Abstract
In this study, a stochastic process which represents a single-item inventory control model with (s,S)-type policy is constructed when the demands of a costumer are dependent on the inter-arrival times between consecutive arrivals. Under the assumption that the demands can be expressed as a monotone convex function of the inter-arrival times, it is proved that this process is ergodic, and closed form of the ergodic distribution is given. Moreover, a sharp lower bound for this distribution is obtained.
Highlights
IntroductionCustomers arrive at the depot at random times {Tn}, and the amount of their demands can be modeled by a sequence of random variables {ηn}
Consider a single-item inventory control model as follows
If there exists enough supply in the stock, the demanded items of the customer are satisfied from the stock, else an immediate replenishment order takes place so that to raise the inventory level to an order-up-to level S >
Summary
Customers arrive at the depot at random times {Tn}, and the amount of their demands can be modeled by a sequence of random variables {ηn}. We will assume that no product is returned or defective and the supplier of this depot is reliable so that the replenishment is not delayed. This model is known as (S, s)-type policy inventory control model and it has been extensively studied under various assumptions in the literature (see Scarf [ ], Rabta and Aissani [ ], Chen and Yang [ ], Khaniyev and Atalay [ ], Khaniyev and Aksop [ ])
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