Alessandro Arlotto

Journal Article Stochastic Systems · June 1, 2020 We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with items arriving according to a Bernoulli process over n discrete time periods. Items have equal rewards and independent weights that are drawn from a ... Full text Cite

Uniformly Bounded Regret in the Multisecretary Problem

Journal Article Stochastic Systems · September 1, 2019 In the secretary problem of Cayley [Cayley A (1875) Mathematical questions with their solutions. Ed. Times 23:18–19.] and Moser [Moser L (1956) On a problem of Cayley. Scripta Mathematica 22(3/4):289–292.], n nonnegative, independent, random variables with ... Full text Cite

Strategic open routing in service networks

Journal Article Management Science · February 1, 2019 We study the behavior of strategic customers in an open-routing service network with multiple stations. When a customer enters the network, she is free to choose the sequence of stations that she visits, with the objective of minimizing her expected total ... Full text Cite

A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays

Journal Article Methodology and Computing in Applied Probability · September 1, 2018 It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variable, and, as the Saint Petersburg Paradox reminds us, the expected value does ... Full text Cite

An adaptive O(log n)-optimal policy for the online selection of a monotone subsequence from a random sample

Journal Article Random Structures and Algorithms · January 1, 2018 Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by su ... Full text Open Access Cite

A central limit theorem for temporally nonhomogenous markov chains with applications to dynamic programming

Journal Article Mathematics of Operations Research · November 1, 2016 We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin for temporally nonhomogeneous Markov chains, and th ... Full text Cite

Quickest online selection of an increasing subsequence of specified size

Journal Article Random Structures and Algorithms · September 1, 2016 Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a monotone increasing sub ... Full text Cite

Beardwood-halton-hammersley theorem for stationary ergodic sequences: A counterexample

Journal Article Annals of Applied Probability · August 1, 2016 We construct a stationary ergodic process X1 ,X2 ,... such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1 ,X2 ,..., ... Full text Cite

Optimal online selection of a monotone subsequence: A central limit theorem

Journal Article Stochastic Processes and their Applications · August 28, 2014 © 2015 Elsevier B.V. Consider a sequence of n independent random variables with a common continuous distribution F, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must b ... Full text Cite

Optimal hiring and retention policies for heterogeneous workers who learn

Journal Article Management Science · January 1, 2014 We study the hiring and retention of heterogeneous workers who learn over time. We show that the problem can be analyzed as an infinite-armed bandit with switching costs, and we apply results from Bergemann and Välimäki [Bergemann D, Välimäki J (2001) Stat ... Full text Cite

Markov decision problems where means bound variances

Journal Article Operations Research · January 1, 2014 We identify a rich class of finite-horizon Markov decision problems (MDPs) for which the variance of the optimal total reward can be bounded by a simple linear function of its expected value. The class is characterized by three natural properties, reward n ... Full text Cite

Optimal online selection of an alternating subsequence: A central limit theorem

Journal Article Advances in Applied Probability · January 1, 2014 We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F, and we prove a central limit theorem for the number of selections made by that policy. ... Full text Cite

Online selection of alternating subsequences from a random sample

Journal Article Journal of Applied Probability · December 1, 2011 We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, w ... Full text Cite

Optimal sequential selection of a unimodal subsequence of a random sequence

Journal Article Combinatorics Probability and Computing · November 1, 2011 We consider the problem of selecting sequentially a unimodal subsequence from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does so within a factor of the square root of two ... Full text Cite

Optimal employee retention when inferring unknown learning curves

Journal Article Proceedings Winter Simulation Conference · December 1, 2010 This paper formulates an employer's hiring and retention decisions as an infinite-armed bandit problem and characterizes the structure of optimal hiring and retention policies. We develop approximations that allow us to explicitly calculate these policies ... Full text Cite

Hessian orders and multinormal distributions

Journal Article Journal of Multivariate Analysis · November 1, 2009 Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined ... Full text Cite