Fully polynomial time (Σ,Π)-approximation schemes for continuous nonlinear newsvendor and continuous stochastic dynamic programs

We study the nonlinear newsvendor problem concerning goods of a non-discrete nature, and a class of stochastic dynamic programs with several application areas such as supply chain management and economics. The class is characterized by continuous state and action spaces, either convex or monotone co...

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Vydané v:Mathematical programming Ročník 195; číslo 1-2; s. 183 - 242
Hlavní autori: Halman, Nir, Nannicini, Giacomo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022
Springer
Springer Nature B.V
Predmet:
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Cost function
Full Length Paper
Hardness
Logistics
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mechanical properties
Numerical Analysis
Polynomials
Supply chains
Theoretical
Stochastic dynamic programming
approximation sets and functions
Approximation algorithms
Newsvendor problem
Stochastic inventory control
Hardness of approximation
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:We study the nonlinear newsvendor problem concerning goods of a non-discrete nature, and a class of stochastic dynamic programs with several application areas such as supply chain management and economics. The class is characterized by continuous state and action spaces, either convex or monotone cost functions that are accessed via value oracles, and affine transition functions. We establish that these problems cannot be approximated to any degree of either relative or additive error, regardless of the scheme used. To circumvent these hardness results, we generalize the concept of fully polynomial-time approximation scheme allowing arbitrarily small additive and multiplicative error at the same time, while requiring a polynomial running time in the input size and the error parameters. We develop approximation schemes of this type for the classes of problems mentioned above. In light of our hardness results, such approximation schemes are “best possible”. A computational evaluation shows the promise of this approach.
Bibliografia:ObjectType-Article-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01685-4