NEC and NEC Fielding have harnessed quantum-inspired technology to optimize the delivery planning of maintenance parts, rolling it out as a fully operational system in October 2022. At the Tokyo Parts Center of NEC Fielding, which supplies maintenance parts throughout Tokyo's 23 wards, this technology has transformed what was once a manual daily delivery planning process. The automation has increased operational efficiency, reduced costs, and helped lower greenhouse gas emissions. This initiative showcases how quantum-inspired technology can support green transformation.

1. Introduction

Quantum-inspired technology is expected to play a significant role in green transformation (GX), an initiative focused on addressing environmental challenges like global warming through advanced technologies. This technology is particularly effective at rapidly solving complex combinatorial optimization problems that pose computational difficulties for traditional algorithms. For example, it can design optimal transportation and fuel supply plans that minimize greenhouse gas emissions while supporting economic growth. In manufacturing, it can develop production schedules that maximize efficiency and minimize environmental impact. Through these applications, quantum-inspired technology has the potential to contribute to efforts to combat climate change.

This paper introduces a case study conducted with NEC Fielding, demonstrating how quantum-inspired technology has been successfully applied to optimize delivery planning.

2. NEC Fielding's Business Operations

2.1 Overview of maintenance parts logistics

As part of its operational maintenance services, NEC Fielding manages the logistics of maintenance parts for NEC and third-party enterprise ICT equipment, as well as non-ICT devices such as medical equipment, store facilities, and robots. When a malfunction occurs, customer engineers (CEs) are dispatched to the site to provide maintenance and repair services.

NEC Fielding’s Tokyo Parts Center, located in the southern area of Tokyo, operates a 6,000-square-meter warehouse stocked with approximately 150,000 maintenance parts. The center operates 24/7, 365 days a year, delivering parts to several hundred locations daily using a fleet of 30 small trucks and 8 motorcycles.

2.2 Delivery Planning in Urban Areas

In urban areas, customer engineers (CEs) responsible for maintenance and repairs typically use public transportation for their commutes. Consequently, delivery vehicles must cover areas within Tokyo's 23 wards, ensuring that the necessary parts for maintenance and repair tasks are delivered in sync with the CEs' arrival times at customer locations.

To optimize this process, delivery plans are created based on the CEs' scheduled arrival times, while also considering traffic conditions and cost efficiency. Multiple orders are consolidated into a single delivery whenever possible to minimize logistics costs. There are two key reasons why CEs and delivery vehicles arrive at customer sites separately, a practice unique to urban environments.

The first reason is that public transportation offers more predictable arrival times than driving. By delivering parts in advance to align with a CE’s scheduled arrival, NEC Fielding ensures a high level of punctuality and service reliability.

The second reason is that parking availability is limited at many customer locations. Given these constraints, CEs cannot transport maintenance parts themselves, drive to the site, and conduct long-duration repairs. Similarly, delivery vehicles cannot remain parked for extended periods and must continuously transport parts while following the most efficient, time-sensitive routes.

By accounting for these urban-specific challenges, NEC Fielding develops highly efficient delivery plans that not only maintain a high level of service quality but also comply with local regulations.

3. Current State and Challenges in Delivery Planning

3.1 Complexity of delivery planning

When a maintenance request is received due to equipment failure, delivery planning must be coordinated alongside customer engineer (CE) dispatch. This involves not only scheduling CEs but also arranging for the transport of maintenance parts to the required locations. The delivery planning process must account for hundreds of destinations, selecting the optimal delivery method (small truck or motorcycle), and consolidating multiple deliveries into efficient routes. The number of possible combinations for these plans is estimated to be 10⁷⁵³, making it computationally infeasible to solve using traditional computing methods. Additionally, this planning process is uniquely complex due to a key requirement: as shown in Fig. 1, CEs and delivery vehicles must arrive separately but within the same time window. This constraint significantly increases the complexity of the problem compared to conventional logistics optimization challenges, making it exceptionally difficult to solve.

3.2 Challenges of reliance on individual expertise and successor development

Until now, experienced employees have been responsible for delivery planning, taking into account not only the vast number of logistical constraints but also tacit knowledge gained through years of experience. This includes insights such as “Although this route is longer, it is faster,” or “This road tends to be congested on certain days.” Using this expertise, they have manually developed daily delivery plans based on maintenance part requests received by the previous day—an effort that typically takes about two hours per plan. If these skilled employees were no longer available to create the plans, delivery efficiency would be expected to decline significantly. Furthermore, training successors to develop the same level of expertise would require a substantial amount of time.

4. Addressing Challenges Utilizing Quantum-Inspired Technology

4.1 Delivery planning optimization using VA

To address the challenges outlined in section 3, NEC implemented vector annealing (VA)—a quantum-inspired technology designed to rapidly solve large-scale combinatorial optimization problems.

The following section will introduce the key features of NEC’s VA technology as applied in this case study, followed by an overview of how VA was used to optimize delivery planning.

4.2 Features of VA

NEC’s vector annealing (VA) technology has four key features that provide significant advantages compared to conventional annealing machines when applied to real-world challenges.

The first feature is that optimization calculations are performed on NEC’s SX-Aurora TSUBASA supercomputer, which uses fast matrix calculations and high-speed memory access to achieve rapid solution processing.

The second feature allows a single SX-Aurora TSUBASA unit to handle large-scale problems involving up to 100,000 bits. Furthermore, by employing multiple units in parallel, it becomes possible to efficiently solve even larger and more complex problems commonly encountered in practice.

The third feature is the implementation of NEC's proprietary Constraint Flip Option algorithm, which efficiently searches for feasible solutions that meet constraints during the annealing process.¹⁾ With this algorithm, VA focuses exclusively on constraint-compliant solutions, achieving high-precision results quickly (Fig. 2). This capability is especially advantageous in situations like NEC Fielding’s daily delivery planning, where input data changes daily. It enables the production of stable and effective solutions even as data trends shift, offering a considerable advantage in real-world applications.

The fourth feature is the inclusion of an auto-tuning function for constraint weighting, which eliminates the need for manual tuning by users and enhances usability.

4.3 Optimization in NEC Fielding's case study

This section provides an overview of how vector annealing (VA) was applied to optimize delivery planning in NEC Fielding’s operations.

In NEC Fielding’s workflow, the contact center receives service requests from customers in response to equipment failures. Based on these requests, the center communicates the required arrival time and destination for maintenance parts to the parts center in real time. The parts center then determines truck assignments, delivery sequences, and routing for the day’s deliveries. In this case study, VA was integrated into the parts center’s delivery planning process to enhance efficiency, as illustrated in Fig. 3.

The problem formulation was designed to minimize total truck travel distance, introducing it as the objective function. Several constraints were incorporated, including ensuring all required maintenance parts are delivered, aligning deliveries with customer engineers’ arrival times, and ensuring all trucks return to the parts center within working hours. By constructing an optimized model from these formulated equations and running it through VA, NEC Fielding was able to rapidly generate the most efficient delivery plan from a vast number of possible routing combinations.

4.4 Results

Through the optimization described above, delivery planning is now fully automated, reducing the time required for next-day planning from approximately two hours to just 12 minutes. The generated plans have been reviewed by experienced personnel and have been highly rated as being on par with those created by seasoned experts. Additionally, some of the optimized routes revealed new, previously unrecognized delivery paths, leading to valuable insights.

This optimization process incorporated knowledge from experienced employees, integrating their expertise into the computational model through extensive interviews. As a result, previously implicit knowledge, such as road congestion patterns, has been formalized and systematized. This not only enhances the efficiency of delivery planning but also allows skilled employees to focus on higher-value tasks beyond logistics planning, contributing to the overall improvement of NEC Fielding’s operational maintenance services.

Furthermore, by extending the optimization model to include same-day emergency deliveries, NEC Fielding achieved an approximately 20% improvement in delivery efficiency.

5. Future Outlook

5.1 Applying VA optimization to support executive decision-making

NEC Fielding’s implementation of vector annealing (VA) optimization has demonstrated its ability to generate realistic and effective solutions within practical timeframes, even as conditions change.

By leveraging this capability, business scenarios that were previously difficult to anticipate can now be analyzed in advance using simulations. Decision-makers can evaluate “what-if” scenarios and assess the potential impact of different strategies before implementation. This ability to simulate business adjustments and gain insights beforehand makes VA a valuable tool for executive decision-making.

For example, in a general logistics operation, a company may need to determine optimal pricing strategies for delivery services based on delivery time.

With VA, it becomes possible to simulate various pricing models, such as: expedited deliveries incurring higher costs, prioritizing speed over efficiency; and standard deliveries optimized for cost-efficiency. By applying VA to historical delivery data, businesses can model different service levels, estimate efficiency gains for each scenario, and quantify potential improvements before making operational decisions. Since transportation costs make up a significant portion of overall shipping fees, this type of analysis can help establish appropriate pricing structures.

5.2 The ultimate goal: Digital Twin

As discussed, the benefits of applying vector annealing (VA) optimization extend beyond addressing operational challenges such as reducing reliance on individual expertise and shortening work hours. By continuously running real-time optimization, VA can also drive economic benefits across business operations.

Moreover, by integrating historical data and AI-predicted future data into VA-based simulations, businesses can analyze various operational parameters and generate valuable insights to support executive decision-making. This approach mirrors the concept of a digital twin—a virtual representation of real-world environments that allows businesses to conduct simulations and optimize strategies before implementing them in the physical world.

NEC views VA-driven optimization as a powerful tool in the development of digital twins, helping to transform customer challenges into business value. Moving forward, NEC will continue to enhance the functionality and performance of VA.

6. Conclusion

In this paper, we introduced a case study on the application of quantum-inspired technology for delivery planning. In this instance, NEC successfully automated a previously manual, experience-based delivery planning process. By optimizing the number of trucks and their travel distances, NEC improved operational efficiency and reduced greenhouse gas emissions while enhancing corporate profitability.

Building on its extensive expertise in solving diverse optimization problems, NEC plans to use vector annealing to address a variety of societal challenges, thereby contributing to the advancement of green transformation.

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