Abstract

In this paper, economic production quantity (EPQ) model for deteriorating item is developed with dynamic demand and deterioration i.e. demand and deterioration of the item increase with time. Here rate of production and holding cost are time dependent, unit production cost is a function of both production reliability indicator and production rate. Set-up cost is also partially production rate dependent. The production process produces some imperfect quantities which are instantly reworked at a cost to bring back those units to the perfect ones. The production process ultimately depends on both time and reliability indicator. The model is formulated as optimal control problem and the total profit function with effect of inflation and time-value of money is expressed as finite integrals over the finite planning horizon. The problem is solved using Euler�Lagrange function based on variational calculus and Newton�Raphson method to determine the optimal production reliability indicator and then corresponding production rate and total profit. Numerical experiment is performed to illustrate the model both numerically and graphically.

Description