生命获利能力决策方法外文文献The Life Profitability Method (LPM) A financial approach to engineering decisions

The Life Profi tability Method LPM A fi nancial approach to engineering decisions Paolo Gardoni Fausto Guevara Lopez Alessandro Contento Department of Civil and Environmental Engineering and MAE Center University of Illinois at Urbana Champaign USA a r t i c l ei n f o Article history Received 1 April 2015 Received in revised form 8 June 2016 Accepted 22 June 2016 Available online 15 July 2016 Keywords Financial measures Life Cycle Cost Life Profi tability Method Optimal decisions a b s t r a c t The Life Cycle Cost Analysis LCCA is often used to guide engineering decisions to incorporate the costs of an asset during its entire service life in the decision making process However researchers have found that decision makers preferences i e design choices are often different from those suggested by the cur rent LCC Analysis To explain these discrepancies researches introduced human risk aversion formula tions that are based on individual perceptions This paper argues that the current LCC analyses are incomplete and they only provide a partial representation of the economic consequences valuable to decision makers The paper proposes the Life Profi tability Method LPM which introduces additional fi nancial measures capable of capturing the future costs and revenues including a non zero growth rate insurance protection and profi tability ratios not accounted for in the LCCA The LPM allows for optimal decisions based on more complete fi nancial information 2016 Elsevier Ltd All rights reserved 1 Introduction In recent years there has been an effort to evaluate new designs and rehabilitations of existing assets structures or infrastructures in terms of their associated risks 1 4 These informed decisions consider hazards such as earthquakes and hurricanes and their respective consequences on an asset Decision makers can assess these risks in terms of societal or economic factors For instance the Life Quality Index LQI 5 and the Capability Approach 6 9 measure the reduction in societal well being These methods can be useful for government agencies or corporations trying to evalu ate the likely societal implications of certain decisions For asset level decisions several researches proposed to calculate the expected life cycle cost of an asset throughout its life span 2 4 10 and to minimize this cost by changing design characteris tics However Goda and Hong 11 13 noted that the monetary consequence i e expected costs may not be directly proportional to the preferences of decision makers That is the design that min imizes the expected cost computed using current formulations is not consistent with the choice of the decision makers Goda and Hong explained this discrepancy by introducing multiple subjec tive risk aversion formulations based behavioral models Cha and Ellingwood 14 also raised this concern and proposed a unique risk aversion behavior in civil structures infrastructures that fol lows a trend similar to the risk aversion in insurance underwriting Theseformulationsshowthattheminimizationofcurrent expected cost lacks the ability to predict design level decisions This paper focuses on the expected cost models The models used up to now are missing information that decision makers con sider valuable To have more complete monetary quantifi cations of the design options we introduce the Life Profi tability Method LPM The LPM is divided into four stages The fi rst stage defi nes design parameters such as structural capacity structural demand and discount rates The second stage builds on previous expected cost methods by incorporating factors such as appreciation depre ciation valuation and insurance coverage The third stage com putes future revenues considering design levels and the presence of damage in the asset The fourth stage introduces a profi tability analysis considering economic ratios between expected costs and revenues Previous methods offer a design analysis in terms of the minimum expected costs The presented formulation uses more fi nancial information thus we believe this formulation better captures the decision attitude of decision makers towards invest ments under uncertainty The paper begins with a literature review of decision methods in engineering and in fi nance We then present the formulation for the LPM Next the LPM is illustrated considering the design of a steel building using a benchmark steel frame building located in Vancouver Canada Finally the results from the LPM are com pared with those from existing decision methods http dx doi org 10 1016 j strusafe 2016 06 006 0167 4730 2016 Elsevier Ltd All rights reserved Corresponding author E mail address gardoni illinois edu P Gardoni Structural Safety 63 2016 11 20 Contents lists available at ScienceDirect Structural Safety journal homepage 2 Decision methods 2 1 Decisions methods in engineering In most of the engineering applications decisions are made con sidering three methods the Life Cycle Cost Analysis LCCA the Utility Theory UT or the Cumulative Prospect Theory CPT As shown in the following all the three methods are directly or indi rectly based on the evaluation of the Life Cycle Cost LCC of the asset considered 2 1 1 Life Cycle Cost Analysis The LCC Analysis is one of the fi rst assessment formulations that considers economic consequences in the decision making process Its objective is to minimize the expected total cost incurred by the asset Generally the LCC includes the initial cost CO Z life mainte nance cost CM T Z and life failure cost CF T Z 2 4 Given a struc ture with a design parameter vector Z and lifespan T the LCC for a structure can be written as LCC T Z CO Z CM T Z CF T Z 1 When the design vector Z is more conservative the initial cost increases whereas the expected failure cost decreases The initial cost CO Z is usually assumed to be deterministic dependent on the initial design level and occurring only at the pre sent time Wen and Kang 2 suggested that the initial cost of an asset is dependent on the structural and nonstructural components such that CO Z COO Z CRN AF 2 where COO Z is a cost per unit area that accounts for repair costs and may account for construction or retrofi t costs as a function of the design level and increases as Z increases CRNis a nonstructural cost per unit area and is the same for all designs and AFis the con struction area The life maintenance cost CM T Z is often assumed to be constant across the design options 15 i e CM T Z CM thus it does not affect the selection of the optimal design The life failure cost CF T Z is assumed to be random throughout the asset lifespan refl ecting uncertainties that arise from the future demands on the asset the asset capacity over time and the time value of money 15 To account for all these uncertainties the method cal culates failure costs that occur at time t Cf Z as a function of struc tural and nonstructural costs The structural costs Cr Z d are related to the asset s reconstruction value and to the damage ratio at time t d Z In the following for brevity the dependence of d Z on Z is omitted The nonstructural costs Cd Z d account for occupancy and nonstructural content damages Some authors 2 11 proposed that these costs can be expressed as a function of design parameters construction area and the damage state after a hazard such that Cr Z d Coo Z CRN AF de 3 Cd Z d H AF df 4 whereHis a constant multiplier throughout the asset s lifespan that considers occupancy factors the powers e and f are parameters that vary depending on the asset s characteristics If d 0 the asset presents no damage whereas if d 1 the asset is completely destroyed Note that this formulation assumes that the cost of repairing the asset is constant throughout the lifespan which may not be true for civil structure infrastructure assets The LCC accounts for the time value of money by discounting each Cf Z to a comparable Present Value PV as follows C f t Z Cf Z 1 cd t Cr Z d Cd Z d 1 cd t Coo Z CRN AF de H AF df 1 cd t 5 where C f t Z is the discounted failure cost at time t andcdrepre sents the discounting rate Finally the asset life failure cost CF T Z is the integral of C f t Z over the interval 0 T CF T Z Z T 0 C f t Z dt 6 In theory rational decision makers choose design levels that minimize the LCC Nevertheless research has shown that decision makers tend to prefer more conservative designs than those that minimize the LCC 12 16 In order to explain this discrepancy researchersintroducedseveralsubjective justifi cationsthat explain the behavior in terms of risk aversion 17 18 In some papers 19 21 the LCCA has been modifi ed in order to account for some possible benefi ts deriving from the assets In these cases the optimal decision is considered as the one that maximize the difference between the benefi ts and costs 2 1 2 Utility Theory The UT was fi rst introduced by Daniel Bernoulli and later for malized in economic theory in 1947 22 It attempts to incorpo rate the decision maker s attitude towards risk This theory introduces a utility function to measure the desirability of conse quences Decisions are made by choosing the option that maxi mizes the expected utility function typically defi ned as 12 E U LCC T Z X n0 l 1 U LCCl T Z pl 7 where U LCC T Z is the utility of LCC T Z plis the probability of the lth sample path of the LCC process and n0is the number of pos sible outcomes 2 1 3 Cumulative Prospect Theory A more recent and general approach to model decisions is the CPT 13 This model recognizes how decision makers have a sub jective perception of rare events To account for highly unlikely events CPT includes weighting functions and different utility func tions referred to as value functions for gains and losses In struc tural design the weights refl ect the aversion to the low probability related to high consequence events such as large earthquakes and hurricanes The new objective is now to maximize the sum for l from 1 to n0of the products of the value function and the weight function E V LCC T Z X n0 l 1 V LCCl T Z p pl 8 where V LCC T Z is the value function of LCC T Z andp pl is a function written as p pl w X l a 1 pa w X l 1 a 1 pa 9 where w is a general non linear function of the argument and the other quantities were defi ned earlier Because of the arbitrariness in defi ning the CPT s functions V and w Goda and Hong 13 investigated the importance of the functional form on the decision level in the context of seismic design Specifi cally they proposed the following value function V LCC T Z k LCC T Z n 10 12P Gardoni et al Structural Safety 63 2016 11 20 where k n are two model parameters Additionally Goda and Hong 13 proposed the following weighting function w X l a 1 pa exp ln X l a 1 pa u 11 whereuis a model parameter The parameters k n u were chan ged to represent convex concave s shape inverse s shape and lin ear functions Although the study presents a fi rst step towards modeling the risk averse behavior in engineering decisions there remains a need to develop project specifi c values for k n u To assess observed behaviors towards risk researchers focused on developing a value function that is a closer match with the actual engineering decisions Researchers 23 25 found that the sign of the second derivative of a value function with respect to the LCC correlates well to the decision maker s attitude towards risk A positive second derivative implies a risk taking behavior whereas a negative second derivative indicates a risk averse atti tude Based on these characteristics of V LCC T Z and assuming a general risk averse behavior in engineering decision making Cha and Ellingwood 26 proposed the following value function V LCC 1 1 e ca 1 e ca LCCmax LCC LCCmax 12 where LCCmaxis the maximum value of the potential losses andcais a parameter that refl ects the degree of risk aversion for which there is a need to develop project specifi c magnitudes Cha and Ellingwood 14 26 found that the new recommended design level is more conservative than the original optimal level obtained based on the Life Cycle Cost alone i e a larger initial investment is needed and that the decision is highly dependent on the risk aversion factors u ca This paper develops a procedure that enhances current decision methods in engineering with addi tional factors typically available to decision makers 2 2 Decision methods in fi nance net present value and profi tability ratios Decision methods in fi nance are used by decision makers in the planning of long term investments They involve planning analyz ing selecting and managing capital with the ultimate objective of maximizing the wealth of the owners 27 These series of steps are usually known as capital budgeting techniques In North America Discounted Cash Flow DCF methods such as the Net Present Value NPV are among the most popular capital budgeting tech niques 28 The NPV calculates a comparable current value of all present and Future Cash Flows for an investment see 29 for details This method recognizes the magnitude time value and risk of a pro ject s cash fl ows Typically cash fl ows fall into three categories 1 initial investment which is a function of a project s characteris tics and for civil structure infrastructure represents the cost of building the asset 2 expected future cash infl ows and outfl ows due to sales of goods or services and costs i e the rent charges or repair costs 3 investment s terminal value like the selling price of a building or the cost to demolish it Note that initial investments are assumed to occur at present time whereas cash fl ows in Categories 2 and 3 happen in the future and are denomi nated as Future Cash Flow FCF The FCF is affected by the time value of money and the riskiness of the project A fi rst step in considering the underlying uncertain ties is to estimate a value for FCF and modify it to represent a pro portional value as if it were to happen in the present such that PV t FCF 1 cd t 13 where PV t is the present value of the cash fl ow at the time t This method assumes that a FCF is constant throughout the lifespan A more general representation of the numerator in Eq 13 includes the possibility of having FCFs proportional to a pre determined initial value FCF0as FCF t FCF0 1 cr t 14 where FCF t is the FCF at time t andcris the growth rate The dis count and the growth rates are assumed to be mutually indepen dent and constant over time Introducing a growth rate allows the decision maker to consider three different cases 1 depreciationcrcd wherecdis the discounting rate as noted earlier Fig 1 shows the PV of FCF for these three cases Eq 13 of the LCC method is equivalent to havingcr 0 thus is represented by Case 1 in Fig 1 The cases of time dependent and interacting rates would lead other possible paths other than those presented in Fig 1 and can be considered for a future further refi nement of the formulation The proposed formulation is general and could accommodate such dependency However often build ings gain value with time therefore a model that assumes cr 0 would in general not be correct Procedures to estimatecdandcrare transferable to any project the fi rst is usually obtained using the Capital Asset Pricing Model CAPM The CAPM calculates discount rates in terms of a risk free rate and a coeffi cient b The fi rst is associated with government bonds and market premiums that translate into the environment for a specifi c sector whereas b captures the relationship between a general market and a specifi c company or project 29 To calcu late the growth rate decision makers refer to historical informa tion on similar projects and compare it to industry averages 30 By including a growth rate a decision maker accounts for ten dencies in asset valuation However during the asset lifespan it is possible to have events such as earthquakes or hurricanes which change tendencies The NPV method can handle these conse quences by modifying Eq 14 to have infl ows revenues and out fl ows expenses rather than a unique cash fl ow as follows PV t Rev t 1 cd t Cos t 1 cd t Rev0 1 cr t 1 cd t Cos0 1 cr t 1 cd t 15 where Rev0is the present annual revenue Cos0is the present annual expense both of them comparable to FCF0 Rev t and Fig 1 Future value as a function of discount and growth rates P Gardoni et al Structural Safety 63 2016 11 2013 Cos t are the magnitudes of the respective FCFs of revenue and expense Expenses are expected to increase when a hazardous event affects an asset because there is typically an abnormal need for repairs However decision makers can reduce the economic impact of high consequence events by acquiring insurance coverage and transferring the risk Assuming that the asset s expenses at time t are described as Cos t Cos0 1 cr t the insurance coverage reduces future costs such that the effective cost Cos0 t is Cos0 t Cos0 Lcov 1 cr t Ci t 16 where Lcovis the limit for transferred cost the monetary value that an insurance company will pay the owner of a property after a haz ardous event is a function of the design parameters and of the incurred damage cost as clarifi ed later in the paper and Ci t is the cost of acquiring the protection that includes the insurance premium and deductible On the other hand future revenues are expected to decrease if a hazardous event damages the asset beyond a certain damage limit dL This behavior was observed in buildings affected by the North ridge Earthquake where apartment buildings had a drop in rent ft2 even after being repaired 31 Similarly to the expense formula tion revenues at time t are described as Rev t Rev0 1 cr t Therefore the reduction in asset s valuation will yield an effective revenue Rev0 t that can be written as Rev0 t Rev0 1 cr t Rev0 t Rev0 1 cr t 1 w d dL else 17 where w is a reduction factor that accounts for the asset s loss in value The modifi cations to both revenues and expense update Eq 15 as PV0 t Rev0 t 1 cd t Cos0 t 1 cd t 18 Once PV0 t is computed decision makers can choose th