Complete Algorithm for Solving the Scripting Problem on Multi-Task Enabled Arcs

Objective: This paper presents algorithms designed to support a linear model capable of optimizing the routes taken by meter readers to measure the instruments installed in a hydroelectric power plant. Theoretical Framework: The study conducted by Tirkolaee was used as a reference point to address the challenge of determining the most efficient routes, serving as one of the foundations of this work. In addition to solving the PCARP, the article also focused on minimizing the number of vehicles required for the task. However, it does not include a predefined frequency approach as in Chu, nor does it address multiple tasks as in Cleverson and Fausto. Cleverson's work, in turn, is a generalization of Chu's, considering that the edges can have different demands, representing distinct tasks such as reading instruments like Thermometer, Pendulum, Seismograph, and Piezometer. This study distinguishes itself from the others by analyzing the subcycles that may arise during the resolution of the exact model and determining the feasibility of solving the model with constraints that eliminate the subcycles in the first iteration or adding them as necessary. Due to computational advancements, this work presents various methods to achieve the best solution for the PCARP. Method: Develop a model that considers the following characteristics: selection of the combinations of days of the week to perform the tasks assigned to the meter readers; selection of the meter readers who will traverse route y, which includes gallery x and the instruments to be read; the meter reader must pass through the route at least once to perform the task but may need to traverse the edge without performing any specific action to maintain the route's flow; not all meter readers may be qualified to perform all tasks due to a lack of knowledge in handling the equipment required to read certain instruments; the meter reader must start their journey at the depot, represented by vertex "0," and return to this point at the end of the day; the total time to leave the depot, perform the instrument readings, and return must not exceed the meter reader's daily working hours. Results and Conclusion: The results indicate that the Complete Algorithm demonstrated significant efficiency. In tests with various instances, it obtained a solution without subcycles in the first iteration 68% of the time. Additionally, in 63% of the cases, the time taken to reach this solution was shorter, without increasing t