An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem

We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm usi...

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Bibliographic Details
Published in:Mathematics of operations research Vol. 34; no. 1; pp. 210 - 237
Main Authors: Nascimento, Juliana M, Powell, Warren B
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.02.2009
Institute for Operations Research and the Management Sciences
Subjects:
Adaptive control
Algorithms
approximate dynamic programming
Approximation
Asset acquisitions
Dynamic programming
Evaluation
Induction assumption
Integers
Mathematical functions
Mathematical induction
Mathematical inequalities
Operations research
Optimal policy
Stochastic analysis
stochastic approximation
stochastic learning and adaptive control
Studies
United States
ISSN:0364-765X, 1526-5471
Online Access:Get full text
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Summary:We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions.
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ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1080.0360