European Journal of Business and Management www.iiste.org ISSN 2222-1905 (Paper) ISSN 2222-2839 (Online) Vol 3, No.3 268 Optimal Two Stage Flow Shop Scheduling to Minimize the Rental Cost including Job Block Criteria, Set Up Times and Processing Times Associated with Probabilities Deepak Gupta Prof. & Head, Dept. of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, India Tel: +91-9896068604, Email: guptadeepak2003@yahoo.co.in Naveen Gulati Assistant Professor, Dept. of Mathematics, S.D.College, Ambala Cantt , Haryana, India Email: naveengulatimaths@gmail.com Sameer Sharma (Corresponding Author) Assistant Professor, Dept. of Mathematics, D.A.V. College, Jalandhar, Punjab, India Tel: +91-9814819064, Email: samsharma31@yahoo.com Payal Singla Research Scholar, Dept. of Mathematics Maharishi Markandeshwar University, Mullana, Ambala, India Email: payalsingla86@gmail.com Abstract This paper is an attempt to study the two stage flow shop scheduling problem in which the processing time and independent set up times of the jobs are associated with probabilities to minimize the rental cost under restrictive rental policy including equivalent job-block criteria. The study gives an optimal schedule rule in order to minimize the rental cost of machines through heuristic approach. The proposed method is very simple and easy to understand and also, provide an important tool for decision makers. To make the method effective and justified a computer program followed by a numerical illustration is given. Keywords Johnson’s technique, Optimal sequence, Equivalent-job, Flow shop, Rental policy, Makespan, Utilization time, Elapsed time, Idle time. Mathematical Subject Classification: 90B35, 90B30 1. Introduction Scheduling is a important process widely used in manufacturing, production, management, computer science and so on. Appropriate scheduling can reduce rental cost of machines and running time of machines. Finding good schedule for given sets of jobs can help factory supervisors effectively to control job flows and provide solutions for job sequencing. A flow shop scheduling problem consists of