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

Abstract

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.

Keywords

• Optimal control,shortages,time dependent demand

References

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