Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers
Journal of Applied Mathematics and Stochastic Analysis
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 tosdue 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 probabilityγand is lost forever
... nd 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 probabilityδand 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 levelSfor model III. In models II and III, an arriving customer, finding the buffer full, proceeds to an orbit with probabilityγand is lost forever with probability(1−γ). A retrial customer in the orbit, finding the buffer full, returns to the orbit with probabilityδand 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.