Abstract:
Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., Hence, it is needed to develop inventory models with random replenishment. In this paper, an EPQ model for deteriorating items is developed and analyzed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalized Pareto distribution and demand is a function of on hand inventory. Using the differential equations, the instantaneous state of inventory is derived. With suitable cost considerations, the total cost function is obtained. By minimizing the total cost function, the optimal ordering policies are derived. Through numerical illustrations, the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significant influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.
Machine summary:
"Later, Baker and Urban (1988), Mandal and Phaujdhar (1989), Datta and Pal (1990), Venkat Subbaiah, et al.
Very little work has been reported in the literature regarding EPQ models for deteriorating items with random replenishment and generalized Pareto decay having stock dependent demand, even though these models are more useful for deriving the optimal production schedules of many production processes.
Hence, in this paper, we develop and analyze an economic production quantity model for deteriorating items with Weibull rate of replenishment and generalized Pareto decay having demand is a function of on hand inventory.
i) The demand rate is a function of production, which is /; / (1) Where/, / are positive constants, I(t) is the on hand inventory ii) The replenishment is finite and follows a two parameter Weibull distribution with probability density function /; Therefore, the instantaneous rate of replenishment is /; (2) iii) Lead time is zero iv) Cycle length, T is known and fixed v) Shortages are allowed and fully backlogged vi) A deteriorated unit is lost vii) The deterioration of the item is random and follows a generalized Pareto distribution.
Substituting h (t) given in equation (3) in equation (20) and (21) and solving the differential equations, the on hand inventory at time‘t’ is obtained as / (22) / / (23) Stock loss due to deterioration in the interval (0, t) is / This implies / Ordering quantity Q in the cycle of length T is From equation (22) and using the condition I (0) = 0, we obtain the value of ‘S’ as (24) (25) Let be the total cost per unit time."