A MAP/PH(1), PH(2)/2 production inventory model with inventory dependent production rate and multiple servers

This article presents an (s,S) production inventory model with multiple servers in which each server takes multiple vacations. The vacation to the servers is decided according to different service disciplines. Markovian Arrival Process (MAP) is constituted by the arrival of customers and service time follows a phase type distribution. Service commences at the end of a vacation period when at least one customer is in the waiting area and inventory level is positive. The period needed to produce an item to the inventory, when the production is ON, is distributed exponentially with rate γ. Production needs to begin when there is a decline in the inventory level s. The production rate is γδ, δ ∈ [1,r] where r is a finite quantity greater than 1 until the inventory level reaches s. A suitable cost function is defined based on performance measures. Numerical examples are in-cooperated in the study to explain the effects of positive and negative correlated inter-arrival times on the total expected cost. An algorithmic solution to the problem is found using the Matrix Analytic method(MAM). The optimum value of the enhancing parameter δ corresponding to the minimal cost is also obtained.