Feasibility Regions and Critical-Path Uniqueness in Inverse Project Scheduling Using Multilayer Acyclic Digraph Models

Robby Robby (Parahyangan Catholic University, Indonesia)
Levina Michella (Parahyangan Catholic University, Indonesia)
Yanuar Bhakti Wira Tama (Institut Teknologi Kalimantan, Indonesia)

Parameter: Jurnal Matematika, Statistika dan Terapannya
Vol 5 No 1 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya

This paper examines an inverse project scheduling problem formulated using the Critical Path Method (CPM), in which one activity durations are unknown. The objective is to derive analytical conditions that ensure a given project duration is feasible and that a particular path becomes the unique critical path. The project workflow is represented as a multilayered acyclic digraph, which facilitates symbolic analysis of all critical path candidates. A numerical example is implemented in Python on a six-layer network with two nodes per inside layer and one unknown duration. From an initial set of 16 possible paths, only 4 remain after slack-based pruning, enabling symbolic characterization of the feasibility region. The findings contribute to a deeper understanding of structural conditions that guarantee critical path uniqueness in inverse project scheduling problems.