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 LocalSolver to solve a vast, global supply chain optimization problem. LocalSolver 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 LocalSolver in Japan, together with the LocalSolver team. This optimization solution has been used in production daily since 2015.
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
Decisions
- Decide where and when to produce each order
- Decide where to source raw materials
- Decide which routes to take to deliver to distribution centers
Constraints
- Production capacities
- Production times
- Distribution capacities
- Distribution times
Objectives
- 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 LocalSolver (or any other solver), the resulting problem to be solved is gigantic. Here is the typical scale of LocalSolver 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.
LocalSolver wins the benchmark against Cplex, Gurobi, and Xpress
After weeks of extensive benchmarking against leading commercial MIP solvers (Cplex, Gurobi, Xpress), LocalSolver 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, LocalSolver is able to tackle it directly without any decomposition. Having passed all stress tests, LocalSolver was integrated into Pasco‘s Supply Chain Management (SCM) information system. Since 2015, it has been used on a daily basis to save a significant part of Pasco’s production and distribution costs.
We developed the Pasco supply chain optimization model using LocalSolver within a few days of work. LocalSolver 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 LocalSolver, it's possible!
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