A Mathematical Analysis on Linkage of a Network of Queues with Two Machines in a Flow Shop including Transportation Time

This paper represents linkage network of queues consisting of biserial and parallel servers linked to a common server in series with a flowshop scheduling system consisting of two machines. The significant transportation time of the jobs from one machine to another is also considered. Further, the completion time of jobs/customers (waiting time + service time) in the queue network is the setup time for the first machine. The objective of the paper is of two folds, on one hand it minimizes the total waiting time and service time of jobs/customers in the queue network and on other hand it minimizes the idle time of the machines for the optimal sequence of jobs/customers in a given queue flowshop linkage model. A computer programme followed by a numerical illustration is given to justify the proposed algorithm.