State Of The Art

THE TECHNIQUE of linear programming is a mathematical optimisation application and is, among others, used to optimise planning problems of mining, mineral beneficiation, blending, smelting and selling of minerals. Applications vary from the oil industry to precious metals, ferro-alloys, coal, base metals, diamonds, general logistics, transportation, finance, electricity supply and numerous other industries.

THE AIM of a linear programming model applied to a large integrated mining and metallurgical complex, is to design a maximum profit, maximum net present value or a minimum cost plan. The benefit of implementing a linear programming derived business plan typically generates savings of 10% +-5% of turnover.

STATE OF THE ART. Today, LP-models are used to model large integrated mining and metallurgical complexes with the view to finding the optimal production, beneficiation and sales plans for the entire complex as a whole. This may be done under scenarios of varying selling prices, sales volumes, raw material availability and costs as well as various plant throughputs, operating severities and costs. LP is often used as an aid in the design process of new shafts as well as plant and equipment in order to find optimal combinations and sizes of the various production entities within the total system. This plan can then be used, e.g. to estimate capital requirements. Modern software allows the planner to enter user data directly into spreadsheets eg. Excel input classes and tables. The software programmatically generates the mathematical equations which simulate and optimise the problem. A user-friendly report of the optimal plan is then compiled for interpretation prior to implementation. Various "what is best" and "what should be done if" studies are evaluated this way and each run supplies the user with a full set of sensitivity price- and cost ranges, which enables the planner to understand the techno-economics in a structured way.

Linear Programming is typically used to solve the following type of problems:-
         Production planning
         Business expansion, contraction and rationalisation studies
         Techno-economic studies
         Pre-design optimisation
         Market sales price and sales volume sensitivities
         Raw material cost and availability sensitivities
         Optimal allocation of raw materials and resources
         Logistics and transportation
         Contingency planning

L.S.L.P.S. has successfully designed and implemented many LP and MIP models of large integrated mining and metallurgical complexes, constituting many tens of thousands of variables (including integers) within as many constraints.

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