On the Optimum Scenarios for Single Row Equidistant Facility Layout Problem

TL;DR

This paper investigates lower bounding techniques for the NP-hard Single Row Equidistant Facility Layout Problem, proposing enhanced bounds and a conjecture for approximation guarantees to improve solution quality and computational efficiency.

Contribution

It introduces an improved bidirectional lower bound, combines it with Gilmore-Lawler bounds, and proposes a conjecture for a 4/3 approximation scheme for SREFLP.

Findings

Enhanced lower bounds for SREFLP identified.

A new optimum scenario for SREFLP is proposed.

Conjecture of a 4/3 approximation scheme is introduced.

Abstract

Single Row Equidistant Facility Layout Problem SREFLP is with an NP-Hard nature to mimic material handling costs along with equally spaced straight-line facilities layout. Based on literature, it is obvious that efforts of researchers for solving SREFLP turn from exact methods into release the running time tracing the principle of the approximate methods in time race, regardless searching their time complexity release in conjunction with a provable quality of solutions. This study focuses on Lower bounding LB techniques as an independent potential solution tool for SREFLP. In particular, Best-known SREFLP LBs are reported from literature and significantly LBs optimum scenarios are highlighted. Initially, one gap of the SREFLP bidirectional LB is enhanced. From the integration between the enhanced LB and the best-known Gilmore-Lawler GL bounding, a new SREFLP optimum scenario is provided. Further improvements to GLB lead to guarantee an exact Shipping/Receiving Facility assignment and propose a conjecture of at most 4/3 approximation scheme for SREFLP.