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In this paper, economic production quantity(EPQ)models for break- able or deteriorating items are developed with time dependent linear variable demands. Here rate of production and holding cost are time dependent and unit production cost is a function of both production reliability indicator and production rate. Set-up cost is also partially production rate dependent. Here two models are developed in optimal control framework considering the effect of time value of money and inflation. Shortages are allowed for both the models. The problems are solved using Eulers-Lagrangian function based on variational calculus and applying generalized reduced gradient method using LINGO 13.0 software to determine the optimal reliability indicator (r) and then corresponding production rates and total profits. Numerical experiments are performed for both the models to illustrate the models both numerically and graphically.

A multi-item EPQ model with imperfect production process for time varying demand with shortages