Inventory models under uncertainty: an adaptive approach

Y. R. Rubinstein, J. Kreimer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Consider the following nonlinear programming (NLP) problem: min xg0(x)= min x∫ψ(x, y)fY(y, x) dy=min E[ψ0(x, Y)]s.t.gj(x)=∫ψj(x, y)f{hook}Y(x, y) dy=E[ψj(x, Y)] ≤ 0, j=1,...,M,where x ∈ X ⊂ Rn,y∈ D ⊂ Rm, ψj(x,Y), j=0,1,...,M are given functions, and fT(y, x)is a probability density function depending on a vector of parameters x. We assume that the pdf (probability density function) fY(y, x) is unknown but a sample Y1,..., YN from it is available. To find the approximate solution of this NLP problem (the exact solution is not available since fY(y,'x) is unknown) we use the sample Y1...YN directly in an adaptive procedure called stochastic approximation in which the optimal solution x* of (1) is approximated iteratively, i.e., step by step. We consider several stochastic optimization models which can be fitted in the framework of the NLP problem (1) and present adaptive stochastic approximation procedures to approximate the optimal solution x*.

Original languageEnglish
Pages (from-to)169-188
Number of pages20
JournalMathematics and Computers in Simulation
Volume28
Issue number3
DOIs
StatePublished - 1 Jan 1986
Externally publishedYes

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