Browsing by Author "Islam, M.A.,"

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Base stock stochastic inventory system in jackson network
(ISOSS Publications, 2019-04) Islam, M.E.,; Islam, M.A.,; Ahmed, S.S.
In this paper, we consider base stock stochastic perishable inventory system in open Jackson network at a service facility. In this network we proposed single server at each node with attached inventory where each node represents a queue in which different nodes have different service rates. Service times are exponentially distributed. Customers arrive in the system according to a Poisson process.There is no priority in serving the customers. All customers at each node are served on a first-come, first-served basis. For this system arriving customers form two waiting line based on the order of their arrivals. The maximum storage capacity for ith warehouse is fixed as Si. When the on hand inventory level drops to a prefixed level si = 0, an order for Qi = 1; (i = 1, 2) units is placed. In this model the replenishment of inventory is instantaneous i.e. demand is refilled one unit at a time. The items of inventory have exponential life times. Matrix Analytical method (MAM)is applied for this system. The proposed method is quite efficient and practically well suited for approximate performance estimates. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state case. Some important system performance measures in the steady state are derived. A suitable cost function is defined and analyzed. The total expected cost rate is also calculated. Sensitivity analysis has been carried out to study the effect of variation of parameters. Some numerical and graphical illustrations are provided.
Modeling and Analysis of Stochastic Perishable Inventory System with Impatient Customers at Service Facility
(Hindawi Limited, 2023-05-16) Islam, M.A.,; Ekramol Islam, M.; Rashid, A.
In this paper, we consider a two-commodity stochastic s,S perishable inventory system of the multiqueue Jackson network at a service facility with reneging and jockeying of the customers. The waiting room capacity of the first queue is M/M/1/∞ and the second queue is M/M/1/C2, where C2<∞. In this network, different queues have different service rates. Service times are exponentially distributed. Customers join the system at a rate of λi;i=1,2 using a Poisson process. We assumed that some customers maybe impatient due to the long waiting time in the queue and can leave the system without service or may switch from the longest queue to the shortest queue to reduce the waiting time. If the inventory levels of the items from the warehouse i at any time reaches below or reorder level si, an order Qi=Si-si>0;i=1,2 units is placed to bring the inventory level up to Si. The joint probability distribution of the number of customers in the system and also the stock level of the warehouse is determined in the equilibrium case. Several important measures of steady-state system performance are derived. Several examples are presented to demonstrate the reneging and jockeying behavior of the customers for this system. A sensitivity analysis is performed to investigate the effect of changing the parameters on the total expected cost of the system
(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
Synthesis, Characterizations of Silver Nanoparticles (AgNPs) and Monitoring for Power Production Using Drumstick Leaves
(Hindawi Limited, 2023-05-23) Islam, M.A.,; Ekramol Islam, M.; Rashid, A.
In this paper, we consider a two-commodity stochastic s,S perishable inventory system of the multiqueue Jackson network at a service facility with reneging and jockeying of the customers. The waiting room capacity of the first queue is M/M/1/∞ and the second queue is M/M/1/C2, where C2<∞. In this network, different queues have different service rates. Service times are exponentially distributed. Customers join the system at a rate of λi;i=1,2 using a Poisson process. We assumed that some customers maybe impatient due to the long waiting time in the queue and can leave the system without service or may switch from the longest queue to the shortest queue to reduce the waiting time. If the inventory levels of the items from the warehouse i at any time reaches below or reorder level si, an order Qi=Si-si>0;i=1,2 units is placed to bring the inventory level up to Si. The joint probability distribution of the number of customers in the system and also the stock level of the warehouse is determined in the equilibrium case. Several important measures of steady-state system performance are derived. Several examples are presented to demonstrate the reneging and jockeying behavior of the customers for this system. A sensitivity analysis is performed to investigate the effect of changing the parameters on the total expected cost of the system.