Optimization of the Number and Frequency of Repairs

Abstract

When managing the production process at an enterprise, it is important to correctly develop a policy for overhauls of machinery and equipment. Usually for this purpose, enterprises use the standards for the repairs frequency recommended in the literature. In publications on the reliability theory, repair policy is considered as an optimization problem. In publications on the theory of reliability, this problem is considered as optimization. In this case, usually the criterion of optimization is some kind of relative indicator, such as availability rate or average operating costs per unit of time. However, such criteria do not fully reflect the economic interests of enterprises – owners of equipment. In a market economy, these enterprises are focused on maximizing their market value. In this paper, we propose to form a repair policy in which the market value of the enterprise, and therefore all its assets, will be most. The corresponding mathematical model is the best use underling the valuation theory. It also takes into account the physical deterioration of machines during their operation, as well as the possibility of random marginal failures, leading to the need to stop using the machine. In this case, the improvement of the technical condition of the machine after its overhaul is described using the Kijima imperfect repair model. The calculations carried with our model allow establishing how the optimal number and timing of repairs depend on such parameters as repair cost and its restoration factor, the rate of physical wear of machines, and the intensity of their resource failures. We show how to use the constructed model to take into account the effect of inflation rates and income and property tax rates on the repair policy.