Age and lifetime based policies for perishable items
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Many inventory systems hold items which perish after a specific time. Upon perishing, the inventory level falls down to zero which may incur irreparable costs to the system. Therefore, developing a genius control policy for managing such inventories is a crucial task. Since the lifetime of items are now affecting the inventory level, applying the traditional inventory policies which are based only on the stock level causes some shortcomings. The traditional inventory policies lack the information regarding the lifetime of items. On the other hand, the optimal policy for perishable items is known to be a periodic review policy keeping the complete information regarding the remaining lead times of orders, inventory onhand, and lifetimes of items. Optimal control policy class for continuous review is still an open question. In this regard, we attempt to contribute the remaining lifetime of items into the inventory policy for perishable items with positive lead time and fixed lifetime under a continuous review with a service level constraint. We develop a class of hybrid control policies which utilize the remaining lifetimes of items in addition to stock levels. We study a stochastic single item inventory system where demand follows a Poisson process and unmet demand is lost. The aging process of a new batch starts when it joins the inventories. We provide an exact analytic model by using an embedded Markov chain process to derive the stationary distribution of the effective lifetimes in the presence of both one and more than one outstanding orders assumptions. Operating characteristics of the system are derived using the renewal reward theorem. Additionally, we propose some control policies based on only the remaining lifetime of items. Our results reveal that the hybrid policies consistently outperform the stock level and remaining lifetime-based polices, especially when demand during the lifetime is sufficiently small and unit perishing cost is high. It is observed that the dominance relations among these two policy classes depend on the particular parameter setting. In particular, when the lifetime of items is long enough, the stock level based policy performs very well. Finally, we present our methodology for finding the optimal solution thorough a heuristic algorithm derived by considering the structure of the objective function and service level constraint, and a sensitivity analysis is performed to evaluate the impact of the key input parameters.
Embedded Markov Chain