Assuming you have 100 kg of dilute ore (containing very small amounts of precious metal = PM), how do we determine the weight of ore to be disposed of and balance retained inside the factory? The ore is not homogeneous meaning the concentration of PM is not same in each kg of ore.
More information about the problem:
- The cost of disposing the entire ore: More the weight disposed of, higher would be the cost - unlike leather waste disposed indiscriminately into Ganges in UP at nominal cost. Let's assume that in our factory any amount of effluents are allowed to be discharged but at a cost which is unknown but not nominal.
- The opposing cost is the pain of holding the ore inside the factory (stink from the non-PM part of ore): Less the amount disposed of outside the factory, more is the amount held inside the factory causing damage to various entities inside the factory because of the stink.
- There is a monthly subsidy provided to the factory for holding the ore within the factory and this provides some revenue. The subsidy cost per kg is independent of the PM content in each kg of ore.
While the price of ore mentioned in point 3 is known accurately, the effluent cost mentioned in point 1 and the holding cost of ore mentioned in point 2 are known only in qualitative terms and not in dollar terms.
Since all three costs are not known in dollar terms, the solution also will be subjective. I would first identify the PM content in each kg of ore.
Now we have to remind ourselves that the goal of the exercise is not to maximize the subsidy received for the ore, rather it is to minimize the ore stored inside the factory.
Now, I have already got the PM in each kg of the ore. I would now sort the ore in increasing order of PM content. The ore with the lowest PM content gets the same subsidy per kg but stinks the most.
While inspecting the sample data (say in Excel),use your judgment to determine which of the worst samples to discharge out (and balance kept inside). This is strictly subjective as mentioned earlier because of lack of cost data for points 1,2.
Estimate that you will send 20kg out of 100kg out and see whether samples 19,20 are similar and that samples 21,22 are similar and that 20,21 are dissimilar in PM content. If this condition is met, then samples 1-20 should be discharged outside. If the condition is not met, move to sample 10 or sample 40 and repeat. If the worst n samples are to be discharged outside then samples n, n+1 should be quite distinct in terms of PM content.
Do this until your heart is at ease with the ore size you have determined to discharge.
If there are other considerations in terms of affinity towards certain specific samples handle those appropriately.
The whole job consists of two steps, typically performed by two different roles.
The first step is to get the PM content for each kg of ore. This can done by the lab chemist.
The second step of deciding which samples to dispose of is a management decision best left to the factory manager.
Since all three costs are not known in dollar terms, the solution also will be subjective. I would first identify the PM content in each kg of ore.
Now we have to remind ourselves that the goal of the exercise is not to maximize the subsidy received for the ore, rather it is to minimize the ore stored inside the factory.
Now, I have already got the PM in each kg of the ore. I would now sort the ore in increasing order of PM content. The ore with the lowest PM content gets the same subsidy per kg but stinks the most.
While inspecting the sample data (say in Excel),use your judgment to determine which of the worst samples to discharge out (and balance kept inside). This is strictly subjective as mentioned earlier because of lack of cost data for points 1,2.
Estimate that you will send 20kg out of 100kg out and see whether samples 19,20 are similar and that samples 21,22 are similar and that 20,21 are dissimilar in PM content. If this condition is met, then samples 1-20 should be discharged outside. If the condition is not met, move to sample 10 or sample 40 and repeat. If the worst n samples are to be discharged outside then samples n, n+1 should be quite distinct in terms of PM content.
Do this until your heart is at ease with the ore size you have determined to discharge.
If there are other considerations in terms of affinity towards certain specific samples handle those appropriately.
The whole job consists of two steps, typically performed by two different roles.
The first step is to get the PM content for each kg of ore. This can done by the lab chemist.
The second step of deciding which samples to dispose of is a management decision best left to the factory manager.
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