Barış Ata

Baris Ata, J. Michael Harrison, Nian Si

Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is exogenously specified, as are its directions of reflection from the orthant's boundary surfaces. A system manager chooses a drift vector $θ(t)$ at each time $t$ based on the history of $Z$, and the cost rate at time $t$ depends on both $Z(t)$ and $θ(t)$. In our initial problem formulation, the objective is to minimize expected discounted cost over an infinite planning horizon, after which we treat the corresponding ergodic control problem. Extending earlier work by Han et al. (Proceedings of the National Academy of Sciences, 2018, 8505-8510), we develop and illustrate a simulation-based computational method that relies heavily on deep neural network technology. For test problems studied thus far, our method is accurate to within a fraction of one percent, and is computationally feasible in dimensions up to at least $d=30$.

Baris Ata, Ebru Kasikaralar

We consider a multi-class queueing model of a telephone call center, in which a system manager dynamically allocates available servers to customer calls. Calls can terminate through either service completion or customer abandonment, and the manager strives to minimize the expected total of holding costs plus abandonment costs over a finite horizon. Focusing on the Halfin-Whitt heavy traffic regime, we derive an approximating diffusion control problem, and building on earlier work by Beck et al. (2021), develop a simulation-based computational method for solution of such problems, one that relies heavily on deep neural network technology. Using this computational method, we propose a policy for the original (pre-limit) call center scheduling problem. Finally, the performance of this policy is assessed using test problems based on publicly available call center data. For the test problems considered so far, our policy does as well as or better than the best benchmark we could find. Moreover, our method is computationally feasible at least up to dimension 500, that is, for call centers with 500 or more distinct customer classes.

Barış Ata, Wouter van Eekelen, Yuan Zhong

We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).