MATHEMATICAL MODELS FOR VEHICLE DEPRECIATION UNDER BOUNDED ROUTINE MAINTENANCE AND REPLACEMENT USING FINITE DIFFERENCE METHODS

Abstract

In this paper, we seek to improve an earlier replacement model that uses dynamic programming to analyze the impact of depreciation on state-owned vehicles. A common assumption associated with the model is that all return functions and decision possibilities are uniform or identical. The method of finite differences is applied to determine the optimal replacement time for automobiles whose economic value deteriorates over time, thereby increasing maintenance and operating costs. The objective of the model is to minimize the average yearly cost of operating vehicles whose costs of maintenance increase with time, while the scrap value is constant. It is assumed that the time value of money is negligible with a zero-interest rate. Hence, the calculation is based on the annual average cost. It is observed from the numerical illustration of the model that the optimal life of a vehicle can be determined by comparing the increased running cost to the decreased depreciation value.  The two models presented in this article have a computational advantage over existing ones in terms of assisting policy makers to determine vehicles’ optimal replacement policy. The policies include deciding which vehicle should be repaired or replaced, thereby averting losses of human and material resources due to accidents.