METHODOLOGICAL APPROACH TO STRATEGIC PERFORMANCE OPTIMIZATION

Transcription

1 ETHODOOGICA APPOACH TO STATEGIC PEFOANCE OPTIIZATION ao Hell * Stjepan Vidačić ** Željo Gaača *** eceived: Peliminay communication Accepted: UDC This pape pesents a matix appoach to the measuing and optimization of oganizational stategic pefomance. The poposed model is based on the matix pesentation of stategic pefomance, which follows the theoetical notions of the balanced scoecad (BSC) and stategy map methodologies, initially developed by Kaplan and Noton. Development of a quantitative ecod of stategic objectives povides an aena fo the application of linea pogamming (P), which is a mathematical technique fo the optimization of linea objective functions. It is believed that the development and mathematical validation of such an algoithm opens new venues fo futue eseach in the quantitative appoach to stategic management, as well as povides oppotunities fo the development of decisionmaing tools elated to the optimization of stategic pefomance.. INTODUCTION Thee ae two goups of authos who disagee in the intepetation of at least one aspect of the stategy (Weihich & Koontz, 998). One goup of * ao Hell, PhD, Faculty of Economics, Univesity of Split, atice hvatse 3, 2000 Split, Coatia; Phone: ; Fax: ; mao.hell@efst.h ** Stjepan Vidačić, PhD, Faculty of oganization and infomatics, Pavlinsa 2, Vaaždin, Coatia; Phone: ; Fax: ; stjepan.vidacic@foi.h *** Željo Gaača, PhD, Faculty of Economics, Univesity of Split, atice hvatse 3, 2000 Split, Coatia; Phone: ; Fax: ; gaaca@efst.h Fist vesion of this pape is pesented at the 23 d Euopean Confeence on Opeational eseach. Its abstact has been published as: Hell,.; Vidačić, S.; Gaača, Ž. (2009): atix Appoach to Entepise Pefomance Optimization, Boo of abstacts of 23d Euopean Confeence on Opeational eseach, Bonn, July 5 8, p. 36. Authos would lie to expess thei gatitude to the paticipants of the confeence fo useful suggestions. 2

2 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization authos sees the concept of stategy as the endpoints (pupose, mission, goals) and means of achieving them (policies and plans). The othe goup puts moe emphasis on the means of achieving the endpoints than on the endpoints themselves. The impotance of some methods and techniques which ae used in the pocess of stategic planning is explained by Stacey (997), who uses the tem taditional wisdom to imply the whole ange of ecommendations and explanations fo a successful implementation of stategic management suggested by most manages and consultants. Balance on the behaviou pattens is chaacteised by pedictability, egulaity, consistency and hamony. An oganisation in the condition of stable balance follows a pedictable oute which hides no supises (Stacey, 997). In that sense, one of the impotant peequisites fo success is the adaptation of an oganisation to its envionment. Namely, unless an oganisation gains undestanding of its futue envionment, it will not be able to plan its own position. Gaining pope undestanding of the futue state of the envionment enables the foecasting of stategic altenatives, as well as the goals and actions necessay fo thei implementation. Possible altenatives become the stategic options of an oganisation, out of which the stategy is selected by using the citeia of acceptability, feasibility, and adequacy. Stategic management evolved fom stategic planning, wheeas the latte focuses on developing and implementation plans (Beman, 2006). The most elevant facto in the system of values within an oganisation is a clea and concise mission of the oganisation. Such a mission epesents the main oientation of an oganisation. As such, the mission is a means of communication within an oganisation and its envionment. Accoding to the aleady defined mission, it is necessay to define the futue couse of development of the oganisation, i.e. the vision of the oganization. Implementation of the vision is fomalized though development stategies of the oganisation. "Stategy is the detemination of the basic longtem goals and objectives of an entepise, and the adoption of couse of action and the allocation of esouces necessay fo caying out goals" (Chandle; 962). In this pape, the tem stategy will efe to decision-maing on the allocation and use of oveall esouces of the oganisation (Bumec, 997). In this context, the stategic planning epesents the pocess of adjusting the oganisation's esouces with the factos fom the envionment (ibid). Based on 22

3 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization the equied pocess of adjusting the oganisation's esouces with the factos fom the envionment, necessay activities ae defined. Implementation of the stategic plan is based on the accomplishment of the planned activities. Each activity contibutes to the accomplishment of a cetain stategic objective of the oganisation. By caying out the activities, the oganisation should, within a peiod of time in the futue, accomplish the tansfomation fom the cuent pefomance (As is) to the futue pefomance (To be). The stategic plan has to answe on fou questions which can be shown by the fomula (.), which eflects the essence of classical stategic fomulation (Chandle, 962): Stategic plan= f (what, who, how, when) (.) It can be said that a stategic plan is a fomal epesentation of a stategy, which is taditionally defined in tems of futue actions necessay fo accomplishing the stategic goals. Such a plan needs to answe the following fou questions: What has to be achieved? By answeing this question, a seies of necessay activities equied fo attaining the set goal ae descibed. Expediency of each of the activities has to be explained. Who is esponsible? The answe to this question defines the human esouces and thei esponsibilities in conducting the planned activities. How can we achieve it? The existent and new esouces equied fo accomplishing the desied goal. When do we want to achieve it? A boad timetable fo conducting the activities, i.e. the time set fo thei ealisation. It is exactly this action diven fomulation of stategic planning that ceates peequisites fo a continuous contol and management of stategy achievement, which should contibute to the highe quality of the development of oganisation. The dynamic envionment, in which the oganisation opeates, changes duing the planned activities o when they ae postponed. Theefoe, the ability to continuously adjust the stategic plan with new conditions epesents the peequisite fo the successful accomplishment of stategic objectives. Accomplishment of stategic objectives can be measued by an oganization's pefomance. Fo many manages, pefomance is not only about doing the ight thing; it is also about doing the pactical thing (Beman, 2006). Pefomance management povides monitoing of the effects of unexpected changes o unaccomplished stategic goals. 23

4 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization Balanced Scoecad methodology (BSC) is a popula appoach to the balanced view on the oganisation's pefomance. It was oiginally developed by Kaplan and Noton (996) in ode to enable oganisations to define thei development stategies, as well as to obseve the success of the stategies' implementation (ee, 2000). Development of the BSC is based on the empiical expeience of the lage numbe of oganisations in ode to avoid disadvantages of measuing effectiveness only by financial indicatos. The BSC suggests the so-called "balanced scoe system" which obseves the oveall success of the oganisation though fou diffeent pespectives (Niven, 2002): financial, custome, intenal business pocesses and leaning/gowth. Financial success is measued by taditional indicatos, such as: pofit, goss magin, net income, incease of sales and so on. Pefomance achieved in the custome elations pespective is detemined by analysing the actions which ae supposed to be undetaen in ode to eep the cuent and attact the futue customes. Afte analysing the esults of the conducted suveys, custome loyalty and satisfaction ae measued by diffeent indicatos, such as the atio between the lost and attacted customes. Pefomance in the context of intenal business pocesses epesents the effectiveness of the oveall oganisation of activities. It is assessed by tansaction costs, stocouts, custome database availability, labou utilization ates and so on. Objectives which ae supposed to be achieved in this segment of measuing have to be complied with the enhancement of efficiency of the business pocesses within an oganisation. eaning, gowth and development enable the intelligent adjustment of the oganisation to the changing envionment and, in that way, ensue futue success. This pespective is usually measued by the numbe of poduction, technological and business innovations, new poducts and sevices, etc. It is the BSC that helps to detemine the pocedues fo "tuning the vision and stategy into eal steps" (Benoide, 2002). The equiement to tae into consideation the extenal envionment and the futue tends of its development is self-imposing. Howeve, the citics of BSC (Hen, Ooschot, 2002) indicate the lac of oientation towad competition. This means that moe emphasis is placed on measuing the stategic effectiveness than on the impotance of stategic decisions (ee & Andew, 2000). Futhe citicism of BSC efes to the modelling of cause-and-effect elations. Ovesimplification of the one-way causality is indicated as a dawbac (Hen & Ooschot, 2002). In the eal wold, one-way causality is a ae phenomenon. Its simplification is elated to time delays and feedbac effects, which ae not included into the model. Although BSC does distinguish between the cause and consequence 24

5 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization teminologically, it does not fully conside the time distance between the two (ibid). In this pape, a novel appoach is used to enhance the BSC methodology in planning the optimal tagets of pefomance, in ode to maximise the oganizational effectiveness. 2. QUANTITATIVE APPOACH TO STATEGIC PEFOANCE easuing effectiveness means detemining the effects achieved by undetaing the activity which aims at a cetain objective. The measuement system, as a suppot to the stategic decision-maing, is not static. It is necessay to design it accoding to the stategic objectives of the oganisation. That is why, due to the fequency, measuing is done peiodically o continuously. The pupose of this pape is to intoduce a quantitative methodology fo the assessment, evaluation and optimization of an oganization's stategic pefomance, based on the mathematical epesentation of the fou pefomance dimensions, suggested by the BSC model. In addition, the subsequent concept of a stategy map, developed by Kaplan and Noton (996), is used to descibe both the influence of the individual pefomance dimension to the oveall oganizational pefomance, as well as the influence of the intedependencies/inteactions (cause-consequence lins) among the pefomance dimensions themselves to the oveall pefomance. Although the oiginal stategy map model is a vey appopiate way to illustate stategy and the dynamics of its implementation, it is believed that the fomulation and validation of a elevant quantitative model of the stategic pefomance and the pocesses/inteactions, leading to its development, could be an inteesting contibution to the field. Using the matix algeba in the effectiveness calculation enables the simplicity, speed and tanspaency of the pefomance calculation, which could have a useful pactical application in the couse of the stategic management pocess, based on the poposed quantitative model of stategic pefomance. Exactly these featues fom the basis of the success of each stategic management system. Howeve, implementation of the matix algeba equies a high level of fomalisation. In Figue, the pocedue of fomalising the stategic pefomance assessment/intevention system, stating fom the "top 25

6 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization level", i.e. the quantitatively expessed vision in the stictly fomalised ecod of matix and vectos, is gaphically epesented. 2.. Quantitative modelling of stategic pefomance A qualitatively descibed vision (shown by the bubble on the top of the figue) is tansfomed into desciptively and quantitatively detemined set objectives 2 (SO). Fo evey set objective, it is necessay to detemine deived objectives (DO) which will enable its accomplishment. The pocedue of deiving the DO equies foming judgments and stategies. The goup of activities is deived fom the stategy and can be seen as the expansion of a desciptive pat of the DO 3. SO and DO contain desciptive and numeical semantic elements. Figue. Pocedue fo quantitative modelling of stategic pefomance The stuctue of stategy depends on the cause-consequence stuctue of the objectives. Namely, it is logical to expect that thee ae influences among cetain activities in the eal system. It means that undetaing one activity can have an influence on the effect of the othe activity. Since evey activity is 2 Set stategic goals ae deived fom the vision which is why they ae named set stategic goals. 3 This esults fom the fact that evey activity is undetaen with the paticula goal (:). Unlie activities, moe stategies can be accomplished though one activity (m:). 26

7 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization undetaen with a pecisely set objective, it can be concluded that the stuctue of objectives is the same as the stuctue of activities. A chain of inteconnected objectives (inteactions among the individual pefomance dimensions/measues) in the context of this pape is called the causesconsequences chain (CCC). Thus, the next step is taen in ode to establish diect elationships among all stategic objectives. The possibility of pocessing a lage numbe of objectives demands a systematic appoach to detemine elationships among stategic objectives which is achievable by using a table. In ode to achieve tanspaency, the symbols fo objectives ae copied in the title column of the table. Aftewads, following the same ode of the title column, symbols ae copied in the title ow of the same table. Now, the table can be filled. Depending on the existence of a diect elationship among objectives, the elements in the table can be assigned the values of o 0. If thee is a diect influence fom the objective in the ow to the objective in the column, the value is enteed. If not, the value 0 is enteed. Each cell in the table is supposed to be filled in this way. If title ows and columns ae exchanged with the index of the table element, the filled table can be seen as a matix of the objectives influence. This matix is named the matix of objectives' stuctue (OS). In this way, fomal peequisites fo using the matix algeba to measue the oganisation s effectiveness ae met. OS is the matix pesentation of all CCCs between the objectives, i.e. it epesents the stategy in a matix fom. evel of the objective s accomplishment is expessed by its own pefomance. This means that if thee is a cause-consequence lin on the semantical level of analysing the objectives, it is supposed that a lin exists among pefomances as well. The CCCs of pefomances ae detemined accoding to the CCC of objectives. In ode to be able to measue the effectiveness of an oganisation as a whole, it is necessay to tae into consideation all cause-consequence lins which exist among pefomances. The coefficient of the influence a "causal" pefomance has on the "consequence" pefomance has to be taen into consideation as well. The coefficient of influence indicates a ponde by which the value of one pefomance influences the value of the othe. It can gain the value fom the segment [0,]. One can pesume, without educing genealisation, that the values of the coefficient equal 0 fo the pefomance among which, accoding to the CCC, thee is no influence. 27

8 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization Defining the CCC depends on the effects whose accomplishment is measued at the end of the planned stategic peiod. Due to the stategic management, the measued values ae compaed with a taget value geneated by the model of stategic effectiveness. This povides a stuctual explanation of the basic postulates of measuing the effects between objectives. In the next step, the fomal mathematical method, used to calculate the oganizational effectiveness, will be pesented. In the context of measuing effectiveness, the stuctue of pefomance may obseve by the objectives stuctue. The matix of the objectives stuctue is shown by the expession (2.2). Accoding to the pevious pocedue (Figue..), the set objectives l ae detemined and the deived objectives ae deived. SOs and DOs gained though such a pocedue epesent elements of the final set of all stategic objectives of the oganisation, which can be pesented by the following expession (2.) C ~ = {C, C 2,..., C n }, n=+l (2.) In the following step, diect influence among objectives can be pesented in the stict mathematical fom of a squae matix: 28 0 c2 c3 cn = c2 0 c23 c2n OS. (2.2) cn cn2 cn3 0 The ode of the squae matix OS epesents the total numbe of the stategic objectives. Accoding to the pocedue of foming the OS, the elements of the matix OS ae c ij {0,}. Foming the ecod based on the ode of objectives fom the supeio to the subodinate ones is achieved by OS tansfomation to the lowe tiangle matix. In the next pat of this pape, the option of OS tansfomation to the lowe tiangle matix is fomally mathematically pesented. ~ Ove the set of the stategic objectives C = {C, C 2,..., C n }, based on the detemined diect influences shown in the OS, the elation to be subodinate

9 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization (BS) is detemined. Futhemoe, the objectives X, Y, Z C ~ ae andomly chosen fomc ~. Based on the BSC concept, it is to be concluded that, if the element X is a subodinate to the objective Y, Y is then not a subodinate to the element X, i.e. X BS Y Y BS X. (2.3) Theefoe, it can be concluded that the elation BS is asymmetic. Fo the elation BS defined in such a way, it is possible to detemine a popety of tansitiveness, as well, i.e. Z BS X and X BS Y Z BS Y. (2.4) The asymmetic (2.3) and tansitive (2.4) elation is called the patial ode elation. Theefoe, the defined elation BS is the patial ode elation. Anothe impotant type of elation in the set C ~ is a elation of the total ode. The total ode elation "<" is the patial ode elation in which evey two elements X and Y ae compaable, i.e. X<Y o Y<X (2.5) An impotant mathematical theoem says that evey patial ode elation can be expanded to the total ode elation. Theefoe, the elation BS can be expanded to the total ode elation "<". Without educing the genealisation, it can be assumed that C < C 2 <...< C n. (2.6) In ode to pove that in this ode of objectives C i, the matix OS is a lowe tiangula matix, the opposite is assumed, i.e. it is assumed that c ij >0, fo some j>i. This would esult in the fact that the pat C i is subodinate to the pat C j, that is: C i BS C j, but then C i < C j as well which contadicts C j < C i (as a esult fom (2.6). This poves the possibility of OS tansfomation to the lowe tiangle matix. By tansfoming it to the lowe tiangle matix, tanspaency of diect objectives has been achieved. In this way, the expession (2.2) is fomulated. It efines the net stuctue of influences among the objectives. By analysing the columns in the matix OS, it is quite easy to identify diect elations between 29

10 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization supeio objectives pesented in the column and its subodinate objective pesented in the ow. The value of the element, which is located on the intesection of the obseved ow and column, identifies the (non)existence of diect influence between objectives which ae pesented in the ow and the column. The objective of each CCC, which is at the beginning, is not influenced by the accomplishment of any othe objective. That is why the elements of the column of the initial objectives equal null. Consequently, the elements of the ow of the last objective in each CCC equal null because they cannot influence any othe objective. In this way, by analysing the OS, it is easy to detemine which of the objectives positioned lowe can cause the consequent change of the accomplishment level of thei supeio objectives and which would those supeio objectives be. If the initial and taget objectives of all CCC ae left out fom the OS, the submatix is gained, which is, by undegoing the same pocedue, given the initial and taget objectives of the shotened CCC. The detemined objectives belong to the fist lowe i.e. highe level of the CCC stuctue. 2.. Pefomance measues stuctue matix As it has aleady been said, the level of the accomplishment of an objective is measued by oganizational pefomance. Thus, each aspect of oganizational pefomance needs to be adequately measued. All measues ae included in the stategic map of pefomance measues, which follows the stuctue and logic of the initial stategic map, poposed by Kaplan and Noton (996). The stategic map of measues is the stuctual equivalent to the stategic map of objectives. Accoding to the BSC, the logical basis fo its constuction is dawn fom the hypothesis that the level of accomplishment of each objective is measued duing a paticula peiod of time and that the measued values ae compaed, in ode to detemine whethe the activities that have been caied out have made the expected effect. While defining objectives and thei measues and while detemining AS IS" and "TO BE" values, the ange of the change of a measue is set. The defined ange of the measue enables the calculation of the elative change of the measue. The elative change of the measue of the objective C j duing the obseved peiod of the stategic cycles is calculated accoding to the expession (2.7): mc j () t mc j ( 0) mc j = ; j=,...,n; t [0,T], (2.7) mc T mc 0 j ( ) ( ) j 30

11 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization whee: n numbe of the objectives, m C j elative measue of the objective C j, mc j (0) initial value of the measue of the objective C j, mc j (t) cuent value of the measue of the objective C j at the end of the obseved peiod, mc j (T) expected value of the measue of the objective C j at the end of the stategic cycles with the time T. The elative change calculated in this way can occu in the segment [0,]. Since evey activity is caied out with a cetain objective, measues ae deived fom the objectives and activities equied fo thei implementation. Accomplishment of a paticula objective is measued by measue. Accoding to the impotance of the measue, its measue unit has been defined. Some measues can be quantified without dimension as, fo instance, the popotion of two values of the same ind. This enables the quantification of the initial, cuent and expected level of the accomplishment of a cetain objective. By detemining the initial and expected level of the accomplishment of a paticula objective, the ange of values, which a measue can have, is defined. In ode to avoid the poblem of diffeent measue units (fo diffeent objectives), while calculating the efficiency of the oganisation, the elative values ae used. Based on these elative values, the absolute values ae calculated in accodance with the expession (2.7). In ode to calculate the effect of the accomplishment of cetain objectives on the accomplishment of othe objectives, the coefficients of influence have been deived. The coefficients of influence indicate the weight with which the value of one measue influences the value of the othe. The value of change of a measue of a consequent objective equals the sum of the poduct of change of a measue of causal objectives and thei coefficients of influence. The initial coefficients of influence can be deived fom the OS so that the OS is the nom accoding to the columns based on the expession (2.8). 3

12 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization c n ij za c 0 n ij i= = cij ij (2.8). i= n 0 za cij = 0 i= The matix gained by the nom of columns of calculated objectives fom the OS is called the matix of measues stuctue (S) and it is shown in the expession (2.9): n = n S, (2.9) n n2 n3 0 whee the elements ij ae calculated based on the expession (2.8). The elements of the S indicate the weight with which the value of a measue in a ow influences the value of a measue in the column. Hence, the ode of measues in the OS is the same as the ode of thei objectives in the OS. The sum of elements in columns which indicates influences on the calculated measues equals one Calculation of total level of accomplishment of objectives et (m C,,m C n ) indicate the ode of values of elative change of n (all) measues at the end of the obseved peiod. The ode of this ecod is defined by the ode of measues in the S. It is possible to define the vecto of the total level of accomplishment of objectives of the obseved peiod which is shown in the expession (2.0) [ mc mcn = ] (2.0) The change of values of measues of the objectives positioned lowe in the CCC esults in the change of values of measues of all thei subodinate objectives. It means that the influence is achieved indiectly, as well. Calculation is equied in ode to detemine the vecto components, i.e. the values of total elative changes of measues. 32

13 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization Calculation of total values of measues can be divided into m steps, whee m stands fo the numbe of the longest CCC. Patial values of evey step i ae the consequence of diect influences. In ode to deal with the lac of diect influence between two objectives in the S, values of the coefficient of influence equal null. In accodance with the BSC concept, values of measues at the beginning of the CCC ae not calculated. They ae taen fom the system and enteed into the model. That is why they ae called egisteed measues. Vecto 0 indicates the vecto of diagnosed values of measues without calculation. Values of the calculated measues in vecto 0 equal null. It is possible to calculate the patial values of measues i+ as a sum of the poduct of accomplished patial values of causal measues (component of vecto i ) and thei coefficients of influences (elements S), i.e. fo all objectives, by using the matix calculation (2.): i S = i+, (2.) i.e. i i [ ] n i i m C m C = [ m C m C n 0 n n ]. (2.2) n n2 n3 0 The total value of the accomplishment of objectives, expessed by the vecto, equals the sum of patial values of measues i, of all steps i.e. fo an indefinite numbe of objectives: = m +. (2.3) If (2.) is included in (2.3), the expession (2.4) is fomulated as follows: = S S m +. (2.4) The elements of i-th powe of the S indicate the intensity of the i-th indiect influence by which the values of the egisteed measues influence the values of the calculated measues. By multiplying 0 with the i-th powe of the S, one gets the values of measues as a consequence of the i indiect 33

14 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization influence. It is possible to calculate the total elative change of measues based on 0 and detemined diect influences, instead of calculating the sum of patial values of measues. Extacting of the vecto 0 in the expession (2.4), the expession (2.5) is fomulated as follows: 34 = 0 (I+ S + + S m + ). (2.5) Accoding to the sum of the infinite ode 4 : = 0 (I S) -. (2.6) The expession which is multiplied by the vecto 0 in the fomula (2.6): SI=(I S) -, (2.7) is called the matix of the sum of influence (SI) and is used fo calculating vectos of the total level of accomplishment of objectives based on the accomplished values of egisteed measues in accodance with the expession (2.8): = 0 SI. (2.8) This defines the pocedue of calculating the level of accomplishment of objectives though which the effectiveness of an oganisation is obseved. 3. OPTIIZATION OF AN OGANISATION S EFFECTIVENESS BY USING INEA POGAING The classical BSC concept, in the phase of planning the effects, includes the implementation of detemined activities. Howeve, in the eal system, 2 3 m I + S + S + S + + S + conveges and has the sum ( ), if all n 2 ode conveges I S ij, whee ij indicates the element in i ow and = j column of the matix S = S S S ( times). As aleady indicated, the elements of m powe of the matix S indicate the intensity of the m indiect influence with which the values of egistated measues have an influence on the values of the calculated measues. Hence, each of the n 2 elements of the matix aims at null if m, i.e. matix S m conveges towads null matix. 4

15 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization implementing the activities can depend on vaious limitations. That is why it is necessay to adjust an expected level of accomplishment of objectives to the potential limitations. The concept of the stategic management shown in the pape emphasised two types of limitations. 3.. imitations due to available esouces The classical type of limitation to accomplish the expected level of accomplishment of objectives is the availability of esouces fo implementing activities by which these objectives can be achieved. That is why it is necessay to establish equied stategic esouces fo its implementation. One type of esouce can be used in moe than one activity. In ode to include all necessay esouces, thei illustations have been fomalised by using the matix of esouces. The natue of each activity indicates the equied esouces fo its implementation. By detemining the accompanied DOs, the measues and the ange of changes have been clealy defined, which should be accomplished by the implementation of the planned activities. This means that all necessay esouces can be geneated fom the activities and DOs. The index of elements in the matix of esouces is defined by the ow DO fom the OS and by the column of the equied esouces. Thei values indicate the equied allocation of esouces fo the 00% level of accomplishment of DOs, which equie the implementation of the obseved activity. Afte all the equied esouces fo implementation of the obseved activity have been detemined, the next activity is consideed i.e. the new line in the matix of activities and DOs. -th DO is detemined and the activities fo thei accomplishment as well as l-th SO. Futhemoe, is the vecto of the total level of accomplishment of objectives and it is defined by the expession (2.8). is the symbol fo the matix of esouces type n. The elements of the fist lines define the equied quantity of the j esouces, j=,...,, in the i activity, i=,...,. epesent the equied esouces fo the accomplishment of SOs. Since SOs ae achieved only by accomplishing DOs, the elements of the last l ow of its matix equals null. The last line fom the matix of esouces which indicates the available quantity of esouces is epesented by the vecto. It is then possible to define the limitation caused by available esouces by the matix inequality, (3.) 35

16 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization 36 ] i.e.. (3.2) [ ] [ n C m C m Afte multiplying the matices, a system of inequations is gained, defined by the expession (3.3) C m C m C m C m C m C m (3.3) Each inequation in expession (3.3) indicates limitation caused by the availability of a paticula esouce. This defines and mathematically fomalises the set of limitations ove the total level of accomplishment of DO, based on the availability of esouces. 3.. imitations caused by stuctue of measues The next type of limitation is caused by the stategy stuctue. It is a consequence of influences that occu between values of measues. The level of accomplishment of the objectives positioned lowe is a peequisite fo the accomplishment of the effect of activities, which ae caied out as a pupose of thei supeio objectives. Coefficients of the influence of measues have been deived and defined by the expessions (2.8) and (2.9). The vecto of the total level of accomplishment of n objectives is defined by the expession (2.8). et the n be the ode of the S, in which thee ae i columns whose values equal null.this means that thee is n i of calculated measues. This

17 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization esults in the existence of n i limitations, which can be defined by the system of inequations (3.4): mc + 2 m C m C m C i i2 m C m C n i n i n i n n2 n2 m C n m C m C n n 0 0. (3.4) 0 The system of inequations (3.4) includes n i inequations, with each of them indicating one limitation to the calculated measue. The numbe of unnowns equals the total numbe of measues n. Coefficients ij fo i j have been taen fom the OS. The calculation pefomed by using the elative measues in the given concept imposes both a peequisite of inequality and maximum value of a measue fo all stategic objectives, i.e. 0 m C i, i=,...,n. (3.5) In this way, all the limitations have been included into the pocedue fo detemining the optimal stategy Optimisation of the total level of accomplishment of objectives The basic featue of the appoach to development of the pesented model is that an oganisation should be obseved as a holistic system. It means that the accomplishment of stategic objectives should not be obseved patially, but in the context of accomplishment of set stategic objectives. Such an appoach indicates that the maximum accomplishment of all DOs is not always optimal. Detemining the optimal level of accomplishment of stategic objectives epesents a poblem which can be solved by using linea pogamming. The poblem of linea pogamming can geneally be the poblem of the maximum o the poblem of the minimum. The natue of the analysed poblem belongs to the poblem of the maximum of the linea pogamming. Namely, taing into consideation limitations caused by available esouces and detemined stuctue of objectives, it is necessay to find the optimal level of accomplishment of deived stategic objectives, in ode to maximise the level of accomplishment of set stategic objectives. 37

18 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization l-th SO is detemined. A function which equies a set maximum i.e. the function of an objective is defined by the expession (3.6) l ax m SSG j. (3.6) l j = In this way, the following elements have been detemined: functions of an objective, defined by the expession (3.6), limitations caused by availability of esouces, defined by the expession (3.3), limitations caused by the stuctue of objectives, defined by the expession (3.4), peequisite of non-negativity and maximum value of measues, defined by the expession (3.5), The obseved poblem includes all equied elements fo implementation of the linea pogamming in ode to define the optimal stategy. The obtained esult indicates the equied levels of accomplishment of all DOs, which then imply the maximum level of accomplishment of SOs. By multiplying the optimised values of measues with, it is possible to calculate the total esouces used, accoding to the paticula activity. It is necessay to emphasise that the concept stats fom the hypothesised influences among the objectives. Based on the measuements pefomed, a diffeent elation among objectives can occu. It can also change the stuctue of stategy and, at the same time, the limitations caused by it. In this case, it is necessay to e-examine the limitations and epeat the pocedue of optimisation Assessment of satisfaction with the level of accomplishment of objectives While defining the stategic objectives, the management detemines the initial AS IS level and pedicts the expected values of the futue TO BE level of accomplishment of objectives. Implementation of matix algeba in the calculation oganisational effectiveness implies using the elative values of measues. Changing the elative values of measues into the absolute ones and vice vesa is made simply by using the fomula (2.7). In this way, it is possible to expess elative values though absolute values which, besides its value, 38

19 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization include the measue units as well. Futhe analysis of the esults, due to the consistent illustation, is based on the elative values of measues. As it has aleady been said that the elative values of measues need to belong to the segment [0,]. If a measue has values which do not belong to this segment, it is necessay to analyse what is the cause of such an event. Satisfaction with the level of accomplishment of objectives is estimated based on the achieved values of measues. Accodingly, management maes decisions elated to futue activities. While using this model fo conducting the activities of stategic management, the achieved values of egisteed measues ae being defined. They ae being defined duing the stategic cycles. Values of calculated measues ae calculated based on the peviously descibed matix model. Assessment of satisfaction with the level of accomplishment of objectives can be simply measued: by using the concepts of unsatisfactoy pefomance (ed), satisfactoy pefomance (yellow) and planned (expected) pefomance (geen). In ode to be able to classify the value of a measue in one of the above mentioned aeas, it is necessay to detemine fou limit values. Hence, limit values ae the values within which achieved and calculated values of measues ae expected to occu. elative values of all measues, at the beginning of the stategic cycles, equal null. This means that the elative value of a measue, which equals null, indicates that change has not been achieved. Theefoe, a lowe limit (D) of unsatisfactoy pefomance fo each measue, expessed though elative value, equals null. elative value of the measue that equals indicates that change has been fully achieved. Theefoe, the uppe limit (G) is the best expected value of a measue and fo each measue, expessed though the elative value, it amounts. The peviously descibed pocedue of the optimisation of expected values of measues is adapted to limitations fom the eal system. Hence, it is logical that the lowe limit of expected satisfaction is influenced by eal possibilities of the accomplishment of objectives. This would mean that each level of the accomplishment of objectives that exceeds eal possibilities epesents an expected condition. Accoding to the classical BSC concept, the limit between the unsatisfactoy and satisfactoy pefomance is intuitively detemined by management, while efeing to the pedicted satisfaction of the owne. In this 39

20 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization pape, it has been suggested that the lowe limit of the satisfactoy pefomance (d) fo all stategic objectives is calculated based on the defined stategy stuctue and expected satisfaction of the owne with the set stategic objectives. The uppe limit of the satisfactoy pefomance (g) is defined by values of measues gained by optimisation. This impoves the pocedue of defining the lowe and uppe limit of the medium success of the BSC concept. The gaphic illustation of measued and calculated values of measues (the so-called BSC taffic light) is pesented by Figue 2. The eason fo deviation of the achieved fom the planned level of accomplishment of objectives can be caused by the fact that planned activities have not been pefomed, o that a wong pediction of cause-consequence elations among objectives was made. In ode to pove that the model is eliable, it is necessay to calculate all values of measues and compae them to the values calculated by using the model. If it is eliable, the calculated values should equal the calculated values in the eal system. Figue 2. Gaphic illustation of the level of accomplishment of objectives Uppe and lowe limits ae equal fo all measues G= and D=0. The middle uppe limit (g) is a esult of optimisation and can be diffeent fo each measue g i =x i. The lowe middle limit (d) is defined by the satisfactoy pecentage of the optimal level of accomplishment of SO d i = y i. Values calculated (light blue) and measued (da blue) measues of an objective C i ae shown in the columns. In case the statistically significant deviation of achieved and measued values of measues occus, then the accomplishment of detemined activities should be fistly defined. If the planned activities have been caied out, the eliability of the model is poved. The eliability of the model is poved by the 40

21 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization fact that the cause-consequence elations among objectives ae pedicted by using the model. If the model is eliable, then the measues of lowe positioned objectives in the CCC will esult in the expected change of measues of thei supeio objectives in the CCC. If consequence measues do not achieve the expected values accoding to influences of values of lowe positioned measues and the model opeates in accodance with the expected tends, it can then be concluded that the model is eliable. In this case, it is necessay to e-examine the set elations among objectives. 4. CONCUSION The pape poposes the application of a mathematical model, based on the matix calculation, which uses the aleady "classical" appoaches to stategic pefomance - the BSC and stategy maps, developed by Kaplan and Noton. It is hoped that the poposed model will facilitate optimisation of oganizational stategic pefomance, which could be of special inteest in the development of elevant softwae pacages and othe foms of manageial decision-maing suppot. The oiginal algoithm shown in the pape and based on the matix calculation by using the IT, enhances the solving of the economic poblem of optimisation of the entepise effectiveness due to the maximisation of accomplishment of the set stategic objectives, which is deived fom the quantitatively fomulated vision of an oganization. EFEENCES. Amans H.; van Ooschot, K. (2002): Developing a Balanced Scoecad with System Dynamics; (etieved on 9. June 2009) 2. Benoide, E. (2002): Factos in SWOT Analysis Applied to ico, Small to edium and age Softwae Entepises: An Austian Study, Euopean anagement Jounal, Vol. 20, No. 5, pp Beman, E.. (2006): Pefomance And Poductivity In Public And Nonpofit Oganizations,. E. Shape, England 4. Bumec, J. (998): Stategic Planning of IS, Jounal of Infomation and Oganisational Science, Vol. 23, No. 2, pp Bumec, J.; Vče, N. (2002): Stategic Planning of Infomation Systems (SPIS) - A Suvey of ethodology, Jounal of Computing and Infomation Technology, Vol. 0, No. 3, Septembe, pp Chandle, A. D. (962): Stategy and Stuctue, IT Pess, Boston 7. Kaplan,. S.; Noton, D. P. (996): The Balanced Scoecad: Tanslating Stategy into Action, Havad Business School Pess, Boston 4

22 . Hell, S. Vidačić, Ž. Gaača: Appoach to stategic pefomance optimization 8. ee, S. F.; Andew S. O. K. (2000): Building Balanced Scoecad with SWOT Analysis and implementing "Sun Tzu's At of Business anagement Stategies" on QFD ethodology, anageial Auditing Jounal, Vol. 5, No. /2, pp Niven P..(2002): Balanced Scoecad Step by Step, Wiley, New Yo 0. Stacey, D.. (997): Stateši menadžment i oganizacijsa dinamia, ATE, Zageb. Weihich, H.; Koontz, H. (998): enadžment, ATE, Zageb PISTUP OPTIIZACIJI STATEŠKIH PEFOANSI Sažeta U ovom se adu pezentia matični pistup mjeenju i optimizaciji stateših pefomansi oganizacije. Pedloženi se model temelji na matičnom pedstavljanju stateših pefomansi, oje slijedi teoetse oncepte Kaplanovih i Notonovih modela balanced scoecad (BSC) i stateših mapa. azvoj vantitativnog pedstavljanja stateših ciljeva otvaa posto za pimjenu lineanog pogamianja (P) matematiče tehnie za optimizaciju lineanih funcija cilja. Vjeuje se da bi azvoj i matematiča validacija ovavog algoitma mogla otvoiti novo podučje za vantitativna istaživanja u statešom menadžmentu, ao i za azvoj alata za potpou odlučivanju u podučju optimizacije stateših pefomansi. 42