How Pasco Shikishima solves a global supply chain problem involving 32 million variables


Pasco Shikishima, a leading Japanese food company ($1.5 billion in annual revenue, 4,000 employees), has chosen Hexaly Optimizer to solve a vast, global supply chain optimization problem. Hexaly won the benchmark against Gurobi, Cplex, and Xpress. The software solution was developed by the optimization experts of the service company Future Architect, with support from MSI, a reseller of Hexaly in Japan, and the Hexaly team.

Pasco Shikishima’s global supply chain optimization problem

Pasco’s supply chain involves 13 factories in Japan, each one with several production lines, more than 100 supply sites, and 26 delivery hubs. Pasco’s catalog contains more than 1,000 products. About 900,000 orders have to be delivered each day in Pasco’s factories. For each order, Pasco has to decide where and when to produce it. Moreover, Pasco has to choose where to source raw materials and which routes to take to deliver the goods to the distribution centers. The goal is to minimize production and distribution costs over several days while respecting production and distribution capacities.

Input data

  • 1,000 catalog products
  • 900,000 orders to produce per day
  • 100 supply sites
  • 13 production sites
  • 26 delivery sites


  • Decide where and when to produce each order
  • Decide where to source raw materials
  • Decide which routes to take to deliver to distribution centers


  • Production capacities
  • Production times
  • Distribution capacities
  • Distribution times


  • Minimize production and distribution costs
  • Maximize use efficiency of raw materials
  • Minimize work-in-progress (WIP)

32 million variables, including 8 million binaries

Once mathematically modeled using Hexaly Optimizer (or any other solver), the resulting problem to be solved is gigantic. Here is the typical scale of Hexaly instances solved at Pasco:

  • 32 million variables
  • 1 million constraints
  • 8 million binary variables
  • 16 objectives

This model is solved in 3 minutes of running time on a basic server, including input and output processing times.

Hexaly wins the benchmark against Cplex, Gurobi, and Xpress

After weeks of extensive benchmarking against leading commercial MIP solvers (Cplex, Gurobi, Xpress), Hexaly proved to be the sole general-purpose mathematical optimization solver able to deliver high-quality solutions quickly to Pasco’s all-Japan supply chain optimization problem. Indeed, MIP solvers need the original problem to be decomposed into 20 subproblems, each one solved separately, resulting in poor-quality solutions for the global problem. On the contrary, Hexaly can tackle it directly without any decomposition. Having passed all stress tests, Hexaly was integrated into Pasco’s Supply Chain Management (SCM) information system. It is used daily to save much of Pasco’s production and distribution costs.

We developed the Pasco supply chain optimization model using Hexaly Optimizer within a few days of work. Hexaly Optimizer provides outstanding solutions, as considered by Pasco planners, in just a few minutes of running times, while the number of variables is gigantic (tens of millions). We could not imagine such a feat being possible initially since state-of-the-art MIP solvers like CPLEX, Xpress, and Gurobi could not tackle the problem in hours. Now we know that using Hexaly, it's possible!

Shinichi Kuroda Project Director, Pasco Shikishima

Please look at our customers‘ webpage for case studies in various industries. Are you interested in trying it out? Get free trial licenses here. In the meantime, feel free to contact us; we will gladly discuss your optimization problems.