\documentclass[11pt,twoside]{article}\makeatletter

\IfFileExists{xcolor.sty}%
  {\RequirePackage{xcolor}}%
  {\RequirePackage{color}}
\usepackage{colortbl}
\usepackage{wrapfig}
\usepackage{ifxetex}
\ifxetex
  \usepackage{fontspec}
  \usepackage{xunicode}
  \catcode`⃥=\active \def⃥{\textbackslash}
  \catcode`❴=\active \def❴{\{}
  \catcode`❵=\active \def❵{\}}
  \def\textJapanese{\fontspec{Noto Sans CJK JP}}
  \def\textChinese{\fontspec{Noto Sans CJK SC}}
  \def\textKorean{\fontspec{Noto Sans CJK KR}}
  \setmonofont{DejaVu Sans Mono}
  
\else
  \IfFileExists{utf8x.def}%
   {\usepackage[utf8x]{inputenc}
      \PrerenderUnicode{–}
    }%
   {\usepackage[utf8]{inputenc}}
  \usepackage[english]{babel}
  \usepackage[T1]{fontenc}
  \usepackage{float}
  \usepackage[]{ucs}
  \uc@dclc{8421}{default}{\textbackslash }
  \uc@dclc{10100}{default}{\{}
  \uc@dclc{10101}{default}{\}}
  \uc@dclc{8491}{default}{\AA{}}
  \uc@dclc{8239}{default}{\,}
  \uc@dclc{20154}{default}{ }
  \uc@dclc{10148}{default}{>}
  \def\textschwa{\rotatebox{-90}{e}}
  \def\textJapanese{}
  \def\textChinese{}
  \IfFileExists{tipa.sty}{\usepackage{tipa}}{}
\fi
\def\exampleFont{\ttfamily\small}
\DeclareTextSymbol{\textpi}{OML}{25}
\usepackage{relsize}
\RequirePackage{array}
\def\@testpach{\@chclass
 \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
  \ifnum \@lastchclass=7 5 \else
   \ifnum \@lastchclass=8 \tw@ \else
    \ifnum \@lastchclass=9 \thr@@
   \else \z@
   \ifnum \@lastchclass = 10 \else
   \edef\@nextchar{\expandafter\string\@nextchar}%
   \@chnum
   \if \@nextchar c\z@ \else
    \if \@nextchar l\@ne \else
     \if \@nextchar r\tw@ \else
   \z@ \@chclass
   \if\@nextchar |\@ne \else
    \if \@nextchar !6 \else
     \if \@nextchar @7 \else
      \if \@nextchar (8 \else
       \if \@nextchar )9 \else
  10
  \@chnum
  \if \@nextchar m\thr@@\else
   \if \@nextchar p4 \else
    \if \@nextchar b5 \else
   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
\gdef\arraybackslash{\let\\=\@arraycr}
\def\@textsubscript#1{{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}}
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\def\abbr{}
\def\corr{}
\def\expan{}
\def\gap{}
\def\orig{}
\def\reg{}
\def\ref{}
\def\sic{}
\def\persName{}\def\name{}
\def\placeName{}
\def\orgName{}
\def\textcal#1{{\fontspec{Lucida Calligraphy}#1}}
\def\textgothic#1{{\fontspec{Lucida Blackletter}#1}}
\def\textlarge#1{{\large #1}}
\def\textoverbar#1{\ensuremath{\overline{#1}}}
\def\textquoted#1{‘#1’}
\def\textsmall#1{{\small #1}}
\def\textsubscript#1{\@textsubscript{\selectfont#1}}
\def\textxi{\ensuremath{\xi}}
\def\titlem{\itshape}
\newenvironment{biblfree}{}{\ifvmode\par\fi }
\newenvironment{bibl}{}{}
\newenvironment{byline}{\vskip6pt\itshape\fontsize{16pt}{18pt}\selectfont}{\par }
\newenvironment{citbibl}{}{\ifvmode\par\fi }
\newenvironment{docAuthor}{\ifvmode\vskip4pt\fontsize{16pt}{18pt}\selectfont\fi\itshape}{\ifvmode\par\fi }
\newenvironment{docDate}{}{\ifvmode\par\fi }
\newenvironment{docImprint}{\vskip 6pt}{\ifvmode\par\fi }
\newenvironment{docTitle}{\vskip6pt\bfseries\fontsize{22pt}{25pt}\selectfont}{\par }
\newenvironment{msHead}{\vskip 6pt}{\par}
\newenvironment{msItem}{\vskip 6pt}{\par}
\newenvironment{rubric}{}{}
\newenvironment{titlePart}{}{\par }

\newcolumntype{L}[1]{){\raggedright\arraybackslash}p{#1}}
\newcolumntype{C}[1]{){\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{){\raggedleft\arraybackslash}p{#1}}
\newcolumntype{P}[1]{){\arraybackslash}p{#1}}
\newcolumntype{B}[1]{){\arraybackslash}b{#1}}
\newcolumntype{M}[1]{){\arraybackslash}m{#1}}
\definecolor{label}{gray}{0.75}
\def\unusedattribute#1{\sout{\textcolor{label}{#1}}}
\DeclareRobustCommand*{\xref}{\hyper@normalise\xref@}
\def\xref@#1#2{\hyper@linkurl{#2}{#1}}
\begingroup
\catcode`\_=\active
\gdef_#1{\ensuremath{\sb{\mathrm{#1}}}}
\endgroup
\mathcode`\_=\string"8000
\catcode`\_=12\relax

\usepackage[a4paper,twoside,lmargin=1in,rmargin=1in,tmargin=1in,bmargin=1in,marginparwidth=0.75in]{geometry}
\usepackage{framed}

\definecolor{shadecolor}{gray}{0.95}
\usepackage{longtable}
\usepackage[normalem]{ulem}
\usepackage{fancyvrb}
\usepackage{fancyhdr}
\usepackage{graphicx}
\usepackage{marginnote}

\renewcommand{\@cite}[1]{#1}


\renewcommand*{\marginfont}{\itshape\footnotesize}

\def\Gin@extensions{.pdf,.png,.jpg,.mps,.tif}

  \pagestyle{fancy}

\usepackage[pdftitle={Job Shop Scheduling Problem for Machine Shop with Shifting Heuristic Bottleneck},
 pdfauthor={}]{hyperref}
\hyperbaseurl{}

	 \paperwidth210mm
	 \paperheight297mm
              
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}
\clubpenalty=8000
\emergencystretch 3em
\hbadness=4000
\hyphenpenalty=400
\pretolerance=750
\tolerance=2000
\vbadness=4000
\widowpenalty=10000

\renewcommand\section{\@startsection {section}{1}{\z@}%
     {-1.75ex \@plus -0.5ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large\bfseries}}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
     {-1.75ex\@plus -0.5ex \@minus- .2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large}}
\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
     {-1.5ex\@plus -0.35ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\large}}
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
     {-1ex \@plus-0.35ex \@minus -0.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\normalsize}}
\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
     {1.5ex \@plus1ex \@minus .2ex}%
     {-1em}%
     {\reset@font\normalsize\bfseries}}


\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
 \@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bfseries \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\@ifundefined{c@section}{\newcounter{section}}{}
\@ifundefined{c@chapter}{\newcounter{chapter}}{}
\newif\if@mainmatter 
\@mainmattertrue
\def\chaptername{Chapter}
\def\frontmatter{%
  \pagenumbering{roman}
  \def\thechapter{\@roman\c@chapter}
  \def\theHchapter{\roman{chapter}}
  \def\thesection{\@roman\c@section}
  \def\theHsection{\roman{section}}
  \def\@chapapp{}%
}
\def\mainmatter{%
  \cleardoublepage
  \def\thechapter{\@arabic\c@chapter}
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \pagenumbering{arabic}
  \setcounter{secnumdepth}{6}
  \def\@chapapp{\chaptername}%
  \def\theHchapter{\arabic{chapter}}
  \def\thesection{\@arabic\c@section}
  \def\theHsection{\arabic{section}}
}
\def\backmatter{%
  \cleardoublepage
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \setcounter{secnumdepth}{2}
  \def\@chapapp{\appendixname}%
  \def\thechapter{\@Alph\c@chapter}
  \def\theHchapter{\Alph{chapter}}
  \appendix
}
\newenvironment{bibitemlist}[1]{%
   \list{\@biblabel{\@arabic\c@enumiv}}%
       {\settowidth\labelwidth{\@biblabel{#1}}%
        \leftmargin\labelwidth
        \advance\leftmargin\labelsep
        \@openbib@code
        \usecounter{enumiv}%
        \let\p@enumiv\@empty
        \renewcommand\theenumiv{\@arabic\c@enumiv}%
	}%
  \sloppy
  \clubpenalty4000
  \@clubpenalty \clubpenalty
  \widowpenalty4000%
  \sfcode`\.\@m}%
  {\def\@noitemerr
    {\@latex@warning{Empty `bibitemlist' environment}}%
    \endlist}

\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
\parskip0pt
\parindent1em
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\newenvironment{reflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemsep}{0pt}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\itshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{sansreflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\itemsep}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\upshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{specHead}[2]%
 {\vspace{20pt}\hrule\vspace{10pt}%
  \phantomsection\label{#1}\markright{#2}%

  \pdfbookmark[2]{#2}{#1}%
  \hspace{-0.75in}{\bfseries\fontsize{16pt}{18pt}\selectfont#2}%
  }{}
      \def\TheFullDate{2015-03-15 (revised: 15 March 2015)}
\def\TheID{\makeatother }
\def\TheDate{2015-03-15}
\title{Job Shop Scheduling Problem for Machine Shop with Shifting Heuristic Bottleneck}
\author{}\makeatletter 
\makeatletter
\newcommand*{\cleartoleftpage}{%
  \clearpage
    \if@twoside
    \ifodd\c@page
      \hbox{}\newpage
      \if@twocolumn
        \hbox{}\newpage
      \fi
    \fi
  \fi
}
\makeatother
\makeatletter
\thispagestyle{empty}
\markright{\@title}\markboth{\@title}{\@author}
\renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2\p@
\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
               \topsep 2\p@ plus1\p@ minus1\p@
               \parsep 2\p@ plus\p@ minus\p@
               \itemsep 1pt}
}
\makeatother
\fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm}
\fancyhf{} 
\setlength{\headheight}{14pt}
\fancyhead[LE]{\bfseries\leftmark} 
\fancyhead[RO]{\bfseries\rightmark} 
\fancyfoot[RO]{}
\fancyfoot[CO]{\thepage}
\fancyfoot[LO]{\TheID}
\fancyfoot[LE]{}
\fancyfoot[CE]{\thepage}
\fancyfoot[RE]{\TheID}
\hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true}
\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}}

\date{}
\usepackage{authblk}

\providecommand{\keywords}[1]
{
\footnotesize
  \textbf{\textit{Index terms---}} #1
}

\usepackage{graphicx,xcolor}
\definecolor{GJBlue}{HTML}{273B81}
\definecolor{GJLightBlue}{HTML}{0A9DD9}
\definecolor{GJMediumGrey}{HTML}{6D6E70}
\definecolor{GJLightGrey}{HTML}{929497} 

\renewenvironment{abstract}{%
   \setlength{\parindent}{0pt}\raggedright
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
   \textcolor{GJBlue}{\large\bfseries\abstractname\space}
}{%   
   \vskip8pt
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
}

\usepackage[absolute,overlay]{textpos}

\makeatother 
      \usepackage{lineno}
      \linenumbers
      
\begin{document}

             \author[1]{Jilcha  Kassu}

             \author[2]{Berhan  Eshetie}

             \affil[1]{  Addis Ababa University}

\renewcommand\Authands{ and }

\date{\small \em Received: 6 February 2015 Accepted: 2 March 2015 Published: 15 March 2015}

\maketitle


\begin{abstract}
        


Job shop scheduling is an Np-Hard combinatory in the field of scheduling problem.Due to this reason, Dejena Aviation Industry (DAVI) has faced a problem to determine the optimum sequences of jobs on machines that can optimize the makespan. The purpose of this study is therefore, to minimize the makespan of the job shop production system of DAVI production system using shifting bottleneck algorithm. Secondary data was collected from the production log book five machines were considered during the production of five jobs. The findings of the shifting bottleneck algorithms showed that an 8.33% reduction in the total makespan of the company job shop production system. Moreover; machine one (41%) and three (36%) are found to be least utilized machines whereas machine three (64%) and five (59%) are relatively the busiest machines.

\end{abstract}


\keywords{job shop scheduling, machine shop, make span, shifting bottleneck.}

\begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) 
\textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark}
\end{textblock*}

\begin{textblock*}{18cm}(1.4cm,1.5cm) % {block width} (coords) 
\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
\end{textblock*}


\let\tabcellsep& 	 	 		 \par
Introduction n today's competitive markets, manufacturers have to respond quickly to orders and meet shipping dates promised to the customers, as failure to do so, at least, may result in a significant loss of good will \hyperref[b0]{[1]}. Among many techniques that makes manufacturers competent in the business arena scheduling is one of the operation to accomplish activities on time and deliver products in their lead time. Customer satisfaction is the last outcome of organizations. This requires an optimum scheduling system that allocate scares resources.\par
Scheduling is the allocation of shared resources over time to competing activities to satisfy customers' requirement. It has been the subject of a significant amount of literature in the field of operations research. Emphasis has also been given on investigating machine scheduling problems where jobs represent activities and machines represent resources so that each machine can process at most one job at a time \hyperref[b0]{[1,}\hyperref[b1]{2]}.\par
Machine scheduling is viewed as a dynamic problem usually an NP-complete combiner's in the production scheduling problems \hyperref[b2]{[3,}\hyperref[b3]{4,}\hyperref[b4]{5,}\hyperref[b0]{1,}\hyperref[b1]{2,} {\ref 6,} {\ref 7,} {\ref 8]}. After a job is processed in a particular machine, the condition of the jobs waiting to be processed on the same machine may be changed due to any of several reasons. For example, new jobs may arrive or the remaining slack times or may be changed even though Author ? ?: Addis Ababa University, Addis Ababa Institute of Technology, Addis Ababa, Ethiopia. e-mails: jkassu@gmail.com, berhan.eshetie@gmail.com no job arrives during the processing time of the previous job on the machine  {\ref [8,} {\ref 9]}. Therefore, it requires a rescheduling effort to determine which job to be processed next.\par
Scheduling is a multifaceted in nature and it consumes large resource. Even for small problems, there is absolutely no guarantee that an optimal final solution can easily be obtained. To this effect, heuristic approach have been used by researchers.\par
Shifting bottle neck heuristics (SBH) is one of the procedures intend to minimize the makespan in a job shop. It follows that in the pre-defined machines sequence there is always one machine with bottleneck in the processing sequences. This heuristic algorithm tries to minimize the effect of the bottleneck process through iterative method in finding maximum makespan (C max ) and maximum lateness time (L max ).\par
Dejena Aviation Industry (DAVI) which is a job shop manufacturing company in Ethiopia faced similar problem in its production system. It experiences a longer makespan in its production system. Therefore the objective of this study is to minimize the makespan of DAVI using shifting bottleneck heuristic algorithm. 
\section[{II.}]{II.} 
\section[{Literature Review}]{Literature Review}\par
Many literatures conducted regarding scheduling, job shop, and shifting bottleneck in the manufacturing systems of a job shop production system. Scheduling is defined as "It is to forecast the processing of a work by assigning resources to tasks and fixing their start times" as defined by \hyperref[b14]{[24,}\hyperref[b15]{25,} {\ref 26]}. Job shop scheduling is a work location in which a number of general purpose work station exist and are used to perform a variety of jobs such as a traditional machine shop with similar machines type located together, batch or individual production.\par
The job shop problem studied in the present paper consists in scheduling a set of jobs on a set of machines with the objective to minimize the makespan, i.e., the maximum of completion times needed for processing all jobs, subject to the constraints that each job has a specified processing order through the machines and that each machine can process at most one job at a time  {\ref [10]}.\par
In the job shop scheduling problem (JSP), there are n jobs that must be processed on a group of m machines. Each job i consists of a sequence of m The job shop scheduling problem, which is among the hardest combinatorial optimization problems that is strongly NP-complete  {\ref [11]}. During the past decades, many researchers have been focusing on the problem and proposed several effective algorithms for it. These algorithms can be classified as optimization and approximation algorithms. The optimization algorithms, mostly used, are based on the branch and bound scheme  {\ref [11]}. These algorithms have made considerable achievement, however, their implementation needs too much computational cost. On the other hand, approximation algorithms, which are more effective for large size problem instances, use several approaches classified as: (a) local search, (b) dispatching priority rules, (c) shifting bottleneck approach, (d) stimulated annealing, and (e) tabu search  {\ref [11]}.\par
Various scholars have been used different approach to solve job shop scheduling problem. Among the many researchers one, Katuri propose Optimization of job shop scheduling using shifting bottle neck technique to reduce total flow time of job shop scheduling problem and arrive the optimal solution [12]. Kai-Pei Chen (2007) proposes an assembly job shop scheduling problem with component availability constraints, a modified disjunctive graph formulation. Also he developed a mixed integer programming model with objective of minimizing the total weight tardiness  {\ref [13]}. Zhi Huang propose a modified shifting bottleneck procedure for job shop scheduling with objective to minimize the make span. In this study dispatching and heuristic approach was used due to the job shop operation practice of the case company. 
\section[{a) Model Representation and algorithm}]{a) Model Representation and algorithm}\par
Generally, JSP uses various representation in its model. In this project let a job shop consists of a set of Mj machines where j=1, 2... m, n jobs, and a predefined plan which states the assignments of these jobs in different machines in some desired sequences (constraints). Each job has a specified number of operations to be carried out in different machines, with individual setup times, processing times, a due date, etc. The job shop sequencing problem deals with the study of an optimal sequencing of the operations (of the jobs) in different machines within the specified constraint requirements  {\ref [14]}.\par
A job-shop does not have the same restriction on workflow as a flow-shop. In a job-shop, jobs can be processed on machines in any order. The usual job shop, from a research standpoint, is one in which there are m machines and n jobs to be processed. Each job requires m operations, one on each machine, in a specific order, but the order can be different for each job \hyperref[b5]{[15,}\hyperref[b6]{16]}.\par
The shifting bottleneck heuristic is an efficient method to find C max and L max objectives in a job shop  {\ref [13]} with an iterative method. At each iteration of the method, a bottleneck machine was identified using 1 /r j / L max approach. A processing sequence of job on the machine bottleneck machine was found so as to minimize L max  {\ref [13]}. The shifting bottleneck algorithm used in this paper is represented as follow: and continue the same iteration until optimum solution is obtained \hyperref[b0]{[1,}\hyperref[b1]{2,} {\ref 6,} {\ref 7,} {\ref 8,} {\ref 9,}\hyperref[b7]{17]}. 
\section[{III.}]{III.} 
\section[{Results and Discussions}]{Results and Discussions}\par
In this study, the jobs selected from list of spare parts manufactured in DAVI which covering 8\% of job orders. The data was collected from jobs: spur gear (J 1 ), shaft with key (J 2 ), adapter (J 3 ), flange (J 4 ) and fitting (J 5 ). These jobs were processed by machines namely power hack saw (M 1 ), lathe machine (M 2 ), milling machine (M 3 ), drilling machine (M 4 ) and grinding machine (M 5 ). The precedence matrix constraint contains for all selected jobs only and machines are presented in Table  {\ref 1}.\par
Table  {\ref 1} : Routing matrix the five jobs and five machinesJobs Precedence constraints J1 M1(2) M2(2) M3(5) M4(2) M5(3) J2 M1(2) M3(2) M4(1) M2(2) M5(2) J3 M1(2) M4(2) M3(3) M2(2) M5(3) J4 M1(1) M2(2) M3(2) M4(1) M5(2) J5 M1(2) M3(2) M4(2) M2(2) M5\textbf{(3)}\par
Once the precedence constraint development of the jobs on each machine were developed by considering machining operation requirements as shown Table  {\ref 1} and setting all the parameters, Lekin scheduling software were used to find the optimum sequences of operations. The findings of the research result with shifting bottleneck heuristic is shown in Table \hyperref[tab_1]{2} and gnat chart for optimum job sequence is shown in Figure  {\ref 1}. There are methods that are built-in-heuristics in minimizing flow times of job shop scheduling. These are: a) Shifting bottleneck heuristics b) Local search heuristic c) Hybrid methods Here in this study shifting bottlenech heuristic has been considered with its three policies/options. The following three policies/options has been utilized in Table \hyperref[tab_1]{2} resulting in performance measurement of the case.\par
? General SB Routine (most objectives)\par
? Objective Specific routines: SB/sumwT (Total Weighted Tardiness) and\par
? Objective Specific routines: SB/Tmax (Maximum Tardiness, Makespan)\par
The key performance measurements are define below.  From Table \hyperref[tab_1]{2} and Figure  {\ref 1}, the findings of the simulation run show that the shifting bottleneck heuristic with the option of shifting bottleneck sum weighted tardiness approach resulted in a minimum makespan of 22 hours with job sequences of job 4-2-5-3-1. The optimum sequence has improved the makespan of DAVI by an 8.33\%. In this sequence the operation started on machine one with job 4 and ends on machine five with job one. The findings of the study also showed that the percentage utilization of each machine. Accordingly, the percentage utilization of machine one is 40.91\%, machine two 45.54\%, machine three 63.63\%, machine four 36.4\% and that of machine five 59.09\% of their available time.\begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.3482638888888889\textwidth}P{0.5017361111111112\textwidth}}
DAVI production system using shifting bottleneck algorithm.\tabcellsep Year 2015\\
\tabcellsep 21\\
\tabcellsep XV Issue I Version I\\
\tabcellsep ( ) Volume J\\
\tabcellsep of Researches in Engineering\\
\tabcellsep Global Journal\end{longtable} \par
  {\small\itshape [Note: operations (Oi1, Oi2..., Oim), where Oik (the k th operation I © 2015 Global Journals Inc. (US) of]} 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.8303030303030303\textwidth}P{0.0196969696969697\textwidth}}
1. initialize\tabcellsep \\
\multicolumn{2}{l}{2. M o = ø (scheduled machines)}\\
\multicolumn{2}{l}{3. G= only conjunctives arcs}\\
\multicolumn{2}{l}{4. G max = critical path in G}\\
\multicolumn{2}{l}{5. Choose a machine Mi;}\\
\multicolumn{2}{l}{6. for each machine M i Ñ?" \{M-M 0 \}}\\
\multicolumn{2}{l}{Generate the 1|r j |L max schedule}\\
\multicolumn{2}{l}{Compute L max (i)}\\
\multicolumn{2}{l}{7. Scheduling the bottleneck machine}\\
\multicolumn{2}{l}{? Let k be the machine that minimizes L max (i)}\\
\multicolumn{2}{l}{? Schedule k by the 1|r j |L max solution}\\
\multicolumn{2}{l}{? Update G}\\
\multicolumn{2}{l}{? Mo= Mo ?\{k\}}\\
\multicolumn{2}{l}{8. Re-Sequence already scheduled machines}\\
\multicolumn{2}{l}{9. For each Mi ? M0? \{k\}}\\
do\tabcellsep \\
\multicolumn{2}{l}{Delete disjunctive arcs for Mi from G}\\
\multicolumn{2}{l}{Form the 1|rj|Lmax}\\
\multicolumn{2}{l}{Reschedule M i according to this schedule}\\
10. While\tabcellsep M = M 0 stop,\\
\multicolumn{2}{l}{else go to 2}\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US)} 		 		\backmatter  			 
\subsection[{Conclusion}]{Conclusion}\par
Job-shop scheduling is an NP-complete combinatorial optimization problems which comprises m machine and n jobs. This research paper aims at scheduling of 5-machines and 5-jobs using shifting bottleneck heuristic algorithm methods built-in-heuristic Lekin scheduling software based on secondary data collected from DAVI production system. The findings of the study showed that the SBH resulted in a total makespan of 22 hours with 8.33\% improvement as compared to the current scheduling system that DAVI operates in its production line. The percentage utilization of machines shows that machine three is the busiest machine whereas machine one and four have relatively the lowest percentage utilization which is less than 50\%. 			 			  				\begin{bibitemlist}{1}
\bibitem[Mönch and Zimmermann ()]{b1}\label{b1} 	 		\textit{A computational study of a shifting bottleneck heuristic for multi-product complex job shops, Production Planning \& Control: The Management of Operations},  		 			Lars Mönch 		,  		 			\& Jens Zimmermann 		.  		 \xref{http://dx.doi.org/10.1080/09537287.2010.490015}{10.1080/09537287.2010.490015}.  		2011. 22 p. .  	 
\bibitem[Nawaz et al. ()]{b10}\label{b10} 	 		‘A heuristic algorithm for the m-machine, n-job flow shop sequencing problem’.  		 			M Nawaz 		,  		 			E E Enscore 		,  		 			I Ham 		.  	 	 		\textit{OMEGA}  		1983. 11 p. .  	 
\bibitem[Kameswari 1 & K. Sreenivasa and Rao ()]{b2}\label{b2} 	 		‘Comparison of Jssp Based Genetic Algorithm with Benchmark Problems for Optimality’.  		 			A L Kameswari 1 \& K. Sreenivasa 		,  		 			Rao 		.  	 	 		\textit{International Journal of Mathematics and Computer Applications Research}  		 Issn 2249-6955.  		2012. 2 p. .  	 	 (Ijmcar) 
\bibitem[Daniel Cortés Rivera et al. ()]{b7}\label{b7} 	 		\textit{Cultural algorithms, an alternative heuristic to solve the job shop scheduling problem, Engineering Optimization},  		 			Ricardo Landa Daniel Cortés Rivera 		,  		 			A Becerra \& Carlos 		,  		 			Coello Coello 		.  		 \xref{http://dx.doi.org/10.1080/03052150600956811}{10.1080/03052150600956811}.  		2007. 39 p. .  	 
\bibitem[Hopp and Spareman ()]{b11}\label{b11} 	 		\textit{Factory Physics Foundation of Manufacturing Management},  		 			W J Hopp 		,  		 			M L Spareman 		.  		2001. Singapore: McGraw-Hill.  	 
\bibitem[Balas and Vazacopoulos ()]{b3}\label{b3} 	 		\textit{Guided local search with shifting bottleneck for job shop scheduling},  		 			E Balas 		,  		 			A Vazacopoulos 		.  		1994. Pittsburgh.  		 			GSIA Carnegie Mellon University 		 	 	 (Tech. Rep.,ManagementScience-ResearchReportMSRR-609) 
\bibitem[Baker ()]{b15}\label{b15} 	 		\textit{Introduction to Sequencing and Scheduling},  		 			K R Baker 		.  		1974. New York: Wiley and Sons.  	 
\bibitem[Özgüven et al. ()]{b13}\label{b13} 	 		‘Mathematical models for job-shop scheduling problems with routing and process plan flexibility’.  		 			Cemal Özgüven 		,  		 			Lale Özbak?r 		,  		 			Yasemin Yavuz 		.  	 	 		\textit{Applied Mathematical Modelling}  		2010. 2010. 34 p. .  	 
\bibitem[Thörnblad]{b4}\label{b4} 	 		\textit{Mathematical optimization of a flexible job shop problem including preventive maintenance and availability of fixtures},  		 			Karin Thörnblad 		.  		 	 
\bibitem[Yan et al. ()]{b8}\label{b8} 	 		‘Modified bottleneck -based heuristic for large scale job-shop based scheduling problem with single bottleneck’.  		 			Zuo Yan 		,  		 			G U Hangu 		,  		 			X I Yugeng 		.  	 	 		\textit{journal of system engineering and electronics}  		2007. 18  (3)  p. .  	 
\bibitem[Uzsoy and Wang ()]{b0}\label{b0} 	 		‘Performance of decomposition procedures for job shop scheduling problems with bottleneck machines’.  		 			Reha Uzsoy 		,  		 			\& Cheng-Shuo Wang 		.  		 \xref{http://dx.doi.org/10.1080/002075400188843}{10.1080/002075400188843}.  	 	 		\textit{International Journal of Production Research}  		2000. 38  (6)  p. .  	 
\bibitem[Pinedo ()]{b14}\label{b14} 	 		 			M Pinedo 		.  		\textit{Scheduling: Theory, Algorithms, and Systems},  				 (New York)  		2001. Prentice-Hall.  	 
\bibitem[Panneerselvam ()]{b12}\label{b12} 	 		\textit{Production and Operation Management},  		 			R Panneerselvam 		.  		2006. New Delhi, India: Prentice Hall.  	 
\bibitem[Huang]{b9}\label{b9} 	 		‘propose a modified shifting bottleneck procedure for job shop scheduling" college of computer science and technology’.  		 			Zhi Huang 		.  	 	 		\textit{P.R. china}  		 		 			Huazhong Universtiy of Science and Technolgy Wuhan 		 	 
\bibitem[Sultana Parveen and Ullah ()]{b6}\label{b6} 	 		‘Review on Job-Shop and Flow-Shop Scheduling using Multi Criteria Decision Making’.  		 			* Sultana Parveen 		,  		 			Hafiz Ullah 		.  	 	 		\textit{Transaction of the Mech. Eng. Div}  		2010. 41  (2) .  	 	 (The Institution of Engineers) 
\bibitem[Silver et al. ()]{b5}\label{b5} 	 		 			E A Silver 		,  		 			D F Pyke 		,  		 			R Peterson 		.  		\textit{Inventory Management and Production Planning and Scheduling Management},  				 (USA)  		1998. John Wiley \& sons.  	 
\end{bibitemlist}
 			 		 	 
\end{document}
