Abstract
This paper models a machine replacement and capacity expansion problem as an infinite-horizon linear program. We establish a strong duality result and show that stationary dual prices are optimal, regardless of initial conditions. These prices measure the economic value of owning vintage machinery and thus define depreciation schedules. We present necessary and sufficient conditions for straight-line depreciation.
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References
American Accounting Association, Accounting and reporting standards for corporate financial statements (American Accounting Association, Columbus, Ohio, 1957).
A.A. Bergh, P.S. Brandon, W.S. Cowing, H.L. Lemberg, K.W. Lu, S.D. Personick and P.E. White, “Technological and market obsolescence of telephone network equipment,” Bell Communications Research Memorandum (1985).
S. Eilon, J.R. King and D.E. Hutchinson, “A study in equipment replacement,”Operational Research Quarterly 17 (1) (1966) 59–71.
J.J.M. Evers,Linear Programming over an Infinite Horizon (Tilburg University Press, Holland, 1973).
J.J.M. Evers, “A duality theory for infinite-horizon optimization of concave input/output processes,”Mathematics of Operations Research 8 (1983) 479–497.
R. Grinold, “Infinite horizon programs,”Management Science 18 (1971) 157–169.
R. Grinold, “Finite horizon approximations of infinite horizon linear programs,”Mathematical Programming 12 (1977) 1–17.
R. Grinold and D. S. P. Hopkins, “Computing optimal solutions for infinite-horizon mathematical programs with a transient stage,”Operations Research 21 (1972) 179–187.
J.M. Henderson and R.E. Quandt,Microeconomic Theory: A Mathematical Approach (3rd edition) (McGraw-Hill, New York, 1980).
H.S. Hotelling, “A general mathematical theory of depreciation,”Journal of the American Statistical Association 20 (1925) 340–353.
C.R. Hulten and F.C. Wykoff, “The measurement of economic depreciation,” in: C.R. Hulten, Depreciation, Inflation, and the Taxation of Income from Capital (The Urban Institute Press, Washington, DC, 1981).
P.C. Jones, J.L. Zydiak and W.J. Hopp, “A linear complementarity approach to solving capacity planning network problems over an infinite horizon,” Technical Report 87-12, Department of Industrial Engineering and Management Sciences, Northwestern University (Evanston, IL, 1987).
D.E. Kieso and J.J. Weygandt,Intermediate Accounting (Wiley, New York, 2nd ed. 1977).
P. A. Samuelson, “Economics of forestry in an evolving society,”Journal of Public Enquiry 14 (1976) 466–492.
J.S. Taylor, “A statistical theory of depreciation based on unit cost,”Journal of the American Statistical Association 18 (2) (1923) 1010–1023.
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This work was partially supported by grants ECS-8312008 and ECS-8619732 from the National Science Foundation.
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Jones, P.C., Zydiak, J.L. & Hopp, W.J. Stationary dual prices and depreciation. Mathematical Programming 41, 357–366 (1988). https://doi.org/10.1007/BF01580773
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DOI: https://doi.org/10.1007/BF01580773