MiningMath

MiningMath

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What is the Bienstock-Zuckerber (BZ) algorithm?

The Bienstock-Zuckerberg (BZ) algorithm is an approach for solving large-scale, complex scheduling problems in the area of mixed-integer linear programming (MILP), such as those encountered in some direct block scheduling (DBS) formulations. First proposed here and here, the BZ algorithm introduced a new way to figure out a possible schedule faster than previously defined methods, even when there are millions of blocks. It focuses on using information from previous steps to speed up finding a solution.

Why was the BZ algorithm proposed?

The BZ algorithm was created because regular software usually struggles with large and complex mining schedules. For example, when there are millions of blocks and many constraints, traditional methods take too long or can’t handle the problem. The BZ algorithm was designed to solve these massive scheduling problems faster and more efficiently, so mining companies could make quicker decisions.

What are the disadvantages and limitations of the BZ algorithm?

Commercial software that utilizes the BZ algorithm will still face some of the common challenges associated with DBS-based solutions. For example, the BZ algorithm is not able to include geometric constraints, as these constraints belong to a different category that requires specialized modeling techniques. Additionally, although the BZ algorithm is faster than many earlier MILP methods, it is still typically applied to individual components of a mining project, such as pit optimization, rather than delivering a unified and optimized solution for the entire project.

What are the advantages of MiningMath's algorithm compared to the BZ algorithm?

MiningMath’s custom Branch & Cut algorithm effectively manages the inherit complexity and computational demands of DBS formulations with its surface-based linearization methods. It can handle large models, including those with over 240 million blocks, with extensive testing demonstrating its capability.

MiningMath offers a wide range of operational constraints. It is the only DBS-based software package able to address open-pit mining planning with geometric constraitns, such as minimum bottom width, minimum mining width, minimum mining length and maximum vertical rate of advance.

Lastly, MiningMath’s algorithm optimizes individual stages or the entire scheduling process in a single step, directly from the block model into one cohesive optimized solution. Unlike other software that might apply BZ or other related DBS algorithms only to individual stages of the mining project, MiningMath’s unified approach can deliver more comprehensive and effective outcomes.

Start using MiningMath now!

With MiningMath’s single-step, optimization engine, you can uncover opportunities that manual or stepwise planning might miss. Ultimately, this engine is able to optimize resource utilization and can improve project outcomes. Transform your mine planning process by leveraging MiningMath’s advantages and take your mining projects to new heights of efficiency and success. 

Windows 64-Bit (x86_64) - 121 MB

Windows 64-Bit (x86_64) - 121 MB

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