arXiv subjects

Wouter van Eekelen

Publications and source records attributed to Wouter van Eekelen.

3 recordsLinked to original sources

arXiv2025

A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions

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).

math.OC↗

arXiv2020

MAD dispersion measure makes extremal queue analysis simple

A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival and service time distributions. We address this extremal queue problem by measuring dispersion in terms of Mean Absolute Deviation (MAD) instead of variance, making available recently developed techniques from Distributionally Robust Optimization (DRO). Combined with classical random walk theory, we obtain explicit expressions for the extremal interarrival time and service time distributions, and hence the best possible upper bounds, for all moments of the waiting time. {We also apply the DRO techniques to obtain tight lower bounds that together with the upper bounds provide robust performance intervals. We show that all bounds are computationally tractable and remain sharp, also when the mean and MAD are not known precisely, but estimated based on available data instead.

math.PR↗

arXiv2020

Tight tail probability bounds for distribution-free decision making

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower and upper bounds on the tail probability given a bounded support, mean and mean absolute deviation of the random variable. We obtain these bounds as exact solutions to semi-infinite linear programs. We leverage the bounds for distribution-free analysis of the newsvendor model, monopolistic pricing, and stop-loss reinsurance. We also exploit the bounds for safe approximations of sums of correlated random variables, and to find convex reformulations of single and joint ambiguous chance constraints that are ubiquitous in distributionally robust optimization.

math.OC↗