Assessment of Level of Risk in Decision-Making in Terms of Career Exploitation

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1 Iteratioal Joural of Ecoomics ad Fiacial Issues ISSN: available at http: Iteratioal Joural of Ecoomics ad Fiacial Issues, 05, 5(Special Issue) Ecoomics ad Society i the Era of Techological Chages ad Globalizatio Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio Aleksadr Sergeevich Semeov *, Vladimir Sergeevich Kuzetcov Natioal Mieral Resources Uiversity Uiversity of Mies, Russia Federatio, 9906, Sait-Petersburg, Vasilievsky Ostrov, lie,, Russia, Natioal Mieral Resources Uiversity Uiversity of Mies, Russia Federatio, 9906, Sait-Petersburg, Vasilievsky Ostrov, lie,, Russia. * loader3@yadex.ru ABSTRACT Whe desigig career plots the raw data are stochastic i ature. From the results of the determiatio of these iitial data depeds ot oly the fial result of the desig or evaluatio, but also the feasibility of the developmet of the field. While there are sigificat errors associated with the probabilistic ature of the source data ad measuremet errors ad errors of calculatios. Risk assessmet is a itegral part of project documetatio. The project decisio-makig occurs uder coditios of ucertaity ad risk. To miimize ucertaity, it is first ecessary to idetify the area of potetial risk, to determie the probability of its occurrece ad the potetial cosequeces. If adverse effects caot be excluded, a more complete uderstadig of the problem ad cotributes more midful respose to the potetial risk. Aalysis of the traditioal approaches to desigig ope pits i the face of ucertaity of iput data, revealed that used desig methods do ot accout for the risk that etails the adoptio ad implemetatio of iefficiet desig solutios. Risk assessmet is made i the desig process ad icludes qualitative ad quatitative aalysis. If the evaluatio of the project will be adopted for implemetatio, the miig compaies are already faced with some problems of risk maagemet. Accordig to the results of the project accumulates statistics, which allows you to more accurately idetify risks ad work with them. Whe the ucertaity of the project is too high, the it ca be set back for revisio, the agai, there must be a risk assessmet. Keywords: Ope-pit Mie, A Workig Platform, Risk, Desig, Reliability, Probability, Source Data JEL Classificatios: J54, M4. INTRODUCTION Ucertaity iformatio leads to ucertaity i the choice of desig solutio, while ucertaity determies the approach to the problem. Ucertaity ca be caused by the absece or lack of iformatio. This situatio is typical for operatios i which the role of ucotrollable factors plays a geological coditios. I other cases, there is ucertaity i the result orgaized resistace (Bureia, 009; Geoff, 000; Tufao, 996). Maagemet of project risk - systematic processes associated with idetificatio, risk aalysis ad decisios that mitigate the egative cosequeces of iaccurate iitial geological ad feasibility data, maximizig the probability of achievig the optimal parameters ad idicators of the project (Bureia The problem of the accuracy ad reliability of desig solutios - a characteristic feature of the preset stage of developmet of the miig idustry. I the area of improvig the reliability of the desig, there is a wide rage of quarries outstadig issues. Category accuracy stads as oe of the objective criteria for the results of desig ad evaluatio. Bureia (009), Geoff (000), Rolad (000), A Guide to the Project Maagemet Body of Kowledge (00), Tufao (996), Topka (003), U. S. Bureau of Mies (993). Risk aalysis usig the method of Mote Carlo simulatio is quite a complicated procedure, with oly a computer implemetatio. The result of this aalysis is the probability distributio of possible Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05 65

2 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio outcomes of the project (for example, the probability of NPV<0 ad the expectatio of the amout of damage). You must separate the cocepts of risk ad ucertaity i the mid of their o-idetity. I coditios of ucertaity it is possible to start implemetig the project, to postpoe actio, either to abado its implemetatio. Ulike ucertaity, risk arises whe the decisio to implemet the project, i.e., the risk accepted. Decisios, ad accordigly, the implemetatio of certai actios etail ad takig appropriate risks. Therefore, the completeess ad the quality of their evaluatio depeds o the result: Miimize losses to the successful implemetatio of the project as a whole (Meredith ad Matel 0, Vellai, 007; Grey, 999). Qualitative ad structural chages i the ecoomic model of our coutry, the requiremets of the market of mieral resources, ivestmet especially ope miig, caused the complicatio of the requiremets for the desig decisios, the eed for ratioal ad optimal decisios, reducig the risk of desig; raised the questio of the reorgaizatio of the desig process, extesive developmet of feasibility studies ad the improvemet of desig methods opecast, assessig ad maagig project risk. Whe desigig quarries the raw data are stochastic. From the results of the determiatio of these iitial data depeds ot oly the fial result of the desig or evaluatio, but also the feasibility of developig the deposit. While there may be sigificat errors associated with both the probabilistic ature of the source data ad measuremet errors ad errors of calculatios. Risk assessmet is a itegral part of project documetatio (Arsetie, 00). The project decisio-makig occurs uder coditios of ucertaity ad risk. To miimize the ucertaity i the first place it was ecessary to idetify the area of potetial risk, determie the probability of its occurrece ad the potetial cosequeces. If the egative effects caot be excluded, a more complete uderstadig of problems ad promotes a more deliberate respose to potetial risk (Arsetie, 00). The aalysis of traditioal approaches to the desig of carrier-ditch, i the coditios of ucertaity of the iitial data, it was foud that prima-employed desig methods fail to accout for the risk that etails the adoptio ad implemetatio of iefficiet desig decisios (Arsetie, 00). For reliability improvemet project decisio makig must take ito accout the probabilistic ature of the source data. Cosider the width of workig platforms, amely dyamic desig system parameters with the stochastic ature of. Probabilistic i ature due to the irregularity of coduct blastig i the quarry, aparallactus i the directio of movemet of excavators i the coduct of miig operatios, the orgaizatio works i career ad other reasos of techological ature. A large umber of factors affectig the value of the width of the work sites, are ot reliable. Width of work sites that deped o may radom variables is itself a radom value. Accordig to the theory of probability radom variable is such that experiece, it ca take a certai value, ad do ot kow i advace what (Mustafa ad Al-Bahar, 99). The study of the laws of distributio of the width of the work sites i ope pit mies-aalogues allows you to set quatitative idicators, edit them, ad to ask whe desigig ad plaig of miig operatios defied their values. The distributio law of a radom variable called value, establishes a coectio betwee the possible values of the radom variable ad their correspodig probabilities (Semeov, 04; Qi, 03; Zhag, 00).. METHODOLOGY The laws ad parameters of the distributio width of the workig platforms ca be istalled i statistical processig of data obtaied at existig quarries-aalogues, implemetig steeply dippig ore deposits. The statistical processig of the material is carried out by determiig the characteristics of a radom variable is the empirical average of the expectatio, the cetral momets of the distributio of ormalized idices of asymmetry ad kurtosis (Arsetiev, 00; Bureia, 009; Semeov, 04; Camus, 00). Empirical average width of the workig platforms B = B i,m () В i - the value of the radom variable work sites (i =,, 3 ). The cetral momet of the distributio of the radom variable k-th order µ κ = ( Bi B) The secod cetral momet is called the variace characterizes the dispersio of the radom variable ad is the average of the square of its deviatio from the mea B µ = σ = ( Bi B) The third cetral momet characterizig skewess of a distributio 3 µ 3 = ( Bi B) The fourth cetral momet called kurtosis, characterizig peakedess distributio 4 µ 4 = ( Bi B) The expectatio of the radom variable k () (3) (4) (5) 66 Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05

3 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio EB ( )= B P Р i - the probability of a radom variable B, (i =,, 3.) i P i i (6) Figure : Histograms of the distributio of the width of the workig platforms ore career, earig their steeply dippig deposit The values, µ 3, µ 4 allow us to determie the ormalized asymmetry idex β = µ µ 3 3 / (7) ad the ormalized measure of kurtosis β µ 4 = (8) µ The values of these characteristics are determied by the parameters of all the major distributios. To establish the law, which ca be approximated distributio fuctios, you should use the schedule Pearso (Rolad, 000), where the applied field i the plae ([beta], [beta] ) for differet distributios - ormal, beta distributio, gamma distributio ad log-ormal. Mathematical processig of empirical data coducted by ore quarries-aalogues, has allowed to obtai the distributio of the width of the workig platforms for these quarries. For solvig the problem were treated with the provisios of the miig pits-aalogues. Width measuremet sites were coducted o the etire workig area of the quarry o the horizos of the testig. Whe measurig the width of the work sites received 844 values of ore ad 05 - breed. The results of measuremets of the width of the work sites by ore quarries-couterparts, implemetig steeply dippig deposits, are preseted i Table. Accordig to the results of the measuremets used to costruct the histogram of the width of the work sites (Figure ). Characteristics of the radom variable defied by the formulas ( 5): Ore p = 8, 5 M B = 3 M µ 3 = µ 4 = The breed = 6, 0 M B = 9 M µ 3 = 3669 µ 4 = 6400 Figure sharply asymmetric distributio of the width of the work sites. Variatio series with this distributio is log-ormal (logormal) distributio, where the ormal distributio are subject to the values of the logarithm of the radom variable. Whe usig the logarithmically ormal law are atural or decimal logarithms for all values of the radom variable. Cumulative distributio fuctio of the width of the workig platforms FB ( ) = σ l π l B 0 B e B B ( l l ) σ l (Sigma) l - the variace of the logarithm of the width of the workig platforms; (Sigma) l - the stadard deviatio (stadard) empirical umber; B l - the empirical average of the logarithms of the width of the work sites. A logormal distributio is characterized by the probability desity, which i this case has the form f( B) = B σ l e π (l B Bl ) σ l db (9) (0) The variace of the logarithm of the width of the workig platforms σ l = (lbi l Bmed ) mi () - the umber of measuremets equal to the sum of the frequecies of the empirical distributio; B med - the media value of the width of the work sites, m; m i - frequecy i-th measuremet iterval. The mathematical expectatio of the width of the workig platforms EB ( ) = e B l l + σ () Figure shows the curves of chastoty width workig platforms ore quarries-aalogues. Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05 67

4 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio Normal dispersio may be determied accordig to the formula (49) Figure : The itegral curves of chastoty width career workig platforms σ σ σ = e B ( e e ) l l (3) I the case whe the values of the dispersios ad small curves desity distributio of the ormal ad logormal close to each other ad i the limit, whe seekig the variace to zero, they are the same. Itegrals ad probability desity fuctio of the logormal law ot table roud, so the theoretical probability desity built directly by the formula (0). The values of the logarithms of the width of the workig platforms for career, earig their polymetallic deposit, are preseted i Table. The data preseted i Table reflect the histogram of the logarithms of the width of the work sites (Figure 3) ad the Table : The results of measuremets of the width of the workig platforms ore pit The measuremet Frequecy, m i Cumulative frequecy, М Chastoty, m % Accumulated chastoty itervals of the width Ore The breed Ore The breed Ore The breed Ore The breed of the workig sites Amout Table : The values of the logarithms of the width of the work sites career earig polymetallic deposit Itervals of measuremet the logarithm of the width of the workig platforms Frequecy, m i Cumulative frequecy, m Chastoty, m % Accumulated chastoty Ore The breed Ore The breed Ore The breed Ore The breed Sum Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05

5 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio itegral curves of the particulars of the logarithms of the width of the work sites (Figure 4). Usig expressios (-3), we determie the values of σ l, σ l, EB ( ), B l : At a kow desity fuctio probability distributio may determie the probability that a cotiuous radom variable - width sites, will take the value correspodig to the specified iterval (B, B ). This probability is defied as the defiite itegral of the differetial of the fuctio take withi B to B. Ore l P = 049, l P = 07, The breed l B = 036, l B = 06, EB ( ) p = 30, 6 B l P = 37, EB ( ) B = 9, 4 B l B = 30, PB ( < B < B ) = f( B) db (6) i B B Thus, the probability desity fuctio of the logormal distributio width of the workig platforms ore quarries couterparts, accordig to the expressio (0), (l B p 37, ) f( B p ) = e 049, - Ore (4) 07, B p π f( Bp ) = e 06, B π B (l B p 3, ) 036, - the breed (5) Figure 3: Histograms of the distributio of the logarithms of the width of the workig sites polymetallic career Graphically the probability of a magitude B i the plot (B, B ) is expressed by the area uder the curve of probability desity distributio, that is, with this plot. For this polymetallic career hit probability of the width of the workig sites i the iterval (B = 5 m B = 35 m). P( 5 < B < 35) = RESULT Whe desigig quarries as the risk measure is take the differece betwee the uit ad the probability of occurrece of this evet (Arsetiev, 00; Meredith ad Matel 0, The ower s role i project risk maagemet, 005, Uks ad Thor, 008; Mustafa ad Al-Bahar, 99). R = P( ε ) (7) Possible accoutig of both ecoomic ad psychological cosequeces of risk (Camus, 00; Kerzer, 009). I the justificatio of risk should be take ito accout subjective factors, as defied objective situatio may preset varyig degrees of risk from the poit of view of a specialist i differet coditios. I this case, the risk is uderstood as the probability of ecoomic losses associated with ot ackowledge the calculated values of the width of the work sites. The probability distributio of a radom variable is approximated by a logormal law. Figure 4: The itegral curves of chastoty logarithms width job career sites Degree of risk R(B) ca be expressed through the probability of hittig the actual values B i o a give area, limited left value B mi, ad to the right value B i, at which the total developmet costs ( c) matches c by B mi Bi B R = P( B) = F( l l mi ) σ l (8) P(B) - the likelihood that the actual width of the work sites for a specified period of; (sigma) l - the stadard deviatio of the empirical rage of the logarithm of the radom variable; F(B) - logormal distributio fuctio. I studies (Arsetiev, 00; Rolad, 000; Hill, 993; Semeov 04). the determiatio of the risk level of the ormal distributio law. At a certai desity distributio of the width of the workig Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05 69

6 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio career sites, you ca determie the level of risk of failure to achieve the set width of workig platforms RB ( ) = σ π l l Bi l B0 B e i B Bi ( l 0 l ) σ l db (9) l B 0 - the value of the logarithm of the width of the work sites, the correspodig ( B 3σ ). l l The risk value for ormal distributio of the logarithm of the width of the work sites are preseted i Table 3. A graph of the level of risk of failure to achieve the set width of the workig career sites are preseted i Figure 5. Aalysis of the graph shows that for the coditios of ore pit i the period of developmet, ecoomic risk would be 54% ad 33%, respectively, whe the width of the workig platforms 4 m ad 33.6 m 4. DISCUSSION I paper (Hill, 993) is cosidered as a variat of the deposit developmet assessmet based o regressio aalysis, which ivolves the use of the method of least squares o the basis of: The formulatio of the model view, based o the relevat theory Table 3: The degree of risk associated with differet values of the logarithms of the width of the workig sites The logarithm of the width of the workig sites l B i Level of risk R(B), % B = B.5 00 l 0 l 3 l l B = Bl l l B = Bl l * l B3 = Bl E l B4 = B l l B5 = Bl + l l B6 = Bl + 3 l Figure 5: A graph of the level of risk of failure to achieve the prescribed the width of the workig platforms ore pit of relatioships betwee variables; оf all the factors ifluecig the productivity of a sig, it is ecessary to idetify the most sigificat ifluecig factors; steam regressio sufficiet if there is a domiat factor, which is used as a explaatory variable. It is therefore ecessary to kow which other factors are assumed to be uchaged as i the further aalysis they have to take accout of the simple model ad to move multiple regressio; examie how a chage i oe trait variatio chages the other. But this method has the followig disadvatages: Purposeful rejectio of other factors; the impossibility of idetifyig. measurig certai variables (psychological factors); lack of professioalism researchers simulated; aggregatio of variables (as a result of aggregatio of the iformatio is lost); icorrect determiatio of the structure of the model; the use of temporal iformatio (chage the time period, you ca get differet results regressio); specificatio errors: Wrog choice of a mathematical fuctio; udercout i the regressio equatio of a sigificat factor, the use of paired regressio, istead of multiple); samplig error, as the researcher ofte has to do with sample data whe establishig regular coectio betwee the features. Samplig errors arise due to heterogeeity i the iitial statistical populatio that is i the study of ecoomic processes; measuremet errors are the most dagerous. If the error specificatio ca be reduced by chagig the shape of the model (a kid of mathematical formulas), ad samplig error - icreasig the amout of raw data, the measuremet error ullify all efforts to quatify the relatioship betwee attributes. It is of iterest to idetify the psychological cosequeces of risk. Whe desigig quarries better to deal with reverse fuctio - fears of the cosequeces of icreased risk (Zhag, 00). Discusses four risk attitude: Bold attitude c (ẟ) = a( e ẟ ); (0) Equality attitude p (ẟ) = aẟ; () Cautious attitude 0 (ẟ) = a(e ẟ ); () No risk ẟ = 0 Hp (ẟ) = 0; (3) а: The ratio of proportioality, it is recommeded to take а =.37; d: The relative icrease compared to its miimum value (whe ẟ = 0). The relative icremet of the logarithm of the width of the workig platforms (compared to l B0 = Bl 3σ l ) l B l B δ = l B i 0 0 (4) Values with differet levels of risk are show i Table 4. Figure 6 shows the fuctio of the fears of the cosequeces of the relative icrease of the logarithm of the width of the workig platforms with differet attitudes to risk. 70 Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05

7 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio Figure 6: Fuctio cocers the cosequeces of the relative icrease the logarithm of the width of the workig platforms Table 4: The width of the work sites at differet level of risk Expoet Values with differet levels of risk, % The relative icrease i, ẟ i The logarithm of the width of the workig platforms, l B e ẟ Width of work sites, B, m Table 5: The logarithm of the width of the work sites uder differet attitude to risk Attitude to risk lb В, m ẟ i Level of risk R(B), % Bold Smooth Careful No risk With a bold attitude take ẟ c =.56 (poit. Figure 6). Whe the level of risk 50%. I this case the fuctio level cocers will be H =.87. Whe eve the attitude to risk ẟ p = 0.88 (poit. Figure 6). While cautious attitude ẟ o = 0.59 (poit 3. Figure 6). Obtaied values of the logarithms of the width of the workig area at H =.87 are give i Table 5. Determiig the level of risk (Table 6) is possible usig depedecies Table 6: The depedece of the level of risk R(B) ratio of for a ormal distributio R(B), % R(B), % R(B), % δi = 3 ( ) δ c (5) REFERENCES ad Table 6 for the ormal distributio law. Thus, whe existig i this career, the logormal distributio width of work sites, the optimum width of the work sites will be m risk desig will be 54-33%. Cosideratio of the psychological aspects of the decisio shows that i this case, eve the orietatio of the cost of the miimum width of the work sites at a rate of 4 meters icreases the risk, but to work with high-risk ecoomically feasible. To reduce the level of risk should seek to icrease the value of the expectatio width worksites career, reduce the probability of occurrece of widths worksites less regulatory miimum. 5. CONCLUSION Width career workig platforms should be cosidered as a radom variable, subject to certai laws of distributio. To evaluate the probabilistic ature of the width worksites quarries developig steeply dippig ore deposits, it is advisable to use the logormal distributio. Kowledge of the form of the distributio width career workig platforms allows us to estimate the level of risk of failure i the draft adopted by the width of the work sites associated with the probabilistic ature of the source data. A Guide to the Project Maagemet Body of Kowledge, (00), I: Project Risk Maagemet. Vol.. Pesylvaia, USA: Project Maagemet Istitute. Arsetiev, A.I. (00), Performace Quarries. Sait-Petersburg: State Miig Istitute, Techical Uiversity. p85. Bureia, G. (009), Strategic Aalysis of the Risks of Idustrial Eterprise. Sait-Petersburg SPBGUEF. Camus, J. (00), Maagemet of mieral resources. Miig Egieerig (SME), 5, 7-5. Geoff, K. (000), Risk maagemet systems. Risk Professioal, (), 9-3. Grey, S. (999), Practical risk assessmet for project maagemet. Techometrics, 4(4), Hill, J.H. (993), Geological ad Ecoomical Estimate of Miig Projects. Lodo. Kerzer, H. (009), Project Maagemet a Systems Approach to Plaig, Schedulig, ad Cotrollig. 0 th ed. New York: Joh Wiley. p. Meredith, J., Matel, S. (0), Project Maagemet a Maagerial Approach. 8 th ed. Hoboke, N.J.: Wiley. p589. Mustafa, M., Al-Bahar, J. (99), Project risk assessmet usig the aalytic hierarchy process. IEEE Trasactios o Egieerig Maagemet, 38, Qi, E. (03), Proceedigs of 0 th Iteratioal Coferece o Idustrial Egieerig ad Egieerig Maagemet Theory ad Apply of Idustrial Egieerig. Heidelberg: Spriger. Rolad, K. (000), Towards a grad uified theory of risk. Operatioal Risk. Lodo: Ifroma Busiess Publishig. p6-69. Semeov, A. (04), Assessmet of project risk i the hierarchical Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05 7

8 Semeov ad Kuzetcov: Assessmet of Level of Risk i Decisio-Makig i Terms of Career Exploitatio orgaizatio of the process of desig of complex techical systems. World Applied Scieces Joural, 30(8), The Ower s Role i Project Risk Maagemet, (005). Washigto. DC: Natioal Academies Press. Topka, V. (003), New Critical Path Method Liear Relatios. Proceedigs of 7 th World Cogress o Project Maagemet. Tufao, P. (996), Who maages risk? The Joural of Fiace, 5(4), U. S. Bureau of Mies (993), Surface ad udergroud miig. I: Bureau of Mies cost Estimatig System Hadbook. p63. Uks, R., Thor, L. (008), The maricopa itegrated risk assessmet project: A ew way of lookig at risk. Commuity College Joural of Research ad Practice, 3(), Vellai, K. (007), Strategic Security Maagemet a Risk Assessmet Guide for Decisio Makers. Amsterdam Butterworth-Heiema. Zhag, J. (00), ICLEM 00 Logistics for Sustaied Ecoomic Developmet: Ifrastructure. Iformatio Itegratio: Proceedigs of the 00 Iteratioal Coferece of Logistics Egieerig ad Maagemet. October 8-0; 00, Chegdu, Chia, Resto, Va.: America Society of Civil Egieers. 7 Iteratioal Joural of Ecoomics ad Fiacial Issues Vol 5 Special Issue 05