Journal of Information Engineering and Applications www.iiste.org ISSN 2224-5758 (print) ISSN 2224-896X (online) Vol 1, No.5, 2011 1 Application of Branch and Bound Method for Optimal Two Stage Flow Shop Scheduling Problem with Group Job- Restrictions Deepak Gupta* , Payal Singla, Harminder Singh Department of Mathematics Maharishi Markandeshwar University Mullana, Ambala (India) * E-mail of the corresponding author: guptadeepak2003@yahoo.co.in Abstract: This paper studies two stage flow shop scheduling problem in which equivalent job for group job, processing times on each machine are given. The objective of the study is to get optimal sequence of jobs in order to minimize the total elapsed time. The given problem is solved with branch and bound method.The method is illustrated by numerical example. Keywords: Equivalent job, processing time, elapsed time, Branch and Bound. 1. Introduction: A flowshop scheduling problem has been one of classical problems in production scheduling since Johnson [6] proposed the well known Johnson’s rule in the two-stage flowshop makespan scheduling problem. Yoshida and Hitomi [11] further considered the problem with setup times. Yang and Chern [10] extended the problem to a two-machine flowshop group scheduling problem. Maggu and Dass[9] introduced the concept of equivalent job for a job-block when the situations of giving priority of one job over another arise. Kim, et al.[7] considered a batch scheduling problem for a two- stage flowshop with identical parallel machines at each stage. Brah and Loo [1] studied a flow shop scheduling problem with multiple processors. Futatsuishi, et al. [4] further studied a multi-stage flowshop scheduling problem with alternative operation assignments. Lomnicki [8] introduced the concept of flow shop scheduling with the help of branch and bound method. Further the work was developed by Ignall and Scharge [5], Chandrasekharan [3] , Brown and Lomnicki [2], with the branch and bound technique to the machine scheduling problem by introducing different parameters In this paper we consider a two-stage flowshop scheduling problem with job-block with the help of branch and bound method. The given method is very simple and easy to understand. Thus, the problem discussed here has significant use of theoretical results in process industries. 2. Assumptions: i. No passing is allowed. ii. Each operation once started must performed till completion. iii. Jobs are independent to each other. iv. A job is entity, i.e. no job may be processed by more than one machine at a time. 3.Notations: We are given n jobs to be processed on three stage flowshop scheduling problem and we have used the following notations: Ai : Processing time for job ith on machine A Bi : Processing time for job ith on machine B Cij : Completion time for job i th on machines A and B S 0 : Optimal sequence