Abstract
In this article, a service facility inventory system with server interruptions and a nite number of sources are considered. The inventory is replenished according to ( s; S ) ordering policy. Using the matrix methods, the stationary distribution of the stock level, server status and waiting area level is obtained in the steady state case. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Many impartment system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically. Keywords: Essential and optional service, inventory with service time, service interruption, repair, nite source
Highlights
Schwarz et al [18] introduced the idea of inventory with positive service time
While the server is in working state it may be interrupted at any time with interruption rate α1 during first essential service (FES) and α2 during second optional service (SOS)
Example 3 In this example, we look to the impact of the demand rate λ, essential service rate mu1, second optional service rate μ2, the reorder rate β and the perishable rate γ on the total expected cost rate
Summary
Schwarz et al [18] introduced the idea of inventory with positive service time. They have assumed that when the stock level is empty, each arriving customer enters into the queue. Berman & Sapna [5] considered a queueing-inventory model with single server and finite capacity They assumed that customer arrival follows Poisson process, arbitrarily distributed service times and zero lead times. The discussion in [15] is a retrial queueing-inventory model with positive lead-time and the service process is subject to interruptions. Jeganathan & Periyasamy [11] studied a perishable inventory system with repeated attempts and the service process is subject to interruptions They analyzed the system with the restriction that both the waiting area and orbit size are finite. A finite source queueing-inventory model with server interruptions and extra optional service is motivated by the service facility system with limited customers such as military canteen providing service to soldiers or a company canteen serving the members of the specific working area in the business.
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