Abstract: The $M/M/1$ production-service-inventory model with perishable products is studied. The life time of the perishable product, the production time and the service time are all assumed to be exponentially distributed. Firstly, the steady-state equilibrium condition of the model is obtained by using the quasi-birth-and-death process theory. Secondly, the matrix geometric solution of the steady-state probability vector is obtained, and the calculation formulas of the performance index and cost function are obtained. Finally, the genetic algorithm is used to analyze the sensitivity of the model's optimal production inventory strategy and the effect of system parameters on performance indexes. The results of this paper can provide some theoretical basis for inventory managers of production companies.

Key words: perishable items, $(s,S)$ strategy,  , production-inventory system, generic algorithm, matrix-geometric solution