Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers

A. Krishnamoorthy and K. P. Jose

International Journal of Stochastic Analysis, 2007, vol. 2007, 1-23

Abstract:

We analyze and compare three ( s , S ) inventory systems with positive service time and retrial of customers. In all of these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. When the inventory level depletes to s due to services, an order of replenishment is placed. The lead-time follows an exponential distribution. In model I, an arriving customer, finding the inventory dry or server busy, proceeds to an orbit with probability γ and is lost forever with probability ( 1 − γ ) . A retrial customer in the orbit, finding the inventory dry or server busy, returns to the orbit with probability δ and is lost forever with probability ( 1 − δ ) . In addition to the description in model I, we provide a buffer of varying (finite) capacity equal to the current inventory level for model II and another having capacity equal to the maximum inventory level S for model III. In models II and III, an arriving customer, finding the buffer full, proceeds to an orbit with probability γ and is lost forever with probability ( 1 − γ ) . A retrial customer in the orbit, finding the buffer full, returns to the orbit with probability δ and is lost forever with probability ( 1 − δ ) . In all these models, the interretrial times are exponentially distributed with linear rate. Using matrix-analytic method, we study these inventory models. Some measures of the system performance in the steady state are derived. A suitable cost function is defined for all three cases and analyzed using graphical illustrations.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:037848

DOI: 10.1155/2007/37848

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