Specially Structured Flow Shop Scheduling in Two Stage with Concept of Job Block and Transportation Time to Optimize Total Waiting Time of Jobs Deepak Gupta #1 , Bharat Goyal *2 # Department of Mathematics, Maharishi Markandeshwar (Deemed to be University) Mullana (Ambala), Haryana, India 1 guptadeepak20003@gmail.com * Department of Mathematics, G.S.S.D.G.S. Khalsa College, Patiala, Punjab, India 2 bhartu89@gmail.com Abstract - Flow shop scheduling, where the machines are prearranged in order that the flow of each and every of the products that are processed in them is unidirectional. In the present paper Flow shop scheduling models in two stage are well thought of. The problem is specially structured with the idea that maximum of equivalent processing time on first machine remains always less than the minimum of equivalent processing time on second machine. The intention of the study is to find the schedule which lessens the total of the waiting time of all the jobs. The time to transport jobs from first machine to second machine is considered separately and two jobs considered as a group job. An Algorithm to optimize the desired function and the program in C++ language is proposed. Numerical example by applying the algorithm proposed is solved. Key words - Flow shop scheduling, Job block, Processing time, Transportation time, Waiting time of jobs. I. INTRODUCTION The problem of deciding when to perform given jobs with the purpose of optimizing a function while taking attention of chronological constraints and be located in the limitation of resources is known as scheduling. The procedure of sharing the same pre described order of all the machines by the jobs is known as Flow Shop Scheduling. In the present paper we talk about the n x2 specially structured Flow shop scheduling in which it is assumed that minimum of the equivalent processing time on second fictitious machine can never be less than to the maximum of equivalent processing time on first fictitious machine. The intention of study is minimization of the total of the waiting time of jobs. When the jobs come for the processing, the waiting time for their turn on the first machine is considered to be zero. But in order to process a job on second machine they may have to wait for their turn for many reasons such as the previous job can take some time for the operation on second machine, machine can take time to set up, break down in the machine etc. This time which is devoted in waiting for the processing of job on the second machine is known as the waiting time of the job. And the sum of all the waiting time of jobs is known as the total of the waiting time of all the jobs. II. LITERATURE SURVEY The Johnson’s algorithm [1] for Flow Shop Scheduling problem for n-job, 2-machine and 3-machine to lessen the total elapsed time is popular among the analytical approaches that are used for solving n-job, 2 and 3- machine scheduling problem. The n-job, m-machine problem has been studied very wisely by many researchers. Ignall E. and et.al. [2] applied branch and bound technique for the permutation flow shop scheduling with the intention of minimization of makespan. Maggu P.L. and et. al. [4] made an effort to widen the study by initiating the notion of equivalent job for job block. Bhatnagar V.and et. al.[5] investigate the n-job ,2 machine flow shop scheduling models with the intention to optimize the total of the waiting times of all the jobs. Further to optimize the total elapsed time studies are developed by Singh T. P. and et. al.[6], [9] by taking into account the diverse parameters such as time to transport jobs, time of breakdown machines, group job restrictions and job block etc. Narain L. and et. al. [11] considers the optimality as to optimize the cost of the machines that are hired on rent by making a group job of two jobs. Further Gupta D. and et.al. [15] widened the study by considering specially structured Flow shop scheduling models in two stage to minimize the cost which is consumed on rent of machines. Gupta D. and et. al.[16] while studying the specially structured two stage flow shop scheduling models has also considered the transportation time separated from the processing time with the intention to achieve the schedule which lessens the rental cost of the machines. Gupta D. and et.al. [14],[17],[18] studied Flow Shop Scheduling models in two stage with the idea to optimize the total of the waiting time of all the jobs where the parameters like job block concept, time to transport jobs from first machine to second machine are well thought of. ISSN (Print) : 2319-8613 ISSN (Online) : 0975-4024 Deepak Gupta et al. / International Journal of Engineering and Technology (IJET) DOI: 10.21817/ijet/2018/v10i5/181005022 Vol 10 No 5 Oct-Nov 2018 1273