An optimal approximate dynamic programming algorithm for the lagged asset acquisition problem

Juliana M. Nascimento, Warren Buckler Powell

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)210-237
Number of pages28
JournalMathematics of Operations Research
Volume34
Issue number1
DOIs
StatePublished - Feb 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Approximate dynamic programming
  • Stochastic approximation
  • Stochastic learning and adaptive control

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