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\title{A Solution for the Scheduling Problem in a Multi-Plant and Multi-Product Environment}
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             \author[1]{Nahid  Newaj}

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\date{\small \em Received: 7 December 2013 Accepted: 3 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


Scheduling is an important tool for manufacturing and engineering, where it can have a major impact on the productivity of a process. In this paper, we use flow shop scheduling in KCCL (Kohinoor Chemical Company Limited) & find out the optimum policy in scheduling operating several machines to produce soap & to reduce idle time of machines. Considering different type of machine that also absorbs different production time. The industry tries to identify their idle time & best presidential relationship between the machines. We use Johnson?s scheduling algorithm & a numerical output is achieved.

\end{abstract}


\keywords{johnson?s algorithm, scheduling of chemical industry.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
roduction scheduling tools greatly outperform older manual scheduling methods. These provide the production scheduler with powerful graphical interfaces which can be used to visually optimize realtime workloads in various stages of production, and pattern recognition allows the software to automatically create scheduling opportunities which might not be apparent without this view into the data.\par
In manufacturing, the purpose of scheduling is to minimize the production time and costs, by telling a production facility when to make, with which staff, and on which equipment. Production scheduling aims to maximize the efficiency of the operation and reduce costs.\par
The Chemicals \& Cosmetics Industry is quite large and important sector in Bangladesh in terms of output, export and employment.\par
In the chemical industry, a successful manufacturer must make efficient use of limited resources to meet dynamic customer demand as customer preference change on a seasonal or monthly basis. For this prospect, an ordinary production schedule is not enough. So, we need an advanced scheduling technique. 
\section[{a) Literature Review}]{a) Literature Review}\par
The literature review, focusing entirely on one particular aspect of scheduling theory which is recognized \& the review article which are published. in the sector of aspect. For example the literature as hybrid flow shops  {\ref (Gupta, 1988)}.Whereas our interest is in the identical job and uniform parallel machine environment, the literature on hybrid flow shops has focused on Author: Rajshahi University of Engineering \& Technology, Ruet, Rajshahi, Bangladesh. e-mail: newaj.nahid@gmail.com non-identical jobs and identical parallel machines. The problem of scheduling non-identical jobs on identical parallel machines to minimize the make span is NP-hard even for a single-stage (Garey and \hyperref[b6]{Johnson, 1979)}. For an excellent review of the single stage problem the reader is referred to a paper by \hyperref[b3]{Cheng and Sin (1990)}. With more than a single-stage, the research has focused on developing heuristics (see e.g., Guinet and Solomon, 1996; Gupta Tune, 1994; Lee and Vairaktarakis, 1994; Gupta, 1988). \hyperref[b7]{Lawler et al. (1982)} show that the l-stage problem to minimize the make span with identical jobs \& uniform parallel machines may be solved in polynomial time. 
\section[{II.}]{II.} 
\section[{Problem Description}]{Problem Description}\par
Existing Schedule: In this company the authorities follow any sequence as they like. The two plant named as Frymaco \& Jansen which are evolved with the production of multiple product i.e. toothpaste, shaving cream, shaving cream cool, snow toothpaste menthol. This sometime luckily optimal but maximum time the optimal sequences are not followed due to some problem. If they normally scheduled their work the make span of their process is 64 periods. And the idle time of this process is 16 periods. 
\section[{III.}]{III.} 
\section[{Algorithmic Methods}]{Algorithmic Methods}\par
When scheduling situations become more complicated, for example when two or more processes share resources, it may be difficult to find the best schedule. A number of common scheduling problems, including variations on the example described above, fall into a class of problems that become very difficult to solve as their size (number of procedures and operations) grows. A wide variety of algorithms and approaches have been applied to batch process scheduling. Early methods, which were implemented in some MRP systems assumed infinite capacity and depended only on the batch time. Such methods did not account for any resources would produce infeasible schedules.\par
Mathematical programming methods involve formulating the scheduling problem as an optimization problem where some objective, e.g. total duration, must be minimized (or maximized) subject to a series of constraints which are generally stated as a set of inequalities and equalities. The objective and constraints P Global Journal of Researches in Engineering ( ) G Volume XIV Issue I Version I may involve zero-or-one (integer) variables as well as nonlinear relationships. An appropriate solver is applied for the resulting mixed-integer linear or nonlinear programming (MILP/MINLP) problem. The approach is theoretically guaranteed to find an optimal solution if one exists. The disadvantage is that the solver algorithm may take an unreasonable amount of time. Practitioners may use problem-specific simplifications in the formulation to get faster solutions without eliminating critical components of the scheduling model.\par
Constraint programming is a similar approach except that the problem is formulated only as a set of constraints and the goal is to arrive at a feasible solution rapidly. Multiple solutions are possible with this method. The sequence of the Algorithm is summarizedin the table which is given below: c) A Gantt Chart for proposed Schedule  
\section[{Conclusion}]{Conclusion}\par
Since the chemical industry is mostly based on both human performance and machine performance, there is a chance to develop the technical aspect. For this reason time is the major constraint to utilize the workforce with limited resource. This problem may be solved by using a better schedule. In this sense the flow shop model is noble idea and implementation of this model solving by Jonson's Algorithm is satisfactory.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}A}\end{figure}
 			\footnote{Year 2014 © 2014 Global Journals Inc. (US)} 			\footnote{© 2014 Global Journals Inc. (US)} 		 		\backmatter  			 
\subsection[{Global Journals Inc. (US) Guidelines Handbook 2014}]{Global Journals Inc. (US) Guidelines Handbook 2014}\par
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\bibitem[Carey and Johnson ()]{b6}\label{b6} 	 		\textit{Computers and Intractability: A Guide to the Theory of NP-Completeness},  		 			M R Carey 		,  		 			D S Johnson 		.  		1979. New York: Freeman.  	 
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\end{document}
