Sınır tenörleri optimizasyonu, maden yataklarının değerlendirilmesinin temel bir konusudur. En geniş anlamıyla sınır tenörü; madeni işletme, yerinde bırakma, cevher tesisine gönderme veya atık sahasına boşaltma şeklinde karar vermede ayraç olarak kullanılan tenör oranıdır. Bir maden sahasına uygulanacak sınır tenörü meselesine geleneksel yaklaşım, gelirin maliyeti karşıladığı tenör oranının statik bir sınır tenörü şeklinde maden yatağının ömrü boyunca uygulanması şeklindedir. Bu yaklaşım, paranın zaman değerini göz ardı etmekte ve maden yatağının en karlı şekilde değerlendirilmemesine neden olmaktadır. Maden yatağının ömrü boyunca statik bir sınır tenörü tayini yerine optimum bir sınır tenörleri silsilesi uygulaması, işletmenin indirgenmiş karını artırabilmektedir. Maden yataklarının değerlendirilmesinde, optimum sınır tenörleri tayini çok önemli; ancak, çözümü kolay olmayan bir problemdir. Bu çalışmada, geniş çaplı optimizasyon problemleri için uygun bir ortam sağlayan genetik algoritma kullanılarak, optimum sınır tenörleri tayini yapılmıştır. Sınır tenörü optimizasyonu genel anlamıyla irdelenmiş, genetik algoritma optimizasyon yöntemi hakkında detaylı bilgi verilmiş ve genetik algoritmanın sınır tenörü optimizasyonuna uygulanması amaçlı geliştirilen bir bilgisayar programı tanıtılmıştır. Ayrıca, örnek bir maden yatağı ile ilgili veriler kullanılarak, bu yazılım test edilmiş ve sonuçlar değerlendirilmiştir. Bu çalışma sonucunda, optimum sınır tenörlerinin belirlenmesinde cari satış fiyatı kullanılarak yapılan geleneksel yaklaşımlar değerlendirilmiş ve bu konuda Lane'in geliştirildiği ve sınır tenörleri optimizasyonu için sıkça kullanılan algoritma geliştirilmiştir.

Optimization of cut-off grades is a fundamental issue for mineral deposits appraisal as it assigns the boundaries between ore and waste over time. In its broadest definition, a cut-off grade is any grade that is used to separate two courses of action; to mine or not to mine, to process or to dump. The traditional approach to cut-off grades is to use the break-even grade, at which revenue equals cost. This approach completely ignores the time value of money and usually leads to a sub-optimal valuation of the mineral resource. Determination of an optimum cut-off grades schedule, instead of application of a static cut-off grade for the life of a mine, maximizes discounted profit. The profit from a mining operation is a direct function of the sequences of cut-off grades and associated ore tonnages that define the life-of-mine production schedule. As profit varies with these sequences there will be a sequence, or sequences, that optimize any specified profit criterion. The most widely used cut-off grade optimization criterion is maximum net present value of profits. The objective of maximizing the net present value can be achieved by maximizing profit per unit of time. This process necessitates applying, in the early years of operation, the highest cut-off grade that can provide sufficient ore to satisfy the requirements of the processing plant. As time passes the cut-off grade must be lowered, thereby lowering the opportunity cost. Hence, the highest net present value is achieved. Genetic algorithms constitute a class of stochastic algorithms that use a search method based on the laws of biological genetics and natural evolution. In this approach, individuals of a population are represented as chromosomes and an expanded set of genetic operations takes place. Genetic algorithms are stochastic algorithms whose search methods are based on the principles of biological genetics and natural evolution. It is presumed that the potential solution of any problem is an individual and can be represented by a set of parameters. Genetic algorithms are particularly suited to the solution of large-scale optimization problems. They belong to the class of probabilistic algorithms but are very different from random algorithms as they combine directed and stochastic searches. Another important property of genetic-based search methods is that they maintain a population of potential solutions. Genetic algorithms can also easily escape from local optima by using genetic operators, such as mutation. Among the inputs for a cut-off grade optimization procedure, the selling price of the product of a mine is the most volatile. Therefore, any change in the selling price of a mining product in the global market make every economic valuations obsolete. Basically, nobody knows how the prices will change in the future, but can estimate. In order to make a better mining plan, one must solve the problem of annual dynamic cut-off grades optimally, and that necessitates taking the volatile market conditions into consideration. Therefore, it is accepted in this work that uncertain selling prices of a mining product must be added to the algorithm for finding cut-off grades to be used. Because it is not possible to find the most revenue without finding the best cutoff grades scheme. Using today’s selling price of a commodity, instead of estimated future values of that, may sacrifice to reach the best net present value. In this work, by use of genetic algorithms, that give a very robust searching medium for big scale optimization problems, optimum cut-off grades were determined. Optimization of cut-off grades is mentioned, detailed knowledge is given about application of genetic algorithms to cut-off grade optimization, and a computer program developed for cut-off grade optimization is given. Besides, the software is tested by using data from a sample mineral deposit and the results are evaluated. This paper makes the traditional approaches to the determination of optimum cut-off grades by using current selling price obsolete and improves Lane’s algorithm in this subject.