Fixed assets repair timetable
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BRIEF COMMUNICATIONS FIXED ASSETS REPAIR TIMETABLE V. V. Ostapenkoa† and D. A. Belyaeva‡
UDC 519.8
This paper deals with repairs of fixed assets. Repairs can be current and capital. A repair process model is analyzed under some assumptions on the repair process stationarity. The optimal time for the first capital repair is found. Keywords: optimal moment, minimization of expenses, capital repair, stationary process. INTRODUCTION Fixed assets are means of labor that are used for a long time in processes of production and, at the same time, do not change their natural hardware forms and piecemeal transfer their cost to the cost of made products. During exploitation, fixed assets are worn out. The necessity arises to replace or recover worn constructive elements with a view to restoring their use value and maintaining their working condition. A repair is a work package for maintaining working conditions of fixed assets during their entire service life period. Depending on their recovering and updating functions, all types of repairs are divided into current repairs and capital repairs (overhauls). In contrast to current repairs, capital repairs are much more complicated as to the amount of work to be done and require significant onetime expenditures [1]. The necessity arises to determine the optimal moment of the first capital repair from the commencement of exploitation of an object of fixed assets. An approach to the solution of the general problem on capital repairs is illustrated by the solution of this problem. PROBLEM STATEMENT AND A MATHEMATICAL REPAIR PROCESS MODEL Let us consider some object of fixed assets. Current repair works are performed during its exploitation. When the expenditures on the current repair become too heavy, the necessity arises to carry out a capital repair. The problem lies in the determination of the moment of the first capital repair from the commencement of exploitation. Let f ( t ) be the function of total expenditures for current repairs before a time instant t, and let a be onetime expenditures for a capital repair. We fix a moment T and the number of capital repairs k carried out during this period. We consider the problem of finding the partition of the segment [ 0, T ] by points t i , i = 1, 2, . . . , k, that minimizes the expenditure function k
min
å
i =1
k
f ( t i ),
å
i =1
t i = T.
(1)
The lemma presented below is true. a
Institute of Applied System Analysis of the National Technical University of Ukraine “KPI,” Ministry of Education and Science of Ukraine and NAS of Ukraine, Kiev, Ukraine, †[email protected]; ‡[email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 184–186, March–April 2009. Original article submitted December 3, 2008. 326
1060-0396/09/4502-0326
©
2009 Springer Science+Business Media, Inc.
LEMMA. If the function f is convex, then a uniform partition of the segment [ 0, T ] is optimal, i.e., the solution of problem (1) consists of points t i* = n
T , n = 1, 2, . . . , k. k
r Proof. We denote by t a vector ( t
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