On NP-completeness of the cell formation problem

TL;DR

This paper proves that the cell formation problem with the fractional grouping efficacy objective is NP-complete by reducing it from a known NP-complete problem, establishing its computational complexity.

Contribution

It demonstrates NP-completeness of the CFP with the grouping efficacy objective through a reduction from the bicluster graph editing problem.

Findings

NP-completeness of CFP with fractional grouping efficacy

Equivalence of CFP with linear objective to BGEP

Reduction from linear CFP to grouping efficacy CFP

Abstract

In the current paper we provide a proof of NP-completeness for the CFP problem with the fractional grouping efficacy objective. For this purpose we first consider the CFP with the linear objective minimizing the total number of exceptions and voids. Following the ideas of Pinheiro et al. (2016) we show that it is equivalent to the Bicluster Graph Editing Problem (BGEP), which is known to be NP-complete (Amit, 2004). Then we suggest a reduction of the CFP problem with the linear objective function to the CFP with the grouping efficacy objective.