### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Management Information Systems
- Information Systems

### Cite this

**Comparative studies on dynamic programming and integer programming approaches for concave cost production/inventory control problems.** / Konno, Hiroshi; Egawa, Takaaki; Yamamoto, Rei.

Research output: Contribution to journal › Article

*Computational Management Science*, vol. 6, no. 4, pp. 447-457. https://doi.org/10.1007/s10287-007-0052-1

}

TY - JOUR

T1 - Comparative studies on dynamic programming and integer programming approaches for concave cost production/inventory control problems

AU - Konno, Hiroshi

AU - Egawa, Takaaki

AU - Yamamoto, Rei

PY - 2009/6/9

Y1 - 2009/6/9

N2 - 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 (n4m) 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.

AB - 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 (n4m) 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.

KW - 0-1 integer programming

KW - Concave cost inventory control problem

KW - Dynamic programming algorithm

UR - http://www.scopus.com/inward/record.url?scp=69249223174&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69249223174&partnerID=8YFLogxK

U2 - 10.1007/s10287-007-0052-1

DO - 10.1007/s10287-007-0052-1

M3 - Article

AN - SCOPUS:69249223174

VL - 6

SP - 447

EP - 457

JO - Computational Management Science

JF - Computational Management Science

SN - 1619-697X

IS - 4

ER -