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A detailed review of inventory models involving positive service time is given. These include classical and retrial cases. Also contributions to production inventory with service time is indicated towards the end. In addition directions for future work are indicated.

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This paper deals with a continuous review (s, S) inventory system where arriving demands finding the system out of stock, leave the service area and repeat their request after some random time. This assumption introduces a natural alternative to classical approaches based either on lost demand models or on backlogged models. The stochastic model formulation is based on a bidimensional Markov process which is numerically solved to investigate the essential operating characteristics of the system. An optimal design problem is also considered.