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

Hiroshi Konno, Takaaki Egawa, Rei Yamamoto

Research output: Contribution to journalArticle

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 (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.

Original languageEnglish
Pages (from-to)447-457
Number of pages11
JournalComputational Management Science
Volume6
Issue number4
DOIs
Publication statusPublished - 2009 Jun 9
Externally publishedYes

Fingerprint

Inventory control
Integer programming
Dynamic programming
Cost functions
Costs
Cost function
Production-inventory
Comparative study

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.

In: Computational Management Science, Vol. 6, No. 4, 09.06.2009, p. 447-457.

Research output: Contribution to journalArticle

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