Analysis of a service facility with cross trained servers and optional feedback

This paper studies a problem faced by a service facility with front and back room operations. The servers in the front room deal with serving customers, perhaps from a queue and those in the back room serve a job which is generated by the front room. In this flexible environment, the problem is to determine the allocation of fixed number of servers between the two rooms depending on the state of the system. The contribution of this paper is to consider the effect of unsatisfied customers that reenter the system. For this purpose, two models are proposed. The main objective of this paper is to minimise the mean number of customer waiting in the queue subject to the back room constraint and both the models are solved using linear programming. A numerical study is conducted to analyse the impact of various parameters on the performance of servers.