Recensione dell'articolo: (Nair, Salini S.; Jose, K. P. - "Solution to production inventory systems with orbit, buffer and different service rates." - Palest. J. Math. 8 (2019), no. 2, 328-347)

In this paper the authors study two models of a production inventory system with (s; S) policy. When the inventory level falls to s, production starts, and it stops when the inventory level reaches S. The time for producing each item is exponentially distributed with parameter . The demand from customers is according to a Poisson process with rate . The customers on their arrival enter into a buer that, in the rst model, has capacity equal to the maximum inventory level S. In the second model, the authors consider a buer of varying (nite) capacity, equal to current inventory level. Orders are fullled if inventory is available. Service times are exponentially distributed with parameter . When the inventory level depletes to s due to service provided to the potential customers, the service rate reduces to where 0 < < 1, and this rate is maintained until inventory level reaches zero. When customers enter into the system and nd the buer full, they move to an orbit of innite capacity with probability and are lost forever from the system with probability (1 ). If customers retry from the orbit and nd the buer full, they return to the orbit with probability and are lost forever with probability (1). The time between retrials of customers in the orbit is exponentially distributed with linear rate i when there are i customers in the orbit. For the two models, the authors describe the mathematical formulation with stability and performance measures of the system. They also present numerical results and the cost analysis of the models.