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


PG and Research Department of Mathematics, St. Peter’s College, Kolenchery, Kerala, 682311, India


This paper considers the comparison of two
ðs; SÞ production inventory systems with retrials of unsatisfied
customers. The time for producing and adding each
item to the inventory is exponentially distributed with rate
b. However, a production rate ab higher than b 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 interretrial
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 a 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.