Minimizing Total Cost For A Gaussian Distributed Filling Production System
Mohammad S. Aljohani
Department of Nuclear Engineering,
King Abdul Aziz University,
Saudi Arabia
Ahmad A. Moreb
Industrial & Management Systems Engineering,
Kuwait University,
Kuwait
Abstract
There are two contributing cost components in a filling production system; an overfill cost, and a cost of non-satisfaction of customers because of the under-fill. The difficulty in minimizing the cost function is due to the Gaussian distributed terms involved. This paper offers a closed form analytical solution for the process mean that minimizes the overall cost. The optimal solution strikes a balance between overfill and under-fill costs. A numerical algorithm was presented for comparison purposes in addition to a graphical method to facilitate its use. To demonstrate how the three methodologies and techniques work, a numerical example was included.
Keywords: Optimization, Production system, Overfill cost, Under-fill cost, Cost of Quality.