Stochastic optimization of level-dependent perishable inventory system by Jackson network

Abstract

In this research work, we developed a model to investigate the long-run behavior of the solutions of continuous review ( s , S ) inventory policy for level-dependent perishable products with positive service time on Jackson queueing network. The service facility is assumed that the waiting capacities of each queue are different. In this model, we assume two independent single server nodes in a M / M / 1 queueing system with an associated inventory, where each node represents a queue. In a Poisson process, customers enter the system. The service times ( μ i > 0 ) and lead times ( θ i > 0 ) are independent and also spread exponentially at the node i for 1 ⩽ i ⩽ 2 . If the inventory levels of goods from the warehouse i are below s i at any moment, an order for Q i = ( ( S i - s i ) > 0 ; ∀ i ) units is made, where S i is the highest capacity of storage for each warehouse in the system. In the steady state case, the matrix analytic technique is used to derive the combined probability distribution for the number of customers and inventory level. The overall anticipated cost rate is determined using some essential system performance measures. Numerical and graphical examples are presented to analyze the effect of variation of parameters on the system.