arXiv subjects

Vahid Sarhangian

Publications and source records attributed to Vahid Sarhangian.

9 recordsLinked to original sources

arXiv2026

Review-Period Sensitivity in Multiclass Queue Scheduling

Optimal control of queueing networks is typically studied under continuous-time control. In many service settings, however, managers can adjust decisions only at discrete and potentially infrequent review epochs. We study a multiclass queue scheduling problem in which server assignments can be changed only at the beginning of discrete review periods, and examine how performance depends on the review-period length. We analyze a family of associated fluid control problems parameterized by the review-period length and characterize the first- and second-order sensitivity of the value function. For the two-class case, we derive explicit expressions for these derivatives and characterize their signs. We find that for short review periods, the value function need not be monotone. Once the review period is sufficiently large, the value function becomes monotone nondecreasing and may exhibit a convex or linear region before eventually becoming concave. These results provide insights on when the value of more frequent control, or \emph{flexibility} with respect to server assignments, is higher. We further numerically examine the robustness of these observations for the original stochastic scheduling problem and show that stochasticity smooths the nonmonotonicity at smaller scales, while the qualitative sensitivity patterns remain visible and become more pronounced as the scale of the system increases.

eess.SY↗

arXiv2026

Dual-Based Weight Selection for Approximate Linear Programming

Approximate Linear Programming (ALP) is widely used for large-scale Markov Decision Processes (MDPs), but its performance can be sensitive to the choice of state-relevance weights, which are typically selected heuristically. Performance bounds suggest aligning these weights with the discounted occupancy measure of the induced policy, and existing primal approaches address this through repeated greedy-policy construction. Nonetheless, they lack convergence guarantees and are computationally expensive. We propose a dual-based method that uses projected occupancy information from the ALP dual solution to construct a smooth stochastic policy and update the state-relevance weights, which avoids separate greedy-action calculations. We establish conditions under which the weights match the discounted occupancy of the induced policy and prove uniqueness and global convergence under appropriate smoothing. We also derive an a posteriori policy-loss bound that separates error from the weighted Bellman residual, occupancy mismatch, and stochastic-versus-greedy disagreement. Experiments on classical queueing and multi-priority scheduling problems show that the proposed approach reduces sensitivity to fixed weights and achieves comparable or better policy quality than primal updates at lower computational cost. Finally, we show that adaptive weighting is most valuable when the basis functions are sufficiently expressive for occupancy information to influence the resulting policy.

eess.SY↗

arXiv2026

Comparing Exploration-Exploitation Strategies of LLMs and Humans: Insights from Standard Multi-armed Bandit Experiments

Large language models (LLMs) are increasingly used to simulate or automate human behavior in complex sequential decision-making settings. A natural question is then whether LLMs exhibit similar decision-making behavior to humans, and can achieve comparable (or superior) performance. In this work, we focus on the exploration-exploitation (E&E) tradeoff, a fundamental aspect of dynamic decision-making under uncertainty. We employ canonical multi-armed bandit (MAB) experiments introduced in the cognitive science and psychiatry literature to conduct a comparative study of the E&E strategies of LLMs, humans, and MAB algorithms. We use interpretable choice models to capture the E&E strategies of the agents and investigate how enabling thinking traces, through both prompting strategies and thinking models, shapes LLM decision-making. We find that enabling thinking in LLMs shifts their behavior toward more human-like behavior, characterized by a mix of random and directed exploration. In a simple stationary setting, thinking-enabled LLMs exhibit similar levels of random and directed exploration compared to humans. However, in more complex, non-stationary environments, LLMs struggle to match human adaptability, particularly in effective directed exploration, despite achieving similar regret in certain scenarios. Our findings highlight both the promise and limits of LLMs as simulators of human behavior and tools for automated decision-making and point to potential areas for improvement.

cs.LG↗

arXiv2025

Dynamic Transfer Policies for Parallel Queues

We consider the problem of load balancing in parallel queues by transferring customers between them at discrete points in time. Holding costs accrue as customers wait in the queue, while transfer decisions incur both fixed (setup) costs and variable costs that increase with the number of transfers and travel distance, and vary by transfer direction. Our work is primarily motivated by inter-facility patient transfers to address imbalanced congestion and inequity in access to care during surges in hospital demand. Analyzing an associated fluid control problem, we show that under general assumptions, including time-varying arrivals and convex holding costs, the optimal policy partitions the state-space into a well-defined $\textit{no-transfer region}$ and its complement, implying that transferring is optimal if and only if the system is sufficiently imbalanced. In the absence of fixed transfer costs, an optimal policy moves the state to the no-transfer region's boundary; in contrast, with fixed costs, the state is moved to its relative interior. Leveraging our structural results, we propose a simulation-based approximate dynamic programming (ADP) algorithm to find effective transfer policies for the stochastic system. We investigate the performance and robustness of the fluid and ADP policies in a case study calibrated using data during the COVID-19 pandemic in the Greater Toronto Area, which demonstrates that transferring patients between hospitals could result in up to 27.7% reduction in total cost with relatively few transfers.

math.OC↗

arXiv2025

Robust Confidence Bands for Stochastic Processes Using Simulation

We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes or validate stochastic simulation models by checking whether historical paths from the actual system fall within the constructed confidence band. Unlike existing approaches in the literature, our methodology is widely applicable and directly addresses optimization bias within the constraints, producing tight confidence bands with accurate coverage probabilities. It is tractable, being only slightly more complex than the state-of-the-art baseline approach, and easy to use, as it employs standard techniques. Additionally, our approach is also applicable to continuous-time processes after appropriately discretizing time. In our first case study, we show that our approach achieves the desired coverage probabilities with an order-of-magnitude fewer sample paths than the state-of-the-art baseline approach. In our second case study, we illustrate how our approach can be used to validate stochastic simulation models.

math.OC↗

arXiv2025

Platelet Inventory Management with Approximate Dynamic Programming

We study a stochastic perishable inventory control problem with endogenous (decision-dependent) uncertainty in shelf-life of units. Our primary motivation is determining ordering policies for blood platelets. Determining optimal ordering quantities is a challenging task due to the short maximum shelf-life of platelets (3-5 days after testing) and high uncertainty in daily demand. We formulate the problem as an infinite-horizon discounted Markov Decision Process (MDP). The model captures salient features observed in our data from a network of Canadian hospitals and allows for fixed ordering costs. We show that with uncertainty in shelf-life, the value function of the MDP is non-convex and key structural properties valid under deterministic shelf-life no longer hold. Hence, we propose an Approximate Dynamic Programming (ADP) algorithm to find approximate policies. We approximate the value function using a linear combination of basis functions and tune the parameters using a simulation-based policy iteration algorithm. We evaluate the performance of the proposed policy using extensive numerical experiments in parameter regimes relevant to the platelet inventory management problem. We further leverage the ADP algorithm to evaluate the impact of ignoring shelf-life uncertainty. Finally, we evaluate the out-of-sample performance of the ADP algorithm in a case study using real data and compare it to the historical hospital performance and other benchmarks. The ADP policy can be computed online in a few minutes and results in more than 50% lower expiry and shortage rates compared to the historical performance. In addition, it performs better or as well as an exact policy that ignores uncertainty in shelf-life and becomes hard to compute for larger instance of the problem.

eess.SY↗

arXiv2025

Multiclass Queue Scheduling Under Slowdown: An Approximate Dynamic Programming Approach

In many service systems, especially those in healthcare, customer waiting times can result in increased service requirements. Such service slowdowns can significantly impact system performance. Therefore, it is important to properly account for their impact when designing scheduling policies. Scheduling under wait-dependent service times is challenging, especially when multiple customer classes are heterogeneously affected by waiting. In this work, we study scheduling policies in multiclass, multiserver queues with wait-dependent service slowdowns. We propose a simulation-based Approximate Dynamic Programming (ADP) algorithm to find close-to-optimal scheduling policies. The ADP algorithm (i) represents the policy using classifiers based on the index policy structure, (ii) leverages a coupling method to estimate the differences of the relative value functions directly, and (iii) uses adaptive sampling for efficient state-space exploration. Through extensive numerical experiments, we illustrate that the ADP algorithm generates close-to-optimal policies that outperform well-known benchmarks. We also provide insights into the structure of the optimal policy, which reveals an important trade-off between instantaneous cost reduction and preventing the system from reaching high-cost equilibria. Lastly, we conduct a case study on scheduling admissions into rehabilitation care to illustrate the effectiveness of the ADP algorithm in practice.

math.OC↗

arXiv2024

Dynamic Control of Service Systems with Returns: Application to Design of Post-Discharge Hospital Readmission Prevention Programs

We study a control problem for queueing systems where customers may return for additional episodes of service after their initial service completion. At each service completion epoch, the decision maker can choose to reduce the probability of return for the departing customer but at a cost that is convex increasing in the amount of reduction in the return probability. Other costs are incurred as customers wait in the queue and every time they return for service. Our primary motivation comes from post-discharge Quality Improvement (QI) interventions (e.g., follow up phone-calls, appointments) frequently used in a variety of healthcare settings to reduce unplanned hospital readmissions. Our objective is to understand how the cost of interventions should be balanced with the reductions in congestion and service costs. To this end, we consider a fluid approximation of the queueing system and characterize the structure of optimal long-run average and bias-optimal transient control policies for the fluid model. Our structural results motivate the design of intuitive surge protocols whereby different intensities of interventions (corresponding to different levels of reduction in the return probability) are provided based on the congestion in the system. Through extensive simulation experiments, we study the performance of the fluid policy for the stochastic system and identify parameter regimes where it leads to significant cost savings compared to a fixed long-run average optimal policy that ignores holding costs and a simple policy that uses the highest level of intervention whenever the queue is non-empty. In particular, we find that in a parameter regime relevant to our motivating application, dynamically adjusting the intensity of interventions could result in up to 25.4% reduction in long-run average cost and 33.7% in finite-horizon costs compared to the simple aggressive policy.

eess.SY↗

arXiv2021

Optimization Helps Scheduling Nursing Staff at the Long-Term Care Homes of the City of Toronto

The City of Toronto Long Term Care Homes & Services (LTCH&S) division is one of the largest providers of long-term care in the Canadian province of Ontario, providing care to 2,640 residents at 10 homes across Toronto. Our collaboration with LTCH&S was initiated to facilitate the increasingly challenging task of scheduling nursing staff and reduce high absenteeism rate observed among the part-time nurses. We developed a spreadsheet-based scheduling tool to automate the generation of schedules and incorporate nurses' preferences for different shifts into the schedules. At the core of the scheduling tool is a hierarchical optimization model that generates a feasible schedule with the highest total preference score while satisfying the maximum possible demand. Feasible schedules had to abide by a set of complex seniority requirements which prioritized more senior nurses when allocating the available shifts. Our scheduling tool was implemented in a 391-bed home in Toronto. The tool allowed nursing managers to generate feasible schedules within a fraction of an hour, in contrast to the status-quo manual approach which could took up to tens of hours. In addition, the schedules successfully accounted for preferences with on average above 94% of the allocated shifts ranked as most preferred.

cs.CY↗