Enhancement of bi-objective function model to master straight-line facilities sequences using frequency from-to chart
Authors: GAMAL SHROUQ , K. El-Nemr Mohamed , M. El-Kassas Ahmed 
Published: March 2021

Purpose
The purpose of this study is to understand the functional power of frequency from-to chart (FFTC) as an independent solution-key for generation optimal (exact) facilities sequences with an equal distance of straight-line flow patterns. The paper will propose a bi-objective function model based on the Torque Method then will turn it into a computer-based technique with a permutative manner using the full enumeration method. This model aims to figure out if there is a difference between the moment minimization and backtracking treatment. Furthermore, the proposed technique will measure the performance of related works from literature to numerically highlight their limitations.

Design/methodology/approach
The literature of related works provided two-principles assumed mastering material flow sequences. The researchers gathered and analyzed the three methods – used FFTC as an independent technique – mentioned in the literature then measured their performance with the proposed technique. The proposed technique is based on the computation of torque value using an enhancement of bi-objective function model then application a permutative approach with full enumeration methodology. The bi-objective function model used once to mimic the grand moment value of FFTC and again to study the reflection of minimizing the congestion of backtracking movements on the minimization of total transportation cost.

Findings
Based on the analysis of literature and comparative results of its three case studies using the proposed technique, it is found that: there are optimum facilities sequences with rich opportunities of exact pathway selection. Reduction methodology is an inefficient way to generate exact results. There is a gap between combining the minimization of the grand moment and the treatment of the backtracking problem.

Research limitations/implications
This study is one of the first contributions that discusses the assumption of integration between optimization moment value and its relation to treatment backtracking problem. Also, the illness of reduction methodology to reach optimal solutions. The further direction of this research will highlight the conjecture of searching the exact results for small size problems, analyzing the given data and its logical dimensions, developing logical rules for solving and verifying large size problems based on the exact results (The conjecture of P = NP).

Originality/value
This paper provides a detailed numerical analysis of the most common problems generally faced facility layout problems through understanding the lack of integration between moment minimization and backtracking minimization. Also, the inefficiency of reliance on reduction methodology either in scores of frequencies between facilities with weak relation or the number of permutations. Based on those findings, further study will search the logical philosophy exactly optimizing FFTC manually or without having to deal with a permutative approach for large size problems – which considered non-deterministic polynomial-time problem.