An EOQ inventory model for items with Weibull deterioration, shortages and time varying demand

Abstract

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. Hence, in this paper, we derive the EOQ model for inventory of items that deteriorates at a Weibull distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal service level and the optimal replenishment cycle time. Further, we also verify that the sufficient conditions of optimality of the service level and the replenishment cycle time are satisfied under certain conditions. Finally, three numerical examples and sensitivity analyses are provided to assess the solution procedure.

Key Words:

• EOQ model
• inventory
• deterioration
• shortage
• Weibull distribution
• time-varying demand
• service level
• replenishment cycle time