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This paper considers the comparison of two $$\left( {s,S} \right)$$s,S production inventory systems with retrials of unsatisfied customers. The time for producing and adding each item to the inventory is exponentially distributed with rate $$\beta$$β. However, a production rate $$\alpha \beta$$αβ higher than $$\beta$$β is used at the beginning of the production. The higher production rate will reduce customers’ loss when inventory level approaches zero. The demand from customers is according to a Poisson process. Service times are exponentially distributed. Upon arrival, the customers enter into a buffer of finite capacity. An arriving customer, who finds the buffer full, moves to an orbit. They can retry from there and inter-retrial times are exponentially distributed. The two models differ in the capacity of the buffer. The aim is to find the minimum value of total cost by varying different parameters and compare the efficiency of the models. The optimum value of $$\alpha$$α corresponding to minimum total cost is an important evaluation. Matrix analytic method is used to find an algorithmic solution to the problem. We also provide several numerical or graphical illustrations.

Analysis of two production inventory systems with buffer, retrials and different production rates