Determination of Optimal Reserve between Two Machines in Series with the Repair Time Has Change of Parameter after the Truncation Point

Abstract

In inventory control, suitable models for various real life systems are constructed with the objective of determining the optimal inventory level.  A new type of inventory model using the so-called Setting the Clock Back of Zero (SCBZ) property is analyzed in this paper. There are two machines M₁ and.M₂  in series and the output of M₁ is the input of M₂. Hence a reserve inventory between M₁ and M₂ is maintained. The method of obtaining the optimal size of reserve inventory, assuming cost of excess inventory, cost of shortage and when the rate of consumption of M₂  is a constant, has already been attempted.  In this paper, it is assumed that the repair time of M₁  is a random variable and the distribution of the same undergoes a parametric change after a truncation point X₀ , which is taken to be a random variable.  The optimal size of the reserve inventory is obtained under the above said  assumption . Numerical illustration is also provided