MATHEMATICAL GROUP REPLACEMENT MODEL WITH AN UNBOUNDED PLANNING HORIZON

Abstract

Traditional replacement models often rely on finite planning horizons, a framework misaligned with the perpetual operational needs of real-world systems such as infrastructure, industrial machinery, and fleet vehicles. This limitation necessitates robust strategies for optimising maintenance and replacement decisions over an unbounded planning horizon. This study develops and validates deterministic group replacement model to address this challenge, thereby providing a pragmatic framework for long-term asset management, and minimizing long-run average cost per unit time over an unbounded planning horizon. The model incorporates an exponential failure rate, determines the optimal periodic replacement interval by comparing the cost of individual failures with bulk replacement costs, with the optimal solution obtained numerically using the Newton-Raphson method. When applied to a case study in a bakery, the model demonstrated significant practical utility, it established an optimal replacement interval for baking pans at 4.3 years. Sensitivity analyses revealed that the optimal policy is highly responsive to changes in the maintenance cost growth rate and the group replacement cost, thereby providing managers with critical insight into the financial drivers of their decisions. This study contributes to knowledge by bridging the theory-practice gap in unbounded horizon replacement modelling. It provides computationally tractable and directly applicable unbounded-horizon replacement models, equipping industries, particularly those in resource-constrained environments, with a structured methodology to enhance capital budgeting, reduce lifecycle costs, and ensure operational sustainability over an indefinite planning horizon.