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We propose a new integrated queueing-inventory and reliability model. First, we obtained time-dependent performance measures by using the Laplace transform method. Then, we derived stationary performance measures by using alternative solution methods, including the probability generating function and matrix geometric method. Optimization procedures were developed for both make-to-order and make-to-stock cases. Performance evaluation of the derived time-dependent and stationary performance measures were reviewed first. Then we compared joint replacement and production-inventory control with separate optimization for respective production modes. Finally, the impact of deteriorated services under different demand rates and parameter settings was investigated. Prior studies are neglecting the mutual interaction between production and reliability. This study contributes to filling the gap. In our proposed numerical example, a cost reduction of more than one-third was achieved by joint optimization. The result shows that decision-maker should make his decisions in an integrated manner otherwise the price paid may be significant.

Joint replacement and production control for a queueing system with different failures