How Hexaly solves Toho Titanium’s shipment management problem in minutes


Toho Titanium is a Japanese manufacturer of non-ferrous metals and one of the world leaders in titanium smelting and refining. Titanium is characterized by its lightness, high specific strength, and high corrosion resistance. It is used in various fields, from aerospace materials to consumer products. As part of Toho Titanium’s digital transformation program, the company has developed a shipment management optimization tool based on Hexaly Optimizer. The optimization model was developed by Hexaly’s optimization experts of Surigiken, a Japanese IT company, with the support of MSI, Hexaly’s distributor in Japan. This tool is used daily by Toho Titanium.

Toho Titanium’s shipment management optimization problem

The spongy titanium produced in the smelting process is packed into drums after being screened and analyzed for components. It is then processed and shipped so that its composition and mass satisfy the customer’s specifications. This problem requires processing dozens of shipments simultaneously, and it is not easy to deduce the best option from so many possible combinations. Since the production load of a batch varies greatly depending on its characteristics, the goal is to minimize the cost of batch production work while satisfying the specifications.


Mathematical model and results

The goal of the problem is to minimize compounding work costs through a non-linear multi-objective function. Once modeled using Hexaly Optimizer, the problem has up to 2 million binary variables. Even though the instances are very large, this model is solved in only a few minutes of running time on a basic laptop.

Hexaly won the benchmark against FICO Xpress

In a benchmark against the FICO Xpress MILP solver, Hexaly proved its ability to deal with this vast combinatorial puzzle in short computation times. Toho Titanium then chose Hexaly to solve its shipment management optimization problem and has been using it daily ever since. Since integrating Hexaly into the shipment management application, the company has made significant financial gains through a new work organization.

Before introducing the shipment management application, the problem of mixing and packing a large number of raw materials was managed by experts in Excel. Today, thanks to Hexaly Optimizer, the application provides high-quality solutions quickly. This has allowed us to save money while reducing work time and dependence on skilled workers. It is a significant step in the digital transformation of our department.

Mr. Yuichi Shiga Toho Titanium High Purity Metal Technology Dept.

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