IMPLEMENTASI ALGORITMA KAHN UNTUK DEPENDENCY TERMIN PEMBAYARAN PADA APLIKASI PENGADAAN PT. KARYA AMAURY NUSANTARA

Payment administration for procurement projects using milestone or installment-based contracts requires strict process control because each payment stage may depend on the completion and verification of previous stages. At PT. Karya Amaury Nusantara, payment-term monitoring was previously supported by spreadsheets and physical documents, creating risks of recording errors, delayed monitoring, and payment processing that did not follow the contractual sequence. This study aims to develop a payment-term management system that represents dependencies among payment stages and automatically validates their processing order. The dependencies are modeled as a Directed Acyclic Graph (DAG), while topological sorting using Kahn's algorithm is applied to determine a valid sequence based on in-degree values. The software is developed using the Waterfall model consisting of requirements analysis, system design, implementation, testing, and maintenance. The application is implemented as a web-based system using PHP with the CodeIgniter 4 framework and MySQL database. The implemented functions include company, client, contract, work realization, invoice, payment confirmation, and payment-dependency validation. The progress results indicate that Kahn's algorithm can generate a valid payment-term order, ensuring that a payment stage can only be processed after all prerequisite stages have been completed. The developed system provides a structured foundation for controlling payment processes and integrated contract administration monitoring. Keywords: topological sorting; Kahn's algorithm; dependency; payment terms; procurement system