Robust data analysis in innovation project portfolio management

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1 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 Robust data analyss n nnovaton project portfolo management Bors Ttarenko,*, Amr Hasnaou, Roman Ttarenko 3 and Llya Buuk 4 Moscow State Unversty of Cvl Engneerng, Yaroslavskoe shosse, 6, Moscow, 9337, Russa La Rochelle Busness School, France 3 Stockholm School of Economcs, Russa 4 Russan State Socal Unversty, Moscow Abstract. The paper states the mathematcal model of portfolo management that allows to create an effectve portfolo of nnovaton projects. Wthn the framework of ths model the robust approach to data analyss s appled and expanded for the tasks of regresson analyss of project data. The approach of robust estmaton of regresson parameters based on the maxmum lkelhood method n case of arbtrary contamnaton s suggested. A number of heurstc algorthms for estmatng regresson parameters n the case of symmetrc data contamnaton s revewed and modfed. Introducton There are many defntons of projects portfolo n the recent scentfc lterature. For nstance, Turner and Müller [] defne a portfolo as an organaton where projects are managed together to coordnate nterfaces, prorte resources between projects, and thereby reduce uncertanty. Accordng to [] a portfolo s a group or set of projects wth varyng characterstcs. Artto et al. [3] defne projects portfolo as a collecton of projects that are carred out n the same busness unt sharng the same strategc objectves and the same resource pool. In ths artcle we wll consder nnovaton projects portfolo as a set of nnovaton projects that are grouped n order to ncrease management effcency and to acheve the strategc goals of the organaton. In a rapdly changng envronment and hgh competton, effcent management of the projects portfolo s an mportant tool for the success of any company. Project portfolo management (PPM) nvolves actvtes amed at achevng the strategc goals of the organaton by formng, optmaton, montorng and control as well as management of any changes of the projects portfolo under certan restrctons [4, 5]. Accordng to [6] PPM solves key problems of project orented * Correspondng author: borsttarenko@mal.ru The Authors, publshed by EDP Scences. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 4.0 (

2 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 organatons: overcomes the gap between operatng and project management and becomes a core of all organatonal actvtes. Synergstc effect of a projects portfolo, n partcular, s a smultaneous achevement of the best economc, fnancal, socal and other fnal results. Synerges of a projects portfolo means the stuaton when obtaned usefulness from the mplementaton of the projects portfolo exceeds the usefulness of each projects portfolo separately [6, 7]. Project portfolo management requres the processng of a large amount of nformaton. To make competent and effectve decsons t s necessary to analye carefully the avalable data, to study dependences between factors that nfluence on the decson makng. In stuatons of great uncertanty, n whch projects are mplemented n the modern world, processng methods of not enough robust data are necessary to provde suffcently relable conclusons. Wthn the robust estmaton [8] that appeared n mathematcal statstcs n the 960s and 970s the ways and methods of obtanng robust estmates of statstcal models parameters were dentfed. Over the last 50 years the scope of applcaton of robust methods has been expanded. Most of the modern works on ths subject are devoted to the problems of multvarate statstcal analyss and estmaton of ther parameters n case of the presence of gross errors n data or ther contamnaton by extraneous data [8, 9]. However, the problems of parameters estmaton for regresson dependences are the man nterest for researchers [0-3]. New approaches to robust procedures are also offered [4, 5]. Thus, the robustness concept begns to be nterpreted more wdely than by J. Tukey and P. Huber [8]. Recently, due to the wde applcaton of project management methods, robust methods have been appled n project rsk management [6-8]. Ths paper shows the robust methods that can be effectvely used n nnovaton project portfolo management. The purpose of ths paper s to develop the model that allows to form an optmal projects portfolo and to suggest robust methods that can be effectvely used n nnovaton project portfolo management. Ths paper has the followng structure. In Secton a model of nnovaton project portfolo management that allows to maxme the economc effect of the portfolo s shown. In Secton 3 a robust approach to regresson analyss of project data s suggested. Secton 4 concludes the paper. Formaton of the nnovaton project portfolo management model Formaton of an nnovaton projects portfolo nvolves the settng prortes of projects wthn the organaton and optmaton of the projects components n the portfolo to ensure the best complance of the portfolo wth the strategc goals of the company. To that end, such methods are used that allow to set the prortes of the projects takng nto account defned crtera n the organaton, gven the lmted budget and resources [5]. The effectve nnovaton projects portfolo means a set of projects that delvers the maxmum gans wthn the exstng resource constrants. To solve the problem of the effectve nnovaton projects portfolo formaton t s necessary to develop a mathematcal model that can be appled to projects of all knds, types and scope. Denote needs of the projects n dfferent types of resources by matrx R. Problem of the optmal portfolo formaton s solved under the constrants on the resources: fnancal, materal, labor and other. Let the number of resources s equal to m and the number of -type resources s denoted as W. Thus, we have vector of resources W W, W,., W m... Projects portfolo can be

3 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 formed from a set of n projects P, P,..., P n,.e. there s a vector of projects P P, P,..., Pn. Let denote needs of the projects n dfferent types of the resources by the matrx R: R R R... R m R R... R m R n R n... R nm where R j s a need n j resource of -type project., Defne some ntegral ndcator of the effectveness of the -type project E the vector of effcency of a portfolo E E, E,., E n... Let us ntroduce nto consderaton an nteger bnary varable : 0, f -type project s not ncluded nto portfolo;, f -type project s ncluded nto portfolo. and consder In ths case, the selecton of projects n the portfolo can be hold by solvng the resource allocaton problems for boolean varables (the so-called problems of nteger lnear programmng). Our goal s to select the combnaton of projects, on the one hand that they ft wthn the resource capabltes and on the other hand that they maxme the outcome receved by an enterprse. Mathematcal model enablng to form an effectve portfolo wll be as follows: E E E... E n n max wth lmtatons R R... R n n W ; R R... R n n W ;... R m R m... Rnmn Wm. In vector-matrx form t looks as E ( E, ) max, () RT < W, () where s an nteger vector, Usng ths model, we obtan values for,.,.. n that allows on ther bass to form the optmal projects portfolo for maxmum E economc effect. To solve the problem of formng the optmal project portfolo the known methods for solvng problems of nteger lnear programmng can be appled and they are llustrated n the followng approaches. st approach. The most natural way s to try to use the tradtonal methods of lnear programmng, such as smplex method, just modfyng them a bt. So, t s possble to solve the problem of not payng attenton to the requrement of ntegralty of the varables, and then round the coordnates of the obtaned soluton to the nteger numbers. However, t s 3

4 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 possble to gve some smple examples of such approach falure, when the solutons are actually far from optmal. rd approach. It s based on the effectve exhaustve search methods. Ther number, of course, s too large, therefore ther all exhaustve search s practcally mpossble or very tme and labour-ntensve. Effectve exhaustve search methods are to revew only the most promsng optons and to represent a rapdly convergng teratve procedure. The problem s to work out modaltes for the clppng of the nherently unpromsng solutons based on the resource constrants. Here, t seems the most approprate to apply the Branch and Bound method that conssts n the determned exhaustve search of the soluton tree branches. Ths method s often used n solvng optmaton problems n operatons research and allows to obtan the exact soluton of the problem for a fnte number of steps. Thus, n one varant of the method, varables are added one by one wth a test of ther resource endowment and all the sets are rejected for whch these condtons stop to mplement. The value of the objectve functon s defned for each possble branch and then t s compared wth a maxmum reached value. Uncertan stuaton n whch projects are mplemented gves rse to numerous and vared rsks. Therefore, the analyss and assessment of rsk are very mportant for the formaton of the projects portfolo and, fnally, the rsk largely defnes the projects portfolo effcency. For the formaton of the effcency crtera t s necessary to take nto account both external rsks arsng from the envronment of the enterprse and nternal one accompanyng a project actvty. Solvng problems of nnovaton projects portfolo formaton t s necessary to quantfy the key ndcators of projects rsk. Any experenced specalst can calculate losses on the occurrence of a rsk event, whereas the probablty of occurrence of a rsk event requres the use of specal methods based on the proper use of avalable project nformaton. As a rule, t s ether real data of consderng smlar projects or ther probable models. The unrelablty of data and nadequate models n stuatons of uncertanty are the sources of rsk decson-makng for managng projects. For relable estmates of rsk events probabltes, the authors suggest the use the socalled robust methods descrbed n Secton 3. 3 Robust approach to regresson analyss of project data Classcal methods of estmatng parameters n mathematcal statstcs are based on the precse knowledge of the model dstrbutons of random varables. The basc estmaton method maxmum lkelhood method defnes the best estmate for each probablty dstrbuton. However, a sgnfcant dsadvantage of ths method s that the obtaned estmates are senstve to possble devatons from the assumed model dstrbuton [7]. In practce, the observed dstrbutons match the theoretcal models only approxmately and classcal evaluatons n ths stuaton quckly lose ther optmal features. Ths rases the problem of fndng the estmates, may be not the most optmal, but resstant to such devatons. These estmates are robust estmates. The stablty of statstcal estmates n condtons of contamnated nformaton s relevant enough n the processng of data for managng projects. Whle processng data for the purpose of manageral decson-makng s often requred to establsh lnks between the results of decson-makng and a varety of reasons that nfluence on the results. Ths problem relates to the feld of robust regresson analyss. The dependence between some ndcators,..., n and lnked wth them by another x ndcator n most cases can be expressed n the form of a lnear regresson equaton 4

5 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 x... nn. (3) The estmates of the parameters,..., n n (4) usually are obtaned by method of least squares that conssts n solvng the mnmaton problem N ( x... ) mn n n, (4),..., n.e. n choosng such,..., n that N observed sets ( x,,..., n ) provde the least devaton n terms of (4). Soluton of the problem (4) s equvalent to solvng a set n of lnear equatons N ( x... n ) 0 ( j,..., n ) n j Even Tukey [8] suggested that a possble method of obtanng estmates, that are resstant to gross errors, s to replace the quadratc functons n (4) to another, less senstvty to large fluctuatons x. He suggested to descrbe the presence of gross errors n the observatons by the followng model. Let Py ( ) s the theoretcal dstrbuton of a random varable n (3), but n the sample there are gross errors wth the so called contamnated dstrbuton Hy ( ). Then the resultng dstrbuton has the form P ( y) ( ) Py ( ) Hy ( ) where dstrbuton Py ( ) and contamnatng Hy ( ) are symmetrcal: P( y) P( y), H( y) H( y). In the case when Py ( ) s a functon of the normal dstrbuton, ths model descrbes a stuaton where approxmately ( )N devatons of obey the normal law. The magntude (the ntensty of contamnaton) s consdered to be a known number. For such a case Huber [8] suggested to use developed by hm a common approach for the estmaton of the locaton parameter to obtan sustanable estmates,..., n and nstead of (4) to solve the problem. (5) N F ( x... ) mn n n,..., n (6) wth some properly chosen functon F. Ths problem s reduced to solvng a set of equatons (as a rule, nonlnear already) N f ( x... n ) 0 ( j,..., n ) n j, (7) where f( u) F( u). Let s focus on the methods that use the dea of excluson or modfcaton of certan observatons. In fact, they are the result of the transfer n case of a problem of regresson estmates of truncated mean and Wnsor s mean type. These methods are teratve. At each teraton, excluson or modfcaton of part of the observatons occurs and based on the modfed observatons estmates of the regresson parameters are found usng the least squares method. 5

6 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 Consder the lnear regresson problem (3). Let estmates ˆx for x are found by some method (e.g., least squares). Denote d x xˆ. Put n order devatons d : d d... d N. By analogy wth the estmate of Wnsor s mean, let s construct the Wnsor s regresson lne whch s calculated usng the least squares method on a sample of N ponts from ( x,,..., n ), where x s defned as follows ˆ x x d; d g,,... g; d d, g,..., N g; (8) d Ng, N g,..., N; where g s a number of extreme devatons (largest and smallest) to be modfed by Wnsor. It can be recommended to use ths procedure one of the followng ways. The frst method s a smple teraton method. The number of g ponts modfable n accordance wth (8) remans constant at each teraton. Devatons are calculated usng observatons ( x,,..., n ) at the frst teraton, observatons ( x,,..., n ) at the second, etc. The second method s a method of levels. The number of g ponts (the level of truncaton) ncreases from teraton to teraton, and the procedure of fndng Wnsor s regresson lnes s made each tme wth the ntal data ( x,,..., n ). The thrd method s an teratve method wth ncreasng level. Ths method s a combnaton of the frst two. Devatons are calculated as n the smple teratve method, at frst usng the ntal data ( x,,..., n ), then usng ( x,,..., n ), etc., and the level of truncaton g ncreases from teraton to teraton. 4 Dscusson The suggested model of an effcent nnovaton projects portfolo formaton represents theoretcal and practcal sgnfcance due to the followng reasons. Frst, t clearly dentfes the goal of portfolo management maxmaton of proft of the organaton and t shows the way to acheve t. Second, the authors suggest the ways to acheve ths goal dependng on the qualty of management nformaton. Data analyss when makng management decsons plays a bg role n ensurng ther relablty. In the process of rsk analyss n projects of proper regresson processng of the data s crucal because robust methods gve more relable estmates of regresson parameters. The paper descrbes some heurstc algorthms that are mplemented by the approach of P. Huber n case of symmetrc contamnaton. It seems the actual problem s development of robust estmaton methods of regresson parameters n case of arbtrary contamnaton. The developed methods can be appled not only n the project management problems, but also n the felds such as cluster analyss, regresson models and multvarate analyss, varaton analyss, factor analyss, plannng of experments, smulaton, statstcal estmaton of models parameters, estmaton of systems relablty, general statstcal problems. 6

7 MATEC Web of Conferences 70, 007 (08) SPbWOSCE-07 Currently the robust approach can be mplemented wth the nformaton technology, therefore, t s possble to suggest the followng approaches to ther mplementaton.. Modfcaton of the already developed robust methods for solvng specfc problems and creatng approprate mathematcal software.. Adaptaton of the ready packages of the robust software to the specfc character of the solved problems. 3. Robustfcaton of the avalable mathematcal software n order to create quas-robust procedures. Thus, the applcaton of the suggested approaches to robust data analyss n nnovaton project portfolo management n conjuncton wth the use of nformaton technologes for processng management nformaton wll enhance the relablty of management decsons and can be an effectve tool for project portfolo managers. References. J.R. Turner, R. Müller, Internatonal Journal of Project Management, 7 (003). J.R. Meredth, S.J. Mandel, Project management: a manageral approach (7th ed.) (Hoboken, John Wley & Sons, NJ, 00) 3. K.A. Artto, M. Martnsuo, T. Aalto, Project Portfolo Management: Strategc Management through Projects (Project Management Assocaton Fnland, Helsnk, 00) 4. A. Hyvär, Proceda Socal and Behavoral Scences 9, 9 36 (04) 5. O. Momćlovć, L. Djukc Petromanjanc, S. Doljanca, J. Rajakovć, Annals of the Unversty of Oradea 3, 9 96 (04) 6. H.A. Levne, Project Portfolo Management (Jossey-Bass, Wley Imprnt, USA, 005) 7. B. Malsh, R. Handler. IT portfolo management step-by-step: unlockng the busness value of technology (Hoboken, John Wley & Sons NJ, 005) 8. P. Huber, E. Ronchett, Robust statstcs (J. Wley, New Jersey, 009) 9. C. Agostnell, A. Leung, V.J. Yoha, R.N. amar, TEST 4, (05) A. Ghosh, A. Basu, TEST 5, (06) 0. L. Feng, C. ou,. Wang, L. hu, TEST 4, (05). T. Qngguo, Stat Papers 56, 37 6 (05). S. Hwang, D. Km, M.K. Jeong, B.-J. Yum, Journal of the Operatonal Research Socety 66, (05) 3. J.Á. Víšek, Methodol Comput Appl Probab 7, (05) 4. C. eller, C. Cabral, V. Lachos, TEST 5, (06) 5. B. Ttarenko, Internatonal Journal of Project management 5(), 4 (997) 6. V. Shulenn, Robust methods of mathematcal statstcs (Russa, Tomsk, 06) 7. B. Ttarenko, S. Ttov, R. Ttarenko, Appled Mechancs and Materals , (04) 7

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