Browsing by Author "Islam, M.E."

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    (s, S) stochastic inventory system in Jackson network
    (Inderscience Publishers, 2022-05-05) Islam, M.A.,; Islam, M.E.; Rashid, A.
    In this work, we develop and analyse an (s, S) stochastic perishable inventory system at each node into Jackson network with a service facility in which the waiting hall of first queue has infinite capacity and second queue has finite capacity for the customers. Service times are exponentially distributed. We assume that demands arrive in the system according to a Poisson process with rate λi(> 0, Ai) and demands only single unit item at a time. The maximum storage capacity of the i th warehouse is fixed as Si; i = 1, 2. Whenever the inventory level reaches the reorder level si(0 ≤ si < Si), an order Qi(= Si - si) units is placed to bring the level to Si. The lead-time is exponentially distributed. The items of inventory have exponential life times. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state case. Matrix analytical method is applied to solve for the steady state occupancy probabilities. Various system performance measures in the steady state are derived. A suitable cost function is defined and the long-run total expected cost rate is calculated. Sensitivity analysis has been carried out to study the effect of variation of parameters. Numerical examples and graphical illustrations are provided to illustrate the proposed model. Copyright
  • Thumbnail Image
    Item
    Stochastic optimization of level-dependent perishable inventory system by Jackson network
    (Ain Shams University, 2022-08-23) Amirul Islam, M.; Islam, M.E.; Rashid, A.
    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 (μi>0) and lead times (θi>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 si at any moment, an order for Qi=((Si-si)>0;∀i) units is made, where Si 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.