EPQ models for deteriorating items with stock-dependent production rate and time-dependent demand having three-parameter Weibull decay

In this paper, we develop and analyse an inventory model for deteriorating items with the assumption that the production rate is dependent on stock on hand. It is further assumed that lifetime of the commodity is random and follows a three-parameter Weibull distribution. Using the differential equations, the instantaneous state of inventory is derived. With suitable cost consideration the total cost function is obtained. By minimising the total cost function, the optimal ordering policies are derived. Through numerical illustrations the sensitivity analysis is carried. It is observed that the stockdependent production parameters and the deterioration distribution parameters have significant influence on optimal production scheduling and total cost. This model also includes some of the earlier models as particular cases for specific values of the parameters. This model is much useful in analysing several production processes.