Linear programming formulation of the set partitioning problem
by Moustapha Diaby
International Journal of Operational Research (IJOR), Vol. 8, No. 4, 2010

Abstract: In this paper, we present a linear programming (LP) model of the set partitioning problem (SPP). The number of variables and the number of constraints of the proposed model are bounded by (third-degree) polynomial functions of the number of non-zero entries of the SPP input matrix, respectively. Hence, the model provides a new affirmative resolution to the all-important 'P vs. NP' question. We use a transportation problem-based reformulation that we develop, and a path-based modelling approach similar to that used in Diaby (2007) to formulate the proposed LP model. The approach is illustrated with a numerical example.

Online publication date: Wed, 07-Jul-2010

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Operational Research (IJOR):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com