complex care pathways involving interdependent appointments and prioritization.

We investigate an ambulatory care scheduling problem derived from a real case in Ontario, Canada that offers multi-appointment, multi-class, multi-priority treatments in geographically distributed campuses with multiple resources. We consider a dynamic setting with uncertain patient arrival and use of the emergency department. This problem is formulated as an infinite-horizon Markov decision process model. Since we cannot solve large-sized instances via conventional approaches, we hybridize this model with a neural network to simplify feasibility constraints while respecting all assumptions. Given the curse of dimensionality, we use an affine approximation architecture to estimate the value function. An equivalent linear programming model is solved through column generation in order to compute approximate optimal policies and derive two easy-to-implement scheduling policies. Simulation results demonstrate that the approximate optimal policy and heuristics outperform alternative scheduling policies. Finally, we demonstrate that the application of our methodology can enhance performance metrics in a large ambulatory care center in Canada. We show that a template-based scheduling rule can result in high resource utilization but poor scheduling decisions. However, an efficient scheduling policy equips a booking clerk with intelligent scheduling rules that are difficult for her to predict in real-time and work well in comparison to scheduling templates.

We investigate an ambulatory care scheduling problem derived from a real case in Ontario, Canada that offers multi-appointment, multi-class, multi-priority treatments in geographically distributed campuses with multiple resources. We consider a dynamic setting with uncertain patient arrival and use of the emergency department. This problem is formulated as an infinite-horizon Markov decision process model. Since we cannot solve large-sized instances via conventional approaches, we hybridize this model with a neural network to simplify feasibility constraints while respecting all assumptions. Given the curse of dimensionality, we use an affine approximation architecture to estimate the value function. An equivalent linear programing model is solved through column generation in order to compute approximate optimal policies and derive two easy-to-implement scheduling policies. Simulation results demonstrate that the approximate optimal policy and heuristics outperform alternative scheduling policies. Finally, we demonstrate that the application of our methodology can enhance performance metrics in a large ambulatory care center in Canada. We show that a template-based scheduling rule can result in high resource utilization but poor scheduling decisions. However, an efficient scheduling policy equips a booking clerk with intelligent scheduling rules that are difficult for her to predict in real-time and work well in comparison to scheduling templates.

This paper describes a solution approach for stochastic multi-resource multi-patient staff scheduling problems in inpatient units. Our solution approach has four steps. First, we classify patients into a number of groups with similar care-provider requirements. Second, a predictive Markov model captures patients' flow in the inpatient unit and provides a prediction of the number of patients of each group in the future. This predictive model allows us to generate a potentially large set of possible system utilization scenarios over the planning horizon. Third, a mixed-integer programming model with an expected value objective function seeks to minimize the expected over-staffing and under-staffing costs across all possible scenarios. Lastly, we use simulation to sample system utilization scenarios and the sample average approximation method to find a reliable and generalizable solution to the model across all possible scenarios. We evaluate the performance of the proposed solution using real data from the Children's Hospital of Eastern Ontario's inpatient mental health unit. The results show that the proposed approach significantly decreases the expected cost of the schedules in comparison to the traditional approaches.

With advent of the Covid pandemic, hospitals grappled with how to manage the sudden surge in demand while still treating those in need of service for other reasons. This study aims to provide an adaptive elective admission scheduling policy that maximizes throughput during a pandemic while maintaining the ability of a hospital to empty a specified number of beds over a short warning period (e.g. 5 days). This ability we call nimbleness. We propose a heuristic method based on two mixed-integer linear programming models (MILP) and a simulation model. The first MILP creates the initial schedule for patient admissions over the planning horizon while maximizing patient throughput. The second MILP considers the uncertainty of the emergency arrivals (including pandemic induced) and the patients' length of stay and maximizes the number of scheduled patients admitted while ensuring the hospital's nimbleness. A simulation model is built to create daily random arrivals and discharges. The models connect through an automated feedback loop until the heuristic approach converges on a solution. Numerical results demonstrate the ability of the approach to maintain high throughput while still responding to pandemic surges.

Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Since optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered.

Disaster operations management (DOM) seeks to mitigate the harmful impact of natural disasters on individuals, society, infrastructure, economic activities, and the environment. Due to the increasing number of people affected worldwide, and the increase in weather-related disasters, DOM has become increasingly important. In this survey, we focus on the post-disaster stage of DOM that involves response operations. We review studies that propose optimization models to supporting the following four relief logistics operations: (i) relief items distribution, (ii) location of relief facilities and temporary shelters, (iii) integrated relief items distribution and shelter location, and (iv) transportation of affected population. Optimization models from 127 articles published between 2013 and 2022, focusing on relief logistics operations during natural disasters, are categorized by disaster type and thoroughly analyzed. Each model provides a case study illustrating its application in addressing key relief logistics operations. We also analyse the extent to which these studies address the critical assumptions and methodological gaps identified by Galindo and Batta (Eur J Oper Res 230:201–211, 2013), Caunhye et al. (Socio-econ Plan Sci 46:4–13, 2012), and Kovacs and Moshtari (Eur J Oper Res 276:395–408, 2019) and the neglected research directions noted by the authors of other relevant review papers. Based on our findings, we provide avenues for potential future research. Our analysis shows a slow increase in the total number of papers published until 2018–2019 and a sharp decrease afterwards, the latter most likely as a consequence of the COVID-19 pandemic. More than half of the papers in our selection concern earthquakes while less than ten papers deal with wildfires, cyclones, or tsunamis. The majority of the stochastic optimization models consider uncertainty in the demand and supply of relief items, while some other crucial sources of uncertainty such as funding availability and donations of relief items (e.g., blood products) remain understudied. Furthermore, most of the papers in our selection fail to incorporate key characteristics of disaster relief operations such as its dynamic nature and information updates during the response phase. Finally, a large number of studies use exact commercial software to solve their models, which may not be computationally efficient or practical for large-scale problems, specifically under uncertainty.

In current clinical practice, priority‐specific wait time targets are usually determined based on the consensus of medical specialists and health care administrators. The rationale behind this approach considers clinical urgency but it does not consider the efficient use of clinical resources and the patient volume associated with each priority class. The approach we present here aims to determine wait time targets in a systematic fashion that both respects clinically acceptable maximum recommended wait times and considers clinic size and demand distribution across patient classes. First, we discuss the performance of several advance patient scheduling policies in the literature in terms of average wait times and overtime and select one for illustrative purposes. Second, we simulate the chosen policy given a demand distribution and a fixed system capacity and approximate (using regression and neural networks) the average wait time for each priority class and the use of overtime as a function of potential wait time targets. Finally, using a parameterized cost function, we formulate forward and inverse mathematical problems to determine when the implicit unit wait time costs drop to zero as wait time target values increase. Using illustrative examples with two patient classes, and a practical application with four patient classes, we demonstrate the potential managerial benefits of the proposed approach in terms of improved clinic efficiency and reduced wait times. This approach ensures that wait times are set to the minimum value that still achieves the maximal resource efficiency ensuring that patients wait for service is not extended unnecessarily.

We propose a novel variant of the value-based additive data envelopment analysis model. It conducts a comprehensive robustness analysis of efficiency outcomes for all feasible input and output weights using mathematical programming and the Monte Carlo simulation. We also introduce the original procedures for selecting a common vector of weights and an approach for investigating the stability of results in a multiscenario setting. The presented framework is applied to evaluate the performance of emergency department physicians using data from the Children's Hospital of Eastern Ontario in Ottawa. Our focus is on the physicians' performance when dealing with groups of patients' complaints related to abdominal pain and constipation, fever, extremity injury, head injury, and laceration/puncture. The obtained results emphasize the strong dependence of the physicians' performances on the selected weight vectors. However, they prove helpful in pointing out overall good performers who can serve as universal benchmarks or niche performers being markedly better in providing care to a given complaint group. They also offer a basis for developing an improvement plan for the underperforming physicians, identifying the priorities for a practice-oriented model, and recognizing the most challenging patients' complaints.

While the inventory management problem faced by central banks is complicated in that they must deal with two-way shipments, complex costing agreements and insurance limits on inventory, we were able to develop an adapted version of an (s,S) policy that reduced the costs of the central bank’s inventory management by 25%. Implementation required very little change to the regular practices of the Bank and resulted in very few unintended consequences.

The COVID-19 pandemic severely impacted residential care delivery all around the world. This study investigates the current scheduling methods in residential care facilities in order to enhance them for pandemic conditions. We first define the basic problem that addresses decisions associated with the assignment and scheduling of staff members, who perform a set of tasks required by residents during a planning horizon. This problem includes the minimization of costs associated with the salary of part-time staff members, total overtime, and violations of service time windows. Subsequently, we adapt the basic problem to pandemic conditions by considering the impacts of communal spaces (e.g., shared rooms) and a cohorting policy (classification of residents based on their risk of infection) on the spread of infectious diseases. We introduce a new objective function that minimizes the number of distinct staff members serving each room of residents. Likewise, we propose a new objective function for the cohorting policy that aims to minimize the number of distinct cohorts served by each staff member. A new constraint is incorporated that forces staff members to serve only one cohort within a shift. We present a population-based heuristic algorithm to solve this problem. Through a comparison with two benchmark solution approaches (a mathematical programme and a non-dominated archiving ant colony optimization algorithm), the superiority of the heuristic algorithm is shown regarding solution quality and CPU time. Finally, we conduct numerical analyses to present managerial implications.

In Disaster Relief Operations (DRO), very often a lack of integration of the blood supply chain results in increased costs and higher blood shortage levels. This paper proposes a fully integrated logistics network that allows blood regional units, hospitals, and temporary emergency shelters to share multi-type platelets in both horizontal and vertical manner. This model not only allocates multi-type platelets to patients according to ABO/Rh(d)-compatible blood substitutions but also considers a three-layer logistics network for platelets that accounts for the impact of the age of the platelets on the suitability for different types of injuries. To efficiently solve the model and generate a Pareto front for large-scale instances of the problem, and multiple scenarios, we employ Lagrangian relaxation and the augmented epsilon-constraint method. Finally, to evaluate the performance of the proposed solution approach and derive practical insights, we apply it to a case study based on data about a possible earthquake in Tehran, Iran, and conduct some sensitivity analysis.

Efficient patient scheduling has significant operational, clinical and economical benefits on health care systems by not only increasing the timely access of patients to care but also reducing costs. However, patient scheduling is complex due to, among other aspects, the existence of multiple priority levels, the presence of multiple service requirements, and its stochastic nature. Patient appointment (allocation) scheduling refers to the assignment of specific appointment start times to a set of patients scheduled for a particular day while advance patient scheduling refers to the assignment of future appointment days to patients. These two problems have generally been addressed separately despite each being highly dependent on the form of the other. This paper develops a framework that incorporates stochastic service times into the advance scheduling problem as a first step towards bridging these two problems. In this way, we not only take into account the waiting time until the day of service but also the idle time/overtime of medical resources on the day of service. We first extend the current literature by providing theoretical and numerical results for the case with multi-class, multi-priority patients and deterministic service times. We then adapt the model to incorporate stochastic service times and perform a comprehensive numerical analysis on a number of scenarios, including a practical application. Results suggest that the advance scheduling policies based on deterministic service times cannot be easily improved upon by incorporating stochastic service times, a finding that has important implications for practice and future research on the combined problem. (C) 2019 Elsevier B.V. All rights reserved.

Community care services are becoming increasingly important to health delivery as patients live longer but with chronic disease. In this research, we propose a queuing network approach to capacity planning for a network of services. We take advantage of existing heuristics that calculate the probability of blocking for a given capacity plan and utilize the output of these heuristics to run a simulated annealing approach to optimize capacity allocation across the network subject to a performance guarantee related to the sum of the blocking probabilities. We apply this model to a local health region with a network of six services - acute care, long term care, assisted living, home care, rehabilitation and chronic care. We test the results of the optimization model through a simulation that incorporates more realism than is possible in the queuing model and that also allows us to determine the transient behaviour of the system as it transitions from current capacity levels to the those proposed by the optimization model. (C) 2018 Elsevier B.V. All rights reserved.

The authors describe the development of a decision support tool to simplify the task of scheduling pathologists to subspecialties in the Department of Pathology and Laboratory Medicine at the Ottawa Hospital.

•An accelerated solution method is proposed to solve the two-stage stochastic program.•The method improves the main structure of the sample average approximation algorithm.•The computational process is significantly accelerated to solve real-sized problems.•The relative optimality gaps are significantly reduced using the proposed method.•An improved model is presented for stochastic supply chain network design problems.