Mixed-Integer Linear Programming Model for Reducing the Backlog of Service Orders at Electric Power Utilities

When a power company faces a sudden storm or a surge in equipment failures, the work does not stop; it piles up. This accumulation of uncompleted repair requests is known as a backlog. For utility companies, managing this backlog is a delicate balancing act. They must decide which technician goes to which house, when to send them, and how to handle the inevitable delays caused by bad weather or a shortage of workers. If they get this wrong, customers wait too long for power to be restored, and the company faces heavy fines and angry citizens. The challenge is not just about having enough people to do the work, but about organizing that work so that the most critical repairs happen first, while still making progress on the less urgent ones. This is a problem of logistics and priority, where a small mistake in scheduling can lead to a massive delay in service.

A team of researchers from Brazil has developed a new way to solve this problem using a sophisticated computer model designed to organize field service teams. Instead of simply sending workers out in the order that requests arrive, their system looks at the entire list of jobs, the skills of the available technicians, and the specific urgency of each task. The researchers tested this model against the traditional method used by many companies, which is simply to work through the list from top to bottom, a method known as "first-in, first-out." Their findings show that by using their new approach, a utility company can clear its backlog much faster, spend significantly less money on overtime, and keep its workers from becoming exhausted by chaotic schedules.

The researchers built a mathematical model that acts like a highly efficient dispatcher. In the real world, a power company might have hundreds of technicians and thousands of repair orders waiting to be handled. Some of these orders are emergencies, like a downed power line that could cause a fire or leave a hospital without electricity. Others are routine maintenance tasks that can wait a few days. The new model separates these tasks immediately. It guarantees that every emergency order is assigned to a technician on the very day it is reported, ensuring that critical infrastructure is never left waiting. Once those urgent jobs are secured, the model uses the remaining time and energy of the workforce to tackle the pile of older, delayed orders.

A key feature of this system is how it treats the age of a request. In a standard system, a low-priority repair request might sit in the queue for weeks if new, slightly more urgent requests keep arriving. The new model changes this by automatically increasing the priority of a job the longer it waits. If a routine repair has been sitting in the backlog for several days, the system recognizes that it is becoming more important and moves it up the list. This prevents the situation where minor jobs are forgotten indefinitely while the company chases new emergencies. The model also accounts for the reality of human work, such as technicians taking sick leave, arriving late, or needing to work overtime. It calculates the actual available hours for each worker every single day and assigns tasks accordingly, ensuring that no one is overloaded while others sit idle.

To see if this idea worked in practice, the researchers ran a simulation using real-world data from a utility company. They fed the model 2,847 service orders spread over a 30-day period, a volume that mimics a busy month for a medium-sized city. They compared the results of their new system against the old "first-in, first-out" method. The difference was striking. Under the new system, the average time a customer waited for a repair dropped by nearly 43 percent. While the old method left orders waiting for an average of 14.3 days, the new model reduced that wait to just 8.2 days. This improvement happened even though the new system used 51 percent less overtime than the old one. The researchers found that the old method was inefficient; it forced workers to stay late on low-priority tasks while critical backlog orders remained untouched. The new system focused that extra time where it mattered most.

The financial impact of this efficiency was also substantial. By reducing the need for excessive overtime and avoiding regulatory fines for slow service, the simulation showed a potential saving of 754,000 dollars over the course of that single month. The researchers calculated that the cost to implement the system would be paid back in less than nine days. Beyond the money, the system improved the stability of the workforce. The old method created a chaotic environment where daily overtime hours fluctuated wildly, making it hard to plan shifts or predict when workers would be available. The new system smoothed out these peaks and valleys, creating a more predictable schedule that reduced stress for the technicians and lowered the risk of errors caused by fatigue.

The researchers also tested how well their model would hold up under extreme pressure, simulating scenarios where demand tripled or where half the workforce was unavailable due to a crisis. Even in these worst-case situations, the model maintained its ability to handle emergency repairs without fail. While the old method collapsed under such stress, leaving critical jobs unattended, the new system adapted by prioritizing the most vital tasks and managing the backlog in a way that prevented total gridlock. This resilience suggests that the model is not just a tool for normal days, but a robust safety net for the unpredictable nature of power grid management.

The study concludes that the secret to reducing backlogs is not just hiring more people, but organizing the work they already have more intelligently. By using a system that dynamically adjusts priorities based on how long a job has waited and strictly separates emergencies from routine work, power companies can serve their customers faster and more reliably. The researchers suggest that this approach could be applied to other industries where teams manage a mix of urgent and routine tasks, from telecommunications to water systems. For now, the evidence from the simulation is clear: a smarter way to schedule work can turn a chaotic backlog into a manageable flow, keeping the lights on and the customers satisfied.