Development of mathematical model to decide the optimal graphite product mix to enhance the profit

Abstract

Sri Lanka is the only country in the world known to extract and produce commercially viable quantities of natural crystalline vein graphite. Currently, Bogala graphite mines and Kahatagaha graphite mine are famous underground mines and the largest natural graphite producers, which supply natural vein graphite in the form of various product categories to the international graphite market. Out of that two major mines, Bogala graphite mines extracts approximately 350 metric tons of natural graphite per month. When it comes to extracted graphite from underground (run of mine), the raw graphite consists of various carbon contents in the form of lumps, chips, and powder. Such graphite is subjected to hand sorting or mechanical separation before it is used for further processing to produce various product categories as requested by local or international customers. During the graphite processing stage, it is a real dilemma to decide that with available graphite in raw form in which carbon content varying from 80% to 99%, to produce saleable product to which customer orders with a view to getting maximum profit out of various pricing for various saleable graphite products that Bogala graphite mine produces. So, it is worth finding out which product mix gives the highest monthly revenue utilising its limited monthly underground mine production and limited machine capacities. The problem addressed here is to determine the product mix (combination of sales package) to be adopted by the company for selling her graphite products at which the optimal profit level would be attained.