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 LocalSolver. The optimization model was developed by LocalSolver’s optimization experts of Surigiken, a Japanese IT company, with the support of MSI, LocalSolver’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 titanium smelting process is packed into drums after being screened and analyzed for components. It is then designed and shipped so that its components 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 combinations. Since the production load of a batch varies greatly depending on the combination, the goal was to minimize the cost of batch production work while satisfying the specifications.
Mathematical model and results
Here is the size of the instances to be solved once modeled using LocalSolver, and the key performance figures of the resolution:
- Up to 2 million binary variables
- Minimization of compounding work cost through a nonlinear multi-objective function
This model is solved in a few minutes of running time on a basic laptop.
LocalSolver won the benchmark against FICO Xpress
After a benchmark against the FICO Xpress MILP solver, LocalSolver has proven to deal with this huge combinatorial puzzle in short computation times. Consequently, Toho Titanium adopted LocalSolver to daily solve its shipment management optimization problem. Since the integration of LocalSolver into the shipment management application, Toho Titanium 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 LocalSolver, the application provides high-quality solutions in a short time. This has allowed us to save money while reducing work time and dependence on skilled workers. It is a major step in the digital transformation of our department.