Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.1, No.1, 2011 30 | Page www.iiste.org Heuristic Approach for n-Jobs, 3-Machines Flow Shop Scheduling Problem, Processing Time Associated With Probabilities Involving Transportation Time, Break-Down Interval, Weightage of Jobs and Job Block Criteria Deepak Gupta Prof. & Head, Department of Mathematics, Maharishi Markandeshwar University, Mullana, Haryana, India guptadeepak2003@yahoo.co.in Sameer Sharma (Corresponding Author) Research Scholar, Department of Mathematics, Maharishi Markandeshwar University, Mullana, Haryana, India samsharma31@yahoo.com Seema Sharma Assistant Prof, Department of Mathematics, D.A.V.College, Jalandhar, Punjab, India seemasharma7788@yahoo.com Abstract This paper deals with a new simple heuristic algorithm for n jobs, 3 machines flow shop scheduling problem in which processing times are associated with their corresponding probabilities involving transportation time, break down interval and job block criteria. Further jobs are attached with weights to indicate their relative importance. A heuristic approach method to find optimal or near optimal sequence minimizing the total elapsed time whenever mean weighted production flow time is taken into consideration. The proposed method is very easy to understand and also provide an important tool for decision makers. A numerical illustration is also given to clarify the algorithm. Keywords: Flow shop scheduling, Processing time, Transportation time, Breakdown interval, Weights of job, Optimal sequence 1. Introduction Flow shop scheduling is an important process widely used in manufacturing, production, management, computer science, and so on. Appropriate scheduling not only reduces manufacturing costs but also reduces possibilities for violating the due dates. Finding good schedules for given sets of jobs can thus help factory supervisors effectively control job flow and provide solutions for job sequencing. In flow shop scheduling problems, the objective is to obtain a sequence of jobs which when processed on the machine will optimize some well defined criteria, The number of possible schedules of the flow shop scheduling problem involving n-jobs and m-machines is ( 29 ! m n . Every job will go on these machines in a fixed order of machines. Early research on flow shop problems is based mainly on Johnson’s theorem, which gives a procedure for finding an optimal solution with 2 machines, or 3 machines with certain characteristics. The research in to flow shop scheduling has drawn a great attention in the last decade with the aim to increase the effectiveness of industrial production. Now-a-days, the decision makers for the manufacturing plant must find a way to successfully manage resources in order to produce products in the most efficient way with minimum total flow time. The scheduling problem practically depends upon the important factors