On Optimal Production Scheduling of an EPQ Model with Stock Dependent Production Rate and Pareto Decay

EPQ models play an important role in production and manufacturing units. Much work has been reported in literature regarding EPQ models with finite rate of production. But in many food processing and bottling industries the production is dependent on stock on hand. Hence in this paper we develop and analyze an EPQ model for deteriorating items with stock dependent production rate and Pareto rate of decay. Using the differential equations the instantaneous state of inventory is derived and with suitable cost considerations the optimal quantity, production uptime and production downtime are obtained for two cases of with and without shortages. The sensitivity analysis of the model revealed that the stock dependent production has a significant influence an optimal production schedule and can reduce total cost of production. This model also includes the finite rate of production inventory model with Pareto decay as a particular case.