Optimization Analysis of the Machine Repair Problem with Balking and Variable Number of Servers

This paper analyzes the machine repair problem with a variable number of servers in which failed machines balk (do not enter) with a constant probability. Failure and repair times of the failed machines are assumed to be exponentially distributed. We apply a recursive method to derive analytic steady-state solutions, through which several system performance measures can be obtained. A cost model is developed to determine the optimal maximum number of busy servers and the optimal value of the balking probability. We use the direct search method and the Newton’s method to find the minimum cost until the balking constraint is satisfied. Numerical results provided in which various system performance measures are evaluated under optimal operating conditions. Finally, an application example is provided to demonstrate how the queueing model could be used in real-life situations.

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