Enflasyon ve vergi etkilerini içeren stokastik kapsamlı bakım-onarım ve yenileme modeli
Stochastic overhaul-replacement incorporating inflation and tax effects
Yazar: ERTUĞRUL KARSAK
Danışman: PROF. DR. ETHEM TOLGA
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Doktora, 1994
Konu: Ekonomi = Economics ; Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering
Dizin: Bakım = Maintenance ; Enflasyon = Inflation ; Onarım = Repair ; Vergiler = Taxes

Özet:
ÖZET Artan rekabet ortamı, beraberindeki ekonomik belirsizliklerle birlikte donanım yemleme kararlan için yapılan ekonomik analizlere verilen önemin her geçen gün artmasına neden olmaktadır. Bu çalışmada, teknolojik gelişmeden etkile nen donanımları kullanan işletmeler için kapsamlı bakım-onanm ve yenileme yatırımlarının değerlendirilmesinde uygulanabilecek sistematik bir karar prosedürü nün geliştirilmesi amaç edinilmiştir. Türkiye ekonomisini son 15 yılda etkileyen kronik yüksek enflasyon gözönünde bulundurularak nakit giriş ve çıkışlarındaki farklı fiyat artışlarını yansıtan, zamana bağlı olarak değişen diferansiyel enflasyon oranlan, vergi sonrası nakit akışlan, donanımdan elde edilecek gelir ve hurda değerin oluşturduğu nakit girişlerinin planlama döneminin başlangıcındaki belirsizliği ve kapsamlı bakım- onanm ve yenileme kararlannın stokastik yapısı dikkate alınarak oluşturulan model, sıralı karar problemlerinin çözümünde kullanılan etkin bir algoritma olan dinamik programlama ile çözülerek gerçek dışı varsayımlara yer vermeyen bir yaklaşım izlenmiştir. Modelde, teknolojik gelişmeyi dikkate alan gelir ve maliyet elemanlan, her dönem için donanımın yaşı ve en son kapsamlı bakım-onanm gördüğü yaşın fonksiyonu olarak ifade edilmiştir. Modelin diferansiyel enflasyon oranlanndaki ve planlama ufkundaki değişikliklere duyarlılığı verilen bir örnek uygulama yardımıyla incelenmiştir. Tez çalışmasında, mühendislik ekonomisi yöntemleri, genel enflasyon oranının gelecekteki değerlerinin tahmini için zaman serileri analizi ve optimizasyon yöntemi olarak dinamik programlama kullanılmıştır. -ıx-

Abstract:
SUMMARY STOCHASTIC OVERHAUL-REPLACEMENT MODEL INCORPORATING INFLATION AND TAX EFFECTS In today's industrial atmosphere where high growth rate in technological progress and continuous increase in economic uncertainties are observed, equipment replacement decisions, which are significant determinants of the economic efficiency, appear as key problems in any type of investment. The central issue in economic analysis for equipment replacement is the decline in the value of equipment over time as a result of deterioration and obsolescence. The determination of integrated replacement policies has received considerable attention in the past couple of decades. Terborgh (1949) emphasized the difference between deterioration and obsolescence, and was the first to introduce the subject of obsolescence into equipment replacement study. In his pioneering work, obsolescence was defined as not a characteristic of the machine itself, but as a matter of the relative capabilities of new machines, which Terborgh named as "challengers". Constant salvage values and linear rate of obsolescence were assumed in Terborgh's model. Technological equipment becomes obsolete before its anticipated life expires due to the advances in technological research. The new alternatives, generally with lower cost, higher quality and output rates, reduced work-in-process inventory, etc. may outperform the existing equipment and enhance the replacement decisions. The purpose of this study is to further extend the application of the deterministic deteriorating equipment replacement model. Since the replacement problem can be viewed as a multi-stage decision process, the dynamic programming technique can be applied to find an optimal solution. The computational burden will be eased when dynamic programming is used since the computation time for enumeration increases exponentially with the number of stages while the computation time using dynamic programming is linear with respect to the number of stages. Furthermore, the ability of dynamic programming to deal with certain problem characteristics such as nonlinear objective function coefficients and stochastic outcomes, that other methods can handle with great difficulties if not at all, favourize its usage. In the following chapters of the thesis, a stochastic finite horizon overhaul- replacement model incorporating inflation and tax effects is developed. Three types of alternative policies are available: keep, overhaul and replace. "Overhaul" is defined as the major examination and repair of the equipment, and therefore, introduced in the formulation as an alternative policy. The time periods are discrete and the decision to keep, overhaul or replace is made at the beginning of each period. In each -x-period throughout the planning horizon, the revenue and cost elements which incorporate deterioration and obsolescence are functions of both equipment age and age at last overhaul. It is assumed that successive generations of assets are functionally related to their predecessors in some mathematically predictable way, and thus, cash flows for current and all future challengers can be estimated in advance. Discrete cash flows are used in the model; however for instance, if the cash flows from operations are assumed to flow continuously and uniformly during the period, the funds flow conversion factor can be used to transform these cash flows to end-of-period convention. After-tax cash flows are used in the analysis to incorporate the income tax effects. The time-dependent differential inflation rates are used throughout the analysis to remove the unrealistic assumption of traditional self-canceling approach which proposes that all prices in the economy are influenced by the uniform periodic rate of increase. This argument loses substance in the real world where some goods and services escalate much more rapidly than others, and especially, when inflation rates reach double-digit levels as in many developing countries. In this study, the general inflation rate forecasts required as an input to the equipment overhaul-replacement model are generated using time series analysis. A time series is a collection of observations generated sequentially through time (Vandaele, 1983). Time series analysis operates relying on the assumption that successive observations are expected to be dependent on the past data which is ordered with respect to time. Due to the Box-Jenkins modeling approach and advances in computer technology, time series analysis has become a practical tool for application to problems in business, economics, engineering, demography, etc. The Box-Jenkins approach primarily makes use of three linear filters: the autoregressive, the integration and the moving average filter. Box- Jenkins technique provides a unified approach for identifying which filters are the mo.st appropriate for the series being analyzed, for estimating the parameters describing the filters, for diagnosing the accuracy and reliability of the models that have been estimated, and finally, for forecasting. The notation used throughout this study, is based on a subscript k and index (i,y), where k indicates the period of operation, i indicates the equipment age and y denotes the age at last overhaul. The expected revenue function, the operation and regular maintenance cost function, overhaul cost function, investment cost function, and expected salvage value function are defined respectively as BGk(i,y), IDBMk(i,y), KBOMk(i,y), IYMk and BHDk(i,y). These revenue and cost elements, which are formulated as functions of both equipment age and age at last overhaul in each period, enable us to take deterioration and obsolescence into account. Although the revenue and cost matrices can also be used in place of these analytical functions, we limit our analysis with fairly robust functions in order to ease the computational difficulties. -XI--Xll-In general, stochastic methods are of vital importance in developing and analyzing mathematical models of the real word. In this study, it is assumed that cash flows for revenues generated from equipment and salvage values (cash inflows) are not known with certainty at the time of analysis. Therefore, they are random variables rather than known constants. The key uncertainties are generally represented by cumulative distribution functions in management science applications. The cumulative distribution functions can be defined from historical data, through market research or by the selected individuals who are qualified to make rational estimates of the data being elicited. It is common practice to obtain and use just several points from each of the cumulative distribution functions, especially if the data for a number of cumulative distribution functions must be elicited judgementally from business experts (Keefer and Bodily, 1983). Moreover, beta distribution is a widely used cumulative distribution function in modeling uncertain cash flows (Park and Sharp-Bette, 1 990). Pearson-Tukey three-point approximation technique, which outperforms PERT and other three-point approximations, is utilized as a tool for estimating the means of the aforementioned cash flows. In addition, stochastic nature of the overhaul-replacement problem, which expresses the uncertainty involved due to variability in the outcome of policy decisions, is taken into consideration. For example, if the state of the equipment in stage k is (i,y) and the decision maker selects to keep the equipment (without overhaul), it might fail to operate and an overhaul or even a replacement can be required before the next stage (lc+1). Therefore, transition probabilities in every stage should be defined for each decision alternative. In this study, discrete time Markov chains are used to describe this type of stochastic process. If the decision in stage k is to keep the equipment (ME), the transition probability from state (i,y) to state (i+l,y) is expressed as P^E(i,y;i + l,y), indicating that the decision to keep the equipment for one more period will turn out to be correct with the given probability. When the decision made in stage k is to keep the equipment, the probability of overhauling the equipment before the next stage is p{^B(i,y;i + 1,0. On the other hand, the probability of replacing the equipment before the next stage is defined as P^E(i,y;l,0) when the decision maker selects to keep the equipment in stage k. A similar reasoning applies for overhaul and replace decisions made in stage k. The reward functions associated with these transitions are determined considering the effects of differential inflation rates and income tax. The objective of the model proposed here is to determine an optimal integrated overhaul-replacement policy which maximizes the expected present value of the process over a specified planning horizon. An illustrative application, which resolves the optimal overhaul-replacement policy for a CNC lathe, is provided. The model is run under a number of scenarios, and thus, the sensitivity of the model to the time-dependent differential inflation rates and planning horizon is explored. -xui-The results present that the optimal policy is affected by the differential inflation rates and point out that the analysis neglecting this fact loses substance in an inflation-prone economy. Consequently, the proper handling of inflation in after-tax cash flow analysis needs to be emphasized in determining the optimal overhaul- replacement policy. -xiv-