Abstract. Scheduling in the context of many-server queues has received considerable attention. When there are multiple customer classes and many servers, it is common to make simplifying assumptions that result in a ``low-fidelity'' model, potentially leading to model misspecification. However, empirical evidence suggests that these assumptions may not accurately reflect real-world scenarios. While relaxing these assumptions can yield a more accurate ``high-fidelity'' model, it often becomes complex and challenging, if not impossible, to solve. In this paper, we introduce a novel approach for decision-makers to generate high-quality scheduling policies for large service systems based on a simple and tractable low-fidelity model instead of its complex and intractable high-fidelity counterpart. At the core of our approach is a robust control formulation, wherein optimization is conducted against an imaginary adversary. This adversary optimally exploits the potential weaknesses of a scheduling rule within prescribed limits defined by an uncertainty set by dynamically perturbing the low-fidelity model. This process assists decision-makers in assessing the vulnerability of a given scheduling policy to model errors stemming from the low-fidelity model. Moreover, our proposed robust control framework is complemented by practical data-driven schemes for uncertainty set selection. Extensive numerical experiments, including a case study based on a US call center dataset, substantiate the effectiveness of our framework by revealing scheduling policies that can significantly reduce the system's costs in comparison to established benchmarks in the literature.

Abstract. The rise of online market places has raised customer expectations regarding customization and lead time, posing significant challenges to manufacturing firms and prompting a move from make-to-stock to a more flexible make-to-order system. A major challenge in make-to-order manufacturing is that fluctuations in demand cannot be smoothed by available stock. Many manufacturing firms can create capacity flexibility in addition to using dynamic pricing schemes to maintain a balance between demand and supply. In that scenario, system costs could be cut by managing capacity and demand simultaneously. In this paper, we consider a make-to-order production environment with base capacity and surge capacity as well as the ability to adjust product pricing. Our main focus is on operational decision-making, assuming that base capacity and surge capacity are fixed. Initially, we propose a stochastic optimization model to reflect this complex decision problem. However, our initial model leads to an intractable stochastic optimization problem. To overcome this, we convert the problem to a more tractable diffusion control problem. This approach helps to reveal the conditions under which utilizing flexible capacity is more advantageous than relying solely on fixed capacity in traditional contexts. When flexible capacity is advantageous, we provide a solution to the diffusion control problem that can guide optimal capacity and price adjustments. We discover a rich interplay between capacity adjustment and dynamic pricing. In particular, we find that the price, which aims at reducing congestion, does not monotonically increase with the congestion level when flexible capacity is present. We also demonstrate how to expand the single-product model to accommodate multiple products.

Abstract. We study dynamic matching in a service platform represented by a multi-class, multi-server queueing system. Matching is in the form of job-server assignments, and the service platform lacks knowledge of job-server-specific mean rewards. The objective is to minimize regret, defined as the difference between the cumulative payoff over a time horizon and the maximum payoff possible, with complete knowledge of all system parameters and stochasticity absent. We propose two matching and learning algorithms: one close in spirit to the barrier method in optimization and the other using Lyapunov optimization. Both algorithms estimate job-server assignment rewards using a bandit learning subroutine. When the total service capacity exceeds the demand, both algorithms achieve sub-linear regret and maintain queue stability. Numerical experiments with synthetic and real-world data validate the effectiveness of our algorithms. Our analysis reveals that, despite not being explicitly modeled as part of the managerial objective, queueing delays can impede learning, ultimately reducing platform profitability. Therefore, reducing service delays can be crucial not only to achieving high service levels but also to maximizing rewards.

Abstract. We study a multiple-period stochastic allocation problem that has important applications in the distribution of blood products from production centers to demand points. The single-period version of the problem was proposed and solved by Prastacos in the 1970s and '80s. However, the multiple-period problem presents formidable analytical challenges, and to the best of our knowledge this is the first attempt at a rigorous theoretical analysis of the multiple-period extension of the Prastacos allocation models; we study two classes of models, rotation and retention. We solve the problem of finding the optimal allocations from supply centers to demand centers in many special cases, and pay particular attention to myopic optimality; that is, to situations in which the optimal two-period model is solved simply by applying the optimal single period solution---which is easily computed--- in each period of the horizon. Our analytical work is restricted to a two-period horizon. We use Monte Carlo simulation and a Markov decision model formulation to generate several interesting and actionable insights into the optimality gap associated with the myopic optimal policy in two-period and three-period problems.