A Multi-item Imperfect Optimal Production Problem Through Chebyshev Approximation

Abstract

This paper is developed for multi-item inventory model with finite time horizon. The inventory levels, productions and demands are continuous function of time. Initial and end-pints stocks and demands are known. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total cost is minimum. Once the problem is formulated as an optimal control problem i.e. in the form of an integral, using El-Gendi’s [2] method. Here optimal control problem is solved by numerical approach. This technique is based on the expansion of the control variable in Chebyshev series with unknown coefficients. There is a constraint on the total space termed as space constraint. For simulation, the non-linear optimization technique Generalised Reduced Gradient Method (LINGO 11.0) [5] have been used. The optimum results are illustrated both numerically and analytically.