### Abstract

This paper is concerned with classical concave cost multi-echelon production/inventory control problems studied by W. Zangwill and others. It is well known that the problem with m production steps and n time periods can be solved by a dynamic programming algorithm in O (n^{4}m) steps, which is considered as the fastest algorithm for solving this class of problems. In this paper, we will show that an alternative 0-1 integer programming approach can solve the same problem much faster particularly when n is large and the number of 0-1 integer variables is relatively few. This class of problems include, among others problem with set-up cost function and piecewise linear cost function with fewer linear pieces. The new approach can solve problems with mixed concave/convex cost functions, which cannot be solved by dynamic programming algorithms.

Original language | English |
---|---|

Pages (from-to) | 447-457 |

Number of pages | 11 |

Journal | Computational Management Science |

Volume | 6 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Jun 9 |

Externally published | Yes |

### Keywords

- 0-1 integer programming
- Concave cost inventory control problem
- Dynamic programming algorithm

### ASJC Scopus subject areas

- Management Information Systems
- Information Systems