# Solving the iron ore blending problem

Iron ore miners maximize value for their shareholders. This effectively means that the total net present value of profits from iron ore mining and magnetite pelletizing has to be maximized. As the mine produces iron ore in different grades but the down stream magnetite pelletizing and crude iron production has defined acceptance limits for ore grades and conducive vs. detrimental ore contents, this results in a optimization and production scheduling problem of balancing ore mining and blending over time, such that down stream production receives uniform ore feed and operational margins from all operations are maximized with regards ot their net present value.

In this article I elaborate on my previous introduction on applied analytics in the iron-to-steel value chain. I do so by taking a closer look at the iron ore blending problem and how it can be solved using mathematical programming.

## Conditions and indicators of iron ore blending

Iron ore blending problems face the following conditions and constraints:

• Ore grade values (ratio of metal to total ore in batch).
• High-quality content values (proportion of conducive content).
• Low-quality content values (proportion of detrimental content).
• Minimum production output of a mine.
• Geological reserves (ore capacity).

High-quality contents in iron ore are e.g. Fe2O3 and Fe3O4. Low-quality contents, on the other hand, are e.g. FeCO3 and FeSiO3.

High-quality iron ore contents are conducive for iron production, while low-quality iron ore contents are detrimental for iron ore production. Relevant key performance indicators for the iron ore concentrator are thus;.

• Total amount of iron ore consumed by the ore grade concentrator stage.
• Min. and max. values of the resulting blended ore grade.
• Min. and max. values of high- and low- quality contents.

The iron ore grade has to satisfy customer and/or down stream process requirements (crude iron production) at all points in time of the future production schedule. At the same time, considering the future demand schedule, high- and low- quality contents must not exceed the specified range, as uniform production feed would otherwise not be maintained.

## Analytics methods for iron ore blending problems

The iron ore blending problem is a mathematical optimization and production scheduling problem and can be solved with various operation research techniques.

The mathematical optimization problem has as its main objective to maximize total net present value of the mine and its operations, over its entire lifetime. Relevant constraints are primarily to secure concentrator operations in the magnetite pelletizing process, maintaining defined quality and content ranges with regards to the ore blend. Another constraint is e.g. the mines composite report and its expected capacities.

Various techniques are commercially deployed to solve this problem:

This means that depending on the specific implementation the ore blend scheduling problem is either solved analytically or with heuristic schedule loading simulation. Applicability of analytical methods, e.g. mixed integer programming, depends largly on whether the schedule can be updated by the underlying solver within reasonable time. Commercial software applications can be furthermore be found as integrations into overarching planning systems, or as standalone planning tools.

## Concluding remarks and related content

In this article I took a closer look on the iron ore blending problem. I highlighted why it, in fact, is a scheduling problem. I explained how it can be defined as a mathematical optimization problem. I also pointed out both analytical and simulation methods that are commercially deployed to solve iron blending problems in iron mining and crude iron industry.

This type of blending problem is not only releavnt to iron ore mining. It translates to other types of mines and also describes blending problems in e.g. oil industry.

If you are interested in learning more about the iron-to-steel value chan I recommend that you read the following SCDA article:

If you want to implement an exemplary blending problem in Excel Solver I recommend that you take a look at this SCDA Excel template: