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.