A Diffusion-Based Model for Price Adjustment Dynamics in Delayed Road Construction Projects

Abstract: Delays in road construction projects often lead to unforeseen cost escalations due to price adjustments (PA) associated with labour, materials, and equipment. Predicting and managing these escalations is critical for project budgeting and contingency planning. This paper introduces a diffusion-based model, often used in unsteady open-channel flows [1] and also in traffic-modelling [2], to analyse the dynamics of PA in delayed road construction projects. In this approach, project delays are interpreted as "shock waves," propagating cost escalations that impact PA calculations. The model uses the heat diffusion equation, with delays beyond scheduled completion (assumed as 24 months) increasing PA through incremental diffusion coefficients. These coefficients are derived using historical indices and adjusted based on a statistical distribution reflecting the probability of cost escalation with prolonged delays. Using the explicit finite difference method, the diffusion equation is solved to yield values simulating the month-by-month evolution of PA as projects experience delays, generating characteristic curves for progress stages (e.g., 60%, 70%, 80% completion) across scenarios with various completion times. Each curve illustrates the compounding effect of delays, highlighting price adjustment (PA) increases in extended durations. This framework provides a comprehensive tool for analysing the financial impacts of delays, supporting stakeholders to perform better contingency planning and risk assessment, and thereby supporting informed financial decision-making in infrastructure projects.

Key Words: Price Adjustment in Construction Contracts; Diffusion-based modelling for shock wave propagation; Characteristic curves.

References:
1. Chanson, Hubert (2004). The Hydraulics of Open Channel Flow: An Introduction”; Second Edition, 2004; ISBN 0 7506 5978 5
2. The University of Auckland (2007). “Maths363 (2007): Traffic Flow”, www.math.auckland.ac.nz