Linkage network of biserial queues with a multistage flowshop scheduling in fuzzy environment

This paper addresses the study of a linkage network of biserial queues linked to a common server with a multistage flowshop scheduling system having ‘m’ machines or servers in series under fuzzy environment. Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. Also, the flowshop scheduling is an important task when a number of jobs are to be processed through a series of machines or servers in an order. It is usually assumed that the various arrival rates, service rates and processing times of jobs/tasks are exact. However, the real world is complex and the complexity is due to the uncertainty. To express this uncertainty, the concept of fuzziness is introduced in the queuing-scheduling linkage model. Fuzzy sets theory provides a mathematical way to represent uncertainty, vagueness and fuzziness in humanistic systems. If the various arrival and service rates are expressed by possibility rather than probability, the fuzzy queuing methods would be more realistic than classical queuing theory methods. The α-cut approach and various fuzzy arithmetic operations are used to estimate the uncertainty associated with the input parameters. The objective of the paper is to develop an algorithm to optimize the mean queue length, average waiting time and total elapsed time for the proposed queue-scheduling linkage model in fuzzy environment. The efficiency of the proposed algorithm is tested by a numerical illustration.