How SoftBank increases LPG delivery capacity by 25% with Hexaly

SoftBank is a comprehensive telecommunications and internet company based in Japan. In addition to providing telecommunication services, they introduce new technologies and services like Artificial Intelligence (AI), Internet of Things (IoT), and robotics. This case study focuses on SoftBank’s Liquefied Petroleum Gas (LPG) delivery route optimization problem. Relying on Hexaly as mathematical optimization solver, SoftBank has improved customer satisfaction while decreasing gas waste and delivery costs.

SoftBank’s Liquefied Petroleum Gas (LPG) delivery route optimization problem

The LPG industry in Japan faces many issues, among which high delivery costs and a shortage of human resources due to the aging of the population. LPG manufacturers then have a crucial need to optimize their delivery operations to remain competitive. To answer this need, SoftBank developed Routify, an optimization service based on Hexaly Optimizer. Routify is a comprehensive application optimizing the whole LPG delivery process, from demand forecasting for efficient ordering to optimal delivery routing plan computation.

Predicting remaining gas
Computing optimized delivery routes
Optimized delivery results

Demand forecasting and inventory management

Demand forecasting and inventory management are critical for LPG companies. Indeed, the demand for LPG varies depending on many factors, such as the season and region, and can be hard to predict accurately. Using artificial intelligence techniques, Routify makes adequate predictions on the demand for LPG and the remaining amount of gas in customers’ cylinders, thus helping workers appropriately manage the necessary inventory. The timing and volume of gas deliveries can then be optimized to avoid running out of gas or having excess inventory.

Delivery route optimization

To efficiently deliver LPG to customers, it is also necessary to optimize the delivery routes. Considering the customers’ locations and road conditions, Routify relies on Hexaly Optimizer to provide efficient delivery routes, minimizing travel distance and driving time. To avoid replacing non-empty containers and wasting gas, the software generates routes preferentially going around areas where the need for container replacement is higher. The benefits of computing optimized delivery routes are many. On the one hand, it enables efficient customer deliveries even in a labor shortage context. Indeed, field tests conducted at delivery sites have shown a 25% improvement in gas delivery capacity, that is, the capacity of gas exchanged by delivery staff per hour. On the other hand, minimizing the traveled distances reduces CO2 emissions, and better targeting the containers to replace ensures a diminution in gas waste.

Mathematical model

SoftBank’s LPG delivery problem is extremely complex, with many different operational constraints and objectives. However, Hexaly’s set-based formalism and lambda-function capabilities make its modeling straightforward. As a result, to serve 1,000 customers over a planning horizon of 1 week, Routify computes near-optimal delivery routes in a few minutes of running times.

Input data

  • Customer locations, opening hours, and weekly demand
  • Depot locations and storage capacities
  • Truck characteristics


  • What route for each truck, each day, and each time period?
  • What depot to go back to at the end of each tour?
  • What gas quantity to deliver each day to each customer?


  • Time windows
  • Maximum work
  • Truck capacities
  • Minimal stock
  • Avoid gas shortages for customers


  • Minimize the number of tours
  • Minimize the total delivery time
  • Minimize the amount of gas waste
  • Minimize the total number of customer visits

Why Hexaly?

After benchmarking several optimization solvers, SoftBank chose Hexaly for its powerful optimization capabilities and flexibility. SoftBank’s team appreciated how Hexaly could find fast and efficient solutions to tough problems, such as optimizing delivery operations in the LPG industry. They also appreciated Hexaly ‘s flexible API and unique modeling features, enabling them to easily formulate complex operational constraints. Thanks to the integration of Hexaly into their application, they improved the efficiency of LPG delivery operations and customer satisfaction, as they explained in a press release in 2022.

Hexaly Optimizer is a great tool in the area of optimization. It provides fast and efficient optimal solutions, while being flexible and easy to use. It also delivered excellent results for our challenges and made a significant contribution to optimizing our delivery operations. Thank you for your excellent performance and cooperation.

Hiroyuki Kawamata Product & Business Strategy Division Data Utilization Department, SoftBank

Customers with automatic meter reading terminals, as well as customers without automatic meter reading terminals, can predict the remaining amount of gas, and AI derives a composite delivery plan. Also, the automatic formulation of delivery routes has the scalability to collect a variety of data, and we expect that AI will enable even more efficient delivery operations.

Seiichi Ishii Representative Director, Chairman and President, ISG Co., Ltd.

We sincerely welcome the provision of LP gas delivery optimization service ‘Routify’ by SoftBank. We strongly felt the need for efficient delivery operations and securing personnel to carry out the tasks. SoftBank's Routify uses AI to predict the amount of remaining gas and automatically formulate delivery plans. I have high hopes for digital transformation through the expansion of services that utilize big data.

Hitoshi Onishi President, Tosa Gas Co., Ltd.

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