29 research outputs found
Robust newsvendor problem with autoregressive demand
This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.Ministerio de Economía y CompetitividadJunta de Andalucí
Distributionally Robust Optimization: A Review
The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization
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Robust optimal stopping
This paper studies the optimal stopping problem in the presence of
model uncertainty (ambiguity). We develop a method to practically solve this
problem in a general setting, allowing for general time-consistent ambiguity
averse preferences and general payoff processes driven by jump-diffusions.
Our method consists of three steps. First, we construct a suitable Doob
martingale associated with the solution to the optimal stopping problem using
backward stochastic calculus. Second, we employ this martingale to construct
an approximated upper bound to the solution using duality. Third, we
introduce backward-forward simulation to obtain a genuine upper bound to the
solution, which converges to the true solution asymptotically. We analyze the
asymptotic behavior and convergence properties of our method. We illustrate
the generality and applicability of our method and the potentially
significant impact of ambiguity to optimal stopping in a few examples