## Abstract

We propose a computationally efficient fully polynomial-time approximation scheme (FPTAS) to compute an approximation with arbitrary precision of the value function of convex stochastic dynamic programs, using the technique of K-approximation sets and functions introduced by Halman et al. [Math. Oper. Res., 34, (2009), pp. 674-685]. This paper deals with the convex case only, and it has the following contributions. First, we improve on the worst-case running time given by Halman et al. Second, we design and implement an FPTAS with excellent computational performance and show that it is faster than an exact algorithm even for small problem instances and small approximation factors, becoming orders of magnitude faster as the problem size increases. Third, we show that with careful algorithm design, the errors introduced by floating point computations can be bounded, so that we can provide a guarantee on the approximation factor over an exact infinite-precision solution. We provide an extensive computational evaluation based on randomly generated problem instances coming from applications in supply chain management and finance. The running time of the FPTAS is both theoretically and experimentally linear in the size of the uncertainty set.

Original language | English |
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Pages (from-to) | 317-350 |

Number of pages | 34 |

Journal | SIAM Journal on Optimization |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015 Society for Industrial and Applied Mathematics.

## Keywords

- Approximation algorithms
- Discrete convexity
- Dynamic programming
- Fully polynomial-time approximation scheme
- Inventory control