So far we have shunned the problem of defining accurately what OR are. In order to get a clearer thought of what OR is we shall in fact do some by bearing in mind the particular problem below and then highlight a number of general lessons and concepts from this exact example.
Two Mines Company
The Two Mines Company own two dissimilar mines that produce an ore which, following being crushed, is graded into three classes: high, medium and low-grade. The company has constricted to provide a smelting plant by means of 12 tons of high-grade, 8 tons of medium-grade and 24 plenty of low-grade ore per week. The two mines have dissimilar operating characteristics as full below.
Mine Cost for each day (£'000) manufacture (tons/day)
High Medium Low
X 180 6 3 4
Y 160 1 1 6
This is obviously a very easy (even simplistic) instance but, as with many things, we have to begin at a simple level in order to progress to a more complicated level.
Guessing
To discover the Two Mines problem further we might simply presume (i.e. use our judgement) how many days per week to work and observe how they turn out.
Work single day a week on X, single day a week on Y
This does not appear like a good guess as it outcome in only 7 tonnes a week of high-grade, inadequate to meet the contract requirement for 12 tonnes of high-grade a week. Such a answer is infeasible.
Work 4 days a week on X, 3 days a week on Y
This appears like a better guess as it results in enough ore to meet the contract. We say that such a answer is feasible. Though it is quite expensive (costly).
Before continue guessing we can move toward the difficulty in a structured rational fashion as below. Reflect for a moment though that actually we would like a solution which provisions what is necessary under the contract at minimum cost. Rationally such a minimum cost solution to this decision problem must exist. Though even if we keep guessing we can never be confident whether we have found this minimum cost resolution or not. Providentially our structured move toward will enable us to find the minimum cost solution.
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Resource article: http://www.expertsmind.net/
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