The income approach to the problems of optimizing the repair policy

Occupation: Principal Scientific Researcher
Affiliation: Central Economics and Mathematics Institute, Russian Academy of Sciences
Address: Moscow, Russian Federation

Journal name

Ekonomika i matematicheskie metody

Edition

Volume 58 Issue 2

Pages

112-124

Abstract

The article is devoted to the application of approaches and methods used in the valuation of assets to the problems of reliability theory – the assignment of service life and the timing of preventive repairs to degrading item that are subject to failures. In the works on reliability, changes in the characteristics of the item after repair are described by Kijima models and their modifications, in which the state of item is characterized by a virtual / effective age. A similar indicator has been widely used in appraisal activity since the middle of the last century. Meanwhile, it turns out that indicators of this type do not allow us to adequately describe the state of degraded repairable items. It is proposed to describe their condition by two indicators – the age (operating time) at the beginning of the current inter-repair cycle and the same in this cycle. In combination with Kijima's ideas, this allows us to offer a more adequate model of changing the item’s characteristics after repair. To assign service life and terms of preventive maintenance of items, a well-grounded criterion of optimality is required.It is shown that the usually accepted criterion of the minimum expected maintenance and repair costs per unit of time does not meet the interests of enterprises participating in the market. We propose to use the so-called income approach to valuation, focused on maximizing the market value of the enterprise (in the simplest case, this approach leads to the criterion of the expected discounted costs per unit of work performed by the item). This makes it possible to assess the market value of the work performed by the item necessary for calculations, and the corresponding assessment method can be attributed to the cost approach.We construct and analyze the corresponding mathematical models, provide an algorithm for solving them and a numerical example demonstrating the irrationality of commonly used repair policies.

Keywords

lifetime, repair policy, optimization criterion, degradation, Kijima models, valuation, income approach

Received

05.05.2022

Publication date

18.06.2022

Number of characters

34182

Cite

GOST	Smolyak S. The income approach to the problems of optimizing the repair policy // Ekonomika i matematicheskie metody – 2022. – V. 58. – Issue 2 C. 112-124 [Electronic resource]. URL: https://emm.jes.su/S042473880019997-5-1 (circulation date: 28.04.2024). DOI: 10.31857/S042473880019997-5
MLA	Smolyak, Sergey "The income approach to the problems of optimizing the repair policy." Ekonomika i matematicheskie metody 58.2 (2022):112-124. DOI: 10.31857/S042473880019997-5
APA	Smolyak S. (2022). The income approach to the problems of optimizing the repair policy. Ekonomika i matematicheskie metody 58(2), pp.112-124 DOI: 10.31857/S042473880019997-5

100 rub.

When subscribing to an article or issue, the user can download PDF, evaluate the publication or contact the author. Need to register.

Number of purchasers: 0, views: 318

Readers community rating: votes 0

1. Antonov A.V., Polyakov A.A., Chepurko V.A. (2011). A model for analyzing the reliability of objects with incomplete restoration. Dependability, 3 (38), 33–41 (in Russian).

2. Antonov A.V., Plyaskin A.V., Tataev Kh.N. (2013). On the issue of reliability calculation for redundant structures in view of ageing elements. Dependability, 1, 55–67 (in Russian)]. DOI: 10.21683/1729-2646-2013-0-1-55-67 (in Russian).

3. Aven T. (1983). Optimal replacement under a minimal repair strategy. Advances in Applied Probability, 15, 1, 198–211. DOI: 10.2307/1426990

4. Bartholomew-Biggs M., Zuo M. J., Li X. (2009). Modelling and optimizing sequential imperfect preventive maintenance. Reliability Engineering & System Safety, 94, 53–62. DOI: 10.1016/j.ress.2008.03.002

5. Fedotova M.A. (ed.). (2018). Machinery and Equipment Valuation. Textbook. 2nd ed. Мoscow: INFRA-M. 324 p.

6. Horenbeek A. van, Pintelon L., Muchiri P. (2010). Maintenance optimization models and criteria. International Journal of System Assurance Engineering and Management, 1 (3), 189–200. DOI: 10.1007/s13198-011-0045-x

7. IVS (2019). Effective 31 January 2020. London: International Valuation Standards Council.

8. Jiang R. (2018). Performance evaluation of seven optimization models of age replacement policy. Reliability Engineering & System Safety, 180 (C), 302–311. DOI: 10.1016/j.ress.2018.07.030

9. Kijima M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability, 26, 89–102.

10. Livshits V. N., Smolyak S. A. (1972). Economic and mathematical models of local optimization. In: Proceedings of the Fourth school on mathematical programming and related issues. Issue IV. Moscow, CEMI RAS, 179–213 (in Russian).

11. Livshits V.N., Smolyak S.A. (1971). Service life of fixed assets in the optimal plan. In: The first conference on optimal planning and management of the national economy. Abstracts of reports. Section 1. Issue 1. Moscow: CEMI RAS. 352–357 (in Russian).

12. Methodological recommendations for evaluating the efficiency of investment projects. Second edition (2000). Moscow: Ekonomika 421 p. (in Russian).

13. Mikerin G.I., Smolyak S.A. (2010). Efficiency assessment of investment projects and property valuation: Opportunities for convergence. Moscow: CEMI RAS. 120 p. (in Russian).

14. Smolyak S.A. (1988). Optimization of management of the development of diversified industries. Dr. Econ. Sci. Diss. 08.00.13. Moscow: CEMI RAS (in Russian).

15. Smolyak S.A. (2013). Valuation of machines and equipment in view of curable and incurable depreciation. Economics and Mathematical Methods, 49, 1, 54–72 (in Russian).

16. Smolyak S.A. (2014). Overhaul policy optimization and equipment appraisal concerning its reliability, 2 (22), 102–131 (in Russian).

17. Smolyak S.A. (2016). Valuation of machinery and equipment (secrets of the DCF method). Moscow: Option (in Russian).

18. Smolyak S.A. (2018). On the cost approach to the machinery and equipment valuation. Bulletin of CEMI. Issue 1. DOI: 10.18254/S0000090-2-1 (in Russian).

19. Smolyak S.A. (2019). Optimization of the number and frequency of repairs. Economics of Contemporary Russia, 2, 84–103. DOI: 10.33293/1609-1442-2019-2(85)-84-103 (in Russian).

20. Vilensky P.L., Livshits V.N., Smolyak S.A. (2015). Evaluation of the efficiency of investment projects: Theory and practice. Textbook. 5th ed. Moscow: PolyPrintService 1300 p. (in Russian).

21. Welch R.B. (1943). Depreciation of buildings for assessing purposes. Chicago: International association of assessing officers.