Developing an Integer Chebyshev Goal Programming Model for Budget Allocation Problem A Case Study

Transcription

1 Applied mathematic in Engineering, Management and Technology 2 (6) 2014: Developing an Integer Chebyhev Goal Programming Model for Budget Allocation Problem A Cae Study Mohammad Ali Shafia 1, Saeed Khodamoradi 2, Molem Haghi 3, Hoein Sabzian 4* 1 Department of Indutrial Engineering, Iran Univerity of Science and Technology, Tehran, Iran 2 Department of Humanitie, Shahed Univerity, Tehran, Iran 3 M.A of Public Adminitration, Shahed Univerity, Tehran, Iran 4 PhD Student of Technology Management, Iran Univerity of Science and Technology, Tehran, Iran *abzeyan@yahoo.com Abtract Multi-obective nature of ocio-economic ytem ha made budget planner faced with ome budget allocation challenge among which the unbalanced allocation of budget among organization' multiple goal i believed to be the mot important one. To urmount thi challenge, budget planner need to be informed of powerful budget allocation method. To do o, different budget allocation method have been developed among which the goal programming (GP) model eem to be widely applied. But, GP model in turn have different performance in term of balanced allocation of budget among goal. The prime purpoe of thi tudy i to ue a type of GP model which ha a far better performance in term of balanced allocation. Thi paper i organized into even ection. Section I deal with the introduction. The problem i introduced in thi part. Section II deal with reviewing ome tudie that have been conducted on univerity budget planning o far. In thi ection, related literature i omewhat reviewed. Section III i about reearch methodology. In thi ection, problem of interet i defined in detail and widely ued GP model are explained which Integer Chebyhev Goal Programming (ICGP) i finally elected a the model of reearch. Furthermore, all problem parameter are elucidated in thi ection. Section IV focue on normalization computation technique. In thi ection, normalization technique are explained and Euclidean normalization i elected for computing normalization contant. Section V i about goal' preferential weight computation. In thi ection, Analytic Hierarchy Proce (AHP) a a multi criteria deciion making aid i explained and ued for computing preferential weight. Section VI i about model implementation and olution analyi. In thi ection, the model i applied in a non-public higher education intitution to olve the budget allocation problem and the comparion of the model olution with the current ituation while applying the model, indicate that the quantity of reource and product available at thi intitution i uboptimal. Section VII a the final one end with concluion. In thi ection, model' advantage along with ome uggetion are propoed. The manager of the tudied intitution can ue the olution of thi model a effective guideline becaue intitution' inflow and outflow a ytem' ource and output have been properly covered according to a manufacturing ytem approach. Keyword: Budget Allocation, Imbalanced Allocation of Budget, Non-public Higher Education Intitution, Goal Programming Model, Integer Chebyhev Goal Programming Model. 1. Introduction Since the mid-1960, many tudie have been conducted on reource allocation in univerity management. In recent year, due to the budget limitation univerity management of higher education intitution ha been faced with the difficult ituation in reource allocation. In many organization, epecially univeritie, the conflict between goal i one of their obviou feature. The reource allocation proce between conflicting obective and program i difficult. A a reult, deigning and application of deciion upport tool ha become one of the mot popular interet of academic planner and trategit (Entezari, 2010). Now, the privatization ha been extended to higher education intitution and being agile and adapting quickly to environmental change and requirement i one of the characteritic of an effective univerity. Change in population' age pyramid, deviation in the target population' tate of univeritie, the development of educational technologie, limited financial reource, and targeted reearch in the country, all caue a compulive change in academic management approache. Academic activitie portfolio i compoed of three general reearch, ervice and education pattern. Obviouly, rational and ynergitic relationhip are eential in election the combination of thee activitie in the long-term proect. Therefore, thi approach will be extended the hortterm planning proce and even budgeting. The univeritie are expected that beide traditional way of offering 544

2 Applied mathematic in Engineering, Management and Technology 2014 ervice, they increae financial reource through a variety of income-generating activitie including increaed tuition, increaed tudent' regitration, providing conulting ervice to government and indutry, launching hort-term coure to meet the need of the private ector and o on. Certainly, electing an appropriate volume of each activity i of pecial importance. Given the above, thi fact i raied that conidering the annual reearch and educational obective and program of univeritie and budget contraint, how can a mathematical model be devied for budget allocation to thoe activitie in order to help manager in optimal reource allocation? Anwering thi quetion lead to deign a mathematical model, which with repect to manufacturing ytem approach in the planning hould eentially cover the conflicting goal. In continuation and in ection II, we will dicu cientific literature review and reearch background. 2. Literature review Several method have been propoed in the literature for budget allocation of higher education intitution which in a macro egmentation they can be divided into two categorie, ingle-period and multi-period. To do thi, variou model are ued including linear programming (LP) model, goal-programming (GP) model and imulation-baed model. GP model can be generally claified into two categorie; the firt i baed on the ditance metric including lexicographic, weighted, and chebyhev model. Depending on the nature of tudied variable and goal, the econd category include integer, fuzzy, fractional and binary model. One of the firt tudie which ha been performed on the application of mathematical programming in the budget allocation of higher education intitution can be referred to Hopkin' tudie (1971). For long-term reource planning and budget allocation in the univerity, he deigned a cot imulation model in which budget wa conidered a an output rather than input. Reource allocation through thi model wa aociated with maor hortcoming uch a diregarding the dynamic within the ytem and the lack of careful attention to the multiple and conflicting goal of the college (Hopkin, 1971). Uing a urvey, White (1987) that carried out through 146 article, howed that the exiting mathematical model could be ued in the management of higher education intitution (White, 1987). In a tudy, Caballero et al (2001) treed the need for the ue of quantitative model in olving the problem of univerity' reource allocation. In 2006, they conducted a tudy about reource allocation model in which they deigned an interactive goal-programming model that manager were able to overcome the many challenge of reource allocation through thi model. One prominent feature of thi model i that it allow manager to intelligently deal with the unpredictable and uncertain phenomena of external environment (Caballero et al, 2006). Bau and Pal (2006) alo ued goal programming for budget allocation in the univerity. Their model would properly allocate the budget to achieve the target level of educational, non-educational and reearch member. Furthermore, Ogunlade (2008) deigned a multi-period goal programming model for budget allocation of univerity. Unlike many planning model that are et for one year, thi model wa deigned for a five-year period (Ogunlade, 2008). In their tudie, Nopiah et al (2007) could deign a comprehenive goal programming model for univerity. The extenion of their model allow planner to cover different part of the educational ytem and properly track and monitor the flow of reource allocation (Nopiah, 2007). In a multiyear tudy, which Pal and Sen (2008) conducted on the univerity reource allocation ytem they could provide an efficient goal programming model for proper allocation. The reource trade-off in the educational ytem ha been properly conidered in thi model. In hi reearch, one (2011) alo preented a new model for the enitivity analyi of goal programming model for reource allocation. Safari et al (2012) developed an Integer Lexicographic Goal Program. Thi model poeed 36 deciion variable, 49 goal, 7 ytematic contraint and 53 technical coefficient. After it had been olved, the goal were achieved with a total deviation (I, e. Obective Function Value) equal to unit (Safari et al, 2012). Regarding univerity' department, it hould be noted that a the body i compoed of the link of all bone and biological - neural organ, the tructure of an organization like a body alo relate all unit of the organization. Accordingly, tudying and identifying organizational tructure i a bai for undertanding the relationhip between thee unit and the manner of ditributing reource (both phyical and non-phyical reource) within them. Since the budget i a part of the material reource and i ditributed within the organizational tructure, proper budget allocation i required to correctly identify the organizational tructure. Undertanding of 545

3 Applied mathematic in Engineering, Management and Technology 2014 organizational tructure and the manner of relationhip with it contituent unit give manager an in-depth look and enable them to develop mechanim (model or pattern) for proper budget allocation affair. 3. Reearch Method 3.1.Problem Definition Each higher education intitution include three main operating unit the education and reearch unit are more prominent. Other organizational unit and department are reponible for upporting the activitie of thee two main diviion. _ Educational dutie of higher education intitution may be performed in everal college. Every college contain everal department. Every department run one or more dicipline at the undergraduate, mater, and doctoral level. _ Educational, ervice and reearch obective are achieved through faculty member. Regarding rank and type, faculty member include aitant profeor, aociate profeor, and profeor and with repect to the wage, they are claified into viiting profeor and recruited profeor. _ Reearch function are achieved under the uperviion of reearch deputy of higher education intitution in the form of publihing book and periodical, article, conference, reearch proect (inide and outide of the univerity), patent and o on. _ In recruiting and employing taff (faculty member and other employee), higher education intitution alway oberve a reaonable ratio (faculty member to other taff). Thi ratio i different for adminitrative and technical taff. The number of technical and adminitrative taff hould not be lower than a certain limit. _ The number of allocable computer per year follow an upper limit and the number of computer i not the ame for each educational level. Thee value alo apply to book and library reource. _ The hour allocated to every faculty member for teaching, ervice delivery and reearch (uperviory and adminitrative) dutie obey certain limit. _ In the etablihment and operation of potgraduate coure, the higher education intitution mut alway take into account a certain proportion compared to the number of bachelor' dicipline. The number of exiting undergraduate hould not exceed a certain limit.. _ The ratio of article, patent, and potgraduate tudent to each reearch item follow a pecific quantity. _ The number of publihed book and article compared to the member of faculty member follow a pecific ratio. _ The obective of higher education intitution are well defined in the number of cientific publication, patent, participation in univerity external proect, mall, medium, and large-cale tudie, and annual conference. _ The number of macro or large tudie to total reearche hould not be le than a certain quantity. _ The number of copie of publihable book and ournal would be a certain number. _ In addition, the ratio of aitant profeor, aociate profeor, and profeor to the total member hould be regarded in recruiting and employing faculty member. _ The minimum income earned from higher education intitution' teaching, ervice delivering and reearch activitie hould be oberved. _ Budget Allocated for the cot of higher education intitution uch a alary, purchaing book, computer, and laboratory equipment etc.i defined a a ytem contraint. A indicated in the above decription, etting goal and achieving them are required in the problem pace. Typically, organizational performance indicator can be ued a a criterion for target etting. By reviewing ome of available ource about educational and reearch indicator, the mot common and uitable criteria were elected to define reource allocation goal of higher education intitution. Thee ource include New York Univerity' report of budget allocation proce (NU Publication, 1998), Eatern Wahington Univerity' trategic budget allocation model (EW Publication, 2003), Maryland Univerity' report on budget allocation proce (MU publication, 2005) and Diminnie and Kwak' tudy (Kwak & Diminnie,. 1987). However, applying practice and cae tudie were alo effective to complete the work.analytic Hierarchy Proce (AHP) i alo ued to compute the relative importance of goal. 4.Mathematical Model Formulation 546

4 Applied mathematic in Engineering, Management and Technology 2014 Multi-obective nature of ocio-economic ytem ha made budget planner faced with ome budget allocation challenge among which the unbalanced allocation of budget among organization' multiple goal i believed to be the mot important one. To urmount thi challenge, budget planner need to be informed of powerful budget allocation method. To do o, different Budget allocation method have been developed among which the goal programming (GP) method eem to be widely applied. But, GP Method in turn have different performance in term of balanced allocation of budget among goal.gp model can generally be defined in term of underlying ditance metric and mathematical nature of the deciion variable and/or goal ued in the program. Lexicographic, Weighted, and Chebyhev model are three maor model which are defined in term of underlying ditance metric while fuzzy, integer, binary, and fractional goal programming model are defined in term of mathematical nature of the goal and/or deciion variable (one and Tamiz, 2010). A one and Tamiz ay (2010), a common feature in all of the olution found by both the weighted and lexicographic variant can be found. That i, they are all to be found at extreme point (interection of goal, contraint, and/or axe). Thi lead to a certain imbalance, with ome goal doing very well but other goal being a long way from being achieved. Thi i due to the underlying Manhattan metric that ha a ruthle optimization property. If a balance between the obective i the dominant need, then the Chebyhev goal programming (CGP) hould be applied. Thi variant of Goal Programming wa firt introduced by Flavell. It i known a Chebyhev goal programming, becaue it ue the underlying Chebyhev (L ) mean of meauring ditance. That i, the maximal deviation from any goal, a oppoed to the um of all deviation, i minimized. For thi reaon CGP i ometime termed Minmax goal programming (one and Tamiz, 2010) With regard to the problem of unbalanced allocation of budget among organization' multiple goal, the underlying philoophy, when uing the L ditance metric, i that of balance. That i, the deciion maker i trying to achieve a good balance between the achievement of the et of goal a oppoed to the lexicographic approach which deliberately prioritize ome goal over other or the weighted approach which chooe the et of deciion variable value which together make the achievement function lowet, ometime at the expene of a very poor value in one or two of the goal. CGP i alo the only maor variant that can find optimal olution for linear model that are not located at extreme point in deciion pace (one and Tamiz, 2010). Although goal programming clae are fundamentally different, it i poible to formulate a goal programing that ha a model from each cla. Depending on the tructure of problem, each of thee model may be ued. In term of ditance metric and problem of imbalanced allocation, Chebyhev Model i elected and ince variable of problem under tudy are Integer, an Integer Chebyhev Goal Programming (ICGP) ha been formed in thi paper. Algebraic tructure of Chebyhev Model i repreented in Figure 1. Fig. 1. Algebraic Structure of CGP (one & Tamiz, 2010) Where i the maximal deviation from amongt the et of goal x x i the vector of deciion variable, x... 1 x n f q n q p q x ( ) i the achieved value of qth goal i the negative deviational variable of qth goal i the poitive deviational variable of qth goal x f ( ) n p b q 1,... Q q q q q u n x v p q 1,... Q k q q q q k q q n, p 0 q 1,... Q q F q Min a 547

5 b q uq v q k q F i the apiration level of qth goal Applied mathematic in Engineering, Management and Technology 2014 Preferential weight aociated with the penalization of Preferential weight aociated with the penalization of i normalization contant i the feaible et nq pq 5.Model Parameter The deciion variable of the propoed model include: The quantity of -th ource ued in the higher education intitution 0 The quantity of -th product in higher education intitution p 0 The propoed mathematical model i preented in Table 1. Table 1: Propoed Mathematical Model Obective Function Formulation Min (W1/C1)*PD1<= ; (W2/C2)*ND2<= ; (W3/C3)*PD3<= ; (W4/C4)*ND4<= ; (W5/C5)*ND5<= ; (W6/C6)*ND6<= ; (W7/C7)*ND7<= ; (W8/C8)*ND8<= ;(W9/C9)*ND9<= ;(W10/C10)*ND10<= ; (W11/C11)*ND11<= ; (W12/C12)* ND12<= ; (W13/C13)*ND13<= ; (W14/C14)*PD14 <= ; (W15/C15)*ND15<= ; (W16/C16)*ND16<= ; (W17/C17)*ND17<= ; (W18/C18)*PD18<= ; (W19/C19)*PD19<= ; (W20/C20)*PD20<= ; ( W21/C21)*ND21<= ; (W22/C22)*PD22<= ; (W23/C23)*ND23 <= ; (W24/C24*ND24<= ; (W25/C25)*ND25<= ; (W26/C26)*ND26<= ; 548 Goal contraint with their correponding mathematical formulation Goal 1- maximum number of computer allocated for educational and reearch activitie d d b Goal 2- reference book dedicated to educational and reearch activitie to tudent d d b Goal 3- upper limit of reference book dedicated to educational and reearch activitie d d b Goal 4- upper limit of educational loading of each faculty member in a week p 1 d 4 d 4 b4 1 Goal 5- lower limit of ournal title p d d b Goal 6- patent to each reearch p6 d 6 d 6 b6 7 Goal 7- potgraduate tudent to each reearch in large (macro) cale 1 d 7 d 7 b7 9

6 Applied mathematic in Engineering, Management and Technology 2014 Gal 8- profeor to faculty member 1 d 8 d 8 b8 1 Goal 9- aociate profeor to faculty member 2 d 9 d 9 b9 1 Goal 10- aitant profeor to faculty member 3 d 10 d10 b10 1 Goal 11- faculty to technical taff 1 d11 d11 b11 5 Goal 12- faculty to adminitrative taff 6 d 12 d12 b12 1 Goal 13-upper limit budget allocated to reearch with medium and micro cale i 7 ( ) d d b Goal 14- lower limit of patent p d d b Goal 15- lower limit of outide of the univerity' proect p d d b Goal 16- lower limit of technical taff d d b Goal 17- upper limit of adminitrative taff d d b Goal 18- upper limit of mall-cale reearch d d b Goal 19- upper limit of medium-cale reearch d d b Goal 20- lower limit of large-cale reearch d d b Goal 21- upper limit maor at the undergraduate level p d d b Goal 22- lower limit of conference per year p d d b Goal 23- lower limit of expected revenue from all educational and reearch activitie ( p ) ( p ) 77 p7 ( ) 1 2 d 23 d 23 b Goal 24- large-cale reearch to total tudie 9 i 7 9 i d d b Goal 25- lower limit of each book title copie p d d b Goal 26- lower limit of each ournal title copie p d d b

7 Applied mathematic in Engineering, Management and Technology 2014 Sytematic Contraint Formulation The total budget allocated for alarie, medium and mall-cale tudie, purchaing reference book required for faculty and tudent, computer required to faculty and tudent, chemical intrument, Chemical, laboratory intrument and facilitie (ytem contraint) L Technical coefficient and contant ued in the model are preented in Table Table 2: Technical Coefficient and Contant Decription Average number of potgraduate tudent in any maor Average number of undergraduate tudent in any maor Average number of publihed copie of each book Average number of publihed magazine Average number of people who have participated in the conference Average tuition of potgraduate dicipline Average tuition of undergraduate dicipline Average price of each book Average price of each magazine Average financial value of each outide of univerity' proect Average financial value of each patent Average payment of participant in the univerity' conference Average annual alary of each full profeor Average annual alary of each aociate profeor Average annual alary of each aitant profeor Average annual alary of each profeor Average annual alary of each technical taff Average annual alary of each adminitrative taff Average cot of each mall-cale reearch Average cot of each medium-cale reearch Average cot of each large (macro)-cale reearch Average price of each computer allocated for educational and reearch activitie of faculty and tudent Average price of each volume of reference book dedicated to conduct educational and reearch activitie of faculty and tudent Definition of the contant Total cot of chemical and laboratory intrument per year Total cot of tudent' facilitie and welfare ervice infratructure per year Number of reference book to perform educational and reearch activitie Symbol a a a a a a 6 a Symbol Normalization Contant Computation by Euclidean Method To calculate the normalization contant for goal' unwanted deviation, there are three method. The firt method i Percentage normalization. In thi method, each deviation i turned into a percentage value away from 550

8 Applied mathematic in Engineering, Management and Technology 2014 it target level o all deviation are meaured in the ame unit. The econd method i Zero-One Normalization which i to cale all unwanted deviation into a zero-one range. The value zero will how a deviation equal to zero and the value one will repreent the wort poible value of the deviation within the feaible et. The third method i Euclidean normalization. Thi normalization contant i actually the Euclidean mean of the technical coefficient of the goal. In comparion with other two method, Euclidean method i very computationally robut. In fact, it work with all goal and target level and it computation i not complex. Thu, Euclidean method ha been ued here in order to compute all normalization contant (one and Tamiz, 2010). All goal and their repective normalized contant are preented in Table 3. Table 3: Goal and Their Repective Normalized Contant Goal Normalized Contant Goal 1- maximum number of computer allocated for educational and reearch activitie 1 Goal 2- reference book dedicated to educational and reearch activitie to tudent 1 Goal 3- upper limit of reference book dedicated to educational and reearch activitie 1 Goal 4- upper limit of educational loading of each faculty member in a week Goal 5- lower limit of ournal title Goal 6- patent to each reearch Goal 7- potgraduate tudent to each reearch in large (macro) cale 1 Gal 8- profeor to faculty member Goal 9- aociate profeor to faculty member Goal 10- aitant profeor to faculty member Goal 11- faculty to technical taff Goal 12- faculty to adminitrative taff Goal 13-upper limit of budget allocated to reearch with medium and micro cale Goal 14- lower limit of patent 1 Goal 15- lower limit of outide of the univerity' proect 1 Goal 16- lower limit of technical taff 1 Goal 17- upper limit of adminitrative taff 1 Goal 18- upper limit of mall-cale reearch 1 Goal 19- upper limit of medium-cale reearch 1 Goal 20- lower limit of large-cale reearch 1 Goal 21- upper limit of maor at the undergraduate level 1 Goal 22- lower limit of conference per year 1 Goal 23- lower limit of expected revenue from all educational and reearch activitie Goal 24- large-cale reearch to total tudie Goal 25- lower limit of each book title copie 1000 Goal 26- lower limit of each ournal title copie Preferential Weight Computation by AHP Analytic Hierarchy Proce (AHP) i known a one of the mot applied multi criteria deciion making method. It wa developed by Thoma L. Saaty in 1970 and ha gone ubtantial refinement ince then. Thi method enable deciion maker to derive ratio cale from paired comparion. In thi paper, AHP ha been ued to rank the goal and compute their preferential weight. An AHP quetionnaire wa prepared and ed to dean, deputie and chancellor of the univerity. Almot all of them reponded to the quetionnaire. The quetionnaire wa analyzed by Expert Choice 11 Software and all goal' preferential weight were computed. Table 4 how goal and their repected preferential weight 551

9 Applied mathematic in Engineering, Management and Technology 2014 Table 4: Goal and Their Repected Preferential Weight Goal Preferential Weight Goal 1- maximum number of computer allocated for educational and reearch activitie Goal 2- reference book dedicated to educational and reearch activitie to tudent Goal 3- upper limit of reference book dedicated to educational and reearch activitie Goal 4- upper limit of educational loading of each faculty member in a week Goal 5- lower limit of ournal title Goal 6- patent to each reearch Goal 7- potgraduate tudent to each reearch in large (macro) cale Gal 8- profeor to faculty member Goal 9- aociate profeor to faculty member Goal 10- aitant profeor to faculty member Goal 11- faculty to technical taff Goal 12- faculty to adminitrative taff Goal 13-upper limit budget allocated to reearch with medium and micro cale Goal 14- lower limit of patent Goal 15- lower limit of outide of the univerity' proect Goal 16- lower limit of technical taff Goal 17- upper limit of adminitrative taff Goal 18- upper limit of mall-cale reearch Goal 19- upper limit of medium-cale reearch Goal 20- lower limit of large-cale reearch Goal 21- upper limit maor at the undergraduate level Goal 22- lower limit of conference per year Goal 23- lower limit of expected revenue from all educational and reearch activitie Goal 24- large-cale reearch to total tudie Goal 25- lower limit of each book title copie Goal 26- lower limit of each ournal title copie Model Implementation in an Actual Sytem and Solution Analyi Actual data of a private higher education intitution wa prepared. The model include 74 variable 21 of which are deciion variable and other are poitive deviational and negative deviational variable. Furthermore, there are twenty-ix goal contraint and one ytem contraint. The model i an integer Chebyhev goal programming model which ha a minimization obective function. It i olved by Lingo 11 oftware and it olution are preented in Table 5: 552

10 Applied mathematic in Engineering, Management and Technology 2014 Table 5: Solution of the Model Preferential Normalization Deviated Goal Deviation Value Weight Contant ND ND ND ND ND PD ND ND ND PD ND ND Model Solution Current Statu Univerity' ource ( S ) Obective Function Value NO. of full profeor S NO. of aociate profeor S NO. of aitant profeor S No. of intructor S NO. of technical taff S NO. of adminitrative taff S NO. of micro reearch S NO. of medium reearch S NO. of macro reearch 9 NO. of computer allocated to tudent and faculty' S educational and reearch activitie No. of reference book aigned to tudent and faculty S 11 S Model Solution Current Statu Univerity' Product( P ) NO. of potgraduate dicipline P NO. of undergraduate dicipline P NO. of copie of publihed book P NO. of cientific- reearch ournal P NO. of univerity' external proect P NO. of patent NO. of cientific conference and eminar P organized by the univerity NO. of cientific and reearch paper publihed by p the faculty NO. of publihed book NO. of publihed ournal p 10 P p The above table how that the goal of the higher education intitution adminitrator are achieved with a deviation and among all twenty-ix goal, goal 2, goal 9, goal 10, goal 11, goal 13, goal 15, goal 16, goal 17, goal 21 and goal 24 are under achieved and goal 14 and 19 have become over achieved. Goal 2 i 553

11 Applied mathematic in Engineering, Management and Technology 2014 under achieved to 44 unit, goal 9 i under achieved to 26 unit, goal 10 i under achieved to 26 unit, goal 11 i under achieved to 6 unit, goal 13 i under achieved to unit, goal 14 i over achieved to 1 unit, goal 15 i under achieved to 7 unit, goal 16 i under achieved to 16 unit, goal 17 i under achieved to 2 unit, goal 19 i over achieved to 3 unit, goal 21 i under achieved to 2 unit and finally, goal 24 i under achieved to 24 unit. With regard to uch unwanted deviation and the gap between current tatu and model olution (I.e. recommended tatu), if adminitrator want to achieve the goal of univerity in an optimal manner, they hould do the following action: Univerity ha currently two full profeor; it hould have 7 full profeor in the next year to achieve it goal, therefore, it require three full profeor and hould take an increaing trategy toward full profeor. The item of "aociate profeor" i currently equivalent to four people; univerity need no more aociate profeor in the next year to realize it goal, thu it doe not need to recruit any aociate profeor and hould take a preerving trategy toward aociate profeor. The item of "aitant profeor" i currently equivalent to nine people; in the next year, univerity need no more aitant profeor to achieve it goal, therefore it doe not need to recruit any aociate profeor and hould take a preerving trategy toward aociate profeor. Item of "intructor" currently equal eight people. In the following year, the univerity hould maintain thi level to realize it goal becaue thi value i optimum. Hence, the univerity doe not require the intructor and it hould take a preerving trategy toward the intructor. "Technical taff" i currently equal to forty-two people. To realize it goal, univerity hould reach thi item to forty-four; therefore, it hould add two people to it technical taff. It hould alo take an increaing trategy toward technical taff. "Adminitrative taff" i currently one-hundred people, for the next year, the univerity hould reach thi item to 110 people to achieve it goal; hence it require ten adminitrative taff. It hould take an increaing trategy toward adminitrative taff. During the pat year, the univerity conducted four micro-ized reearche, ix medium-ized reearch, and ix macro-ized tudie. The univerity hould perform one micro-ized reearch, eleven medium-ized reearche, and no more macro-ized tudie. Therefore, the univerity hould take an increaing trategy toward macro and medium-ized reearche and a preerving trategy toward micro- ized tudie. Item of "computer allocated to do teaching and reearch activitie" i currently equal to one-hundred device and in the following year, univerity doe not need to buy any computer. The number of book dedicated to teaching and reearch activitie are currently five-hundred copie, in the next year, the univerity hould buy one hundred and fifty ix copie. The number of potgraduate coure i currently ten maor and in the following year, the univerity hould have fifteen maor in potgraduate degree to realize it goal; thu, it need five maor and univerity hould take an increaing trategy toward thi item. The number of undergraduate coure i currently twenty maor and in the following year, the univerity hould have twenty-two maor in undergraduate degree to realize it goal; thu, it need two maor. The univerity hould take an increaing trategy toward thi item. The univerity currently ha even book title, which ha releaed total 3199 copie of them but in the next year, it doen't need more book title and doen't need to publih any copy of them. The univerity currently ha two periodical that it ha publihed total copie of them but in the next year, it doen't need more periodical title and doen't need to publih any copy of them. The univerity ha currently conducted five univerity' external proect, which hould perform three more univerity' external proect to realize it goal and it hould take the increaing trategy for thi item. The univerity currently ha two patent, which hould reach them to ixteen patent in the following year to achieve it goal. It hould take an increaing trategy toward thi item. The univerity currently ha held three conference, which doen't need to hold any more conference in the next year. The univerity' faculty ha publihed twenty article, which hould publih forty-ix article for the next year, and an increaing trategy hould be taken toward thi item. 9. Concluion Many reearcher and practitioner in higher education have attempted to develop efficient budget allocation method. Since organization are multi obective entitie, their manager encounter ome challenge while wanting to allocate the budget among organizational multiple goal in a balanced manner. Following the conducted tudie and the importance of thi iue in intitution of higher education, an integer chebyhev 554

12 Applied mathematic in Engineering, Management and Technology 2014 goal-programming model wa developed and implemented in a non-public intitution of higher education. With regard to the reearch problem, model' tructure, Simultaneou conideration of ource and output via manufacturing ytem approach for budget planning, the diverity of ource and output in comparion with tudie preented in the literature review and increaed number of contraint and the cope of model are main feature that differentiate thi model from many other model. Thi model i uceptible for being ued in a large number of higher education intitution and outperform other GP model in term of balanced allocation of budget. However, it can be more improved by conidering the following uggetion: A) Manger et target level according to their deire. Thu, it may reult in ome ideal and nonrealitic target level. So, development of a mechanim the help the manager to et the target level more realitically i of paramount importance B) Since many of the devied model are ingle-period, they can't cover the organization in a longer trend. To tackle thi diadvantage, developing a multi-period goal programming model i trongly recommended. Furthermore, manager' attention to Reource Baed View (RBV) and organizational dynamic capabilitie, while planning for budget allocation, i trongly effective and believed to yield very good reult. However, the manager of the tudied intitution can ue the olution of thi model a effective guideline becaue intitution' inflow and outflow a ytem' ource and output have been properly covered according to a manufacturing ytem approach. Reference 1. Akin.L. Ogunlade.(2008). Reource Allocation: a multi-model, a multi-goal approach, Economic of Education Review, Vol.27, No ABS.(2007), Autralian Bureau of Statitic, Reearch and Experimental Higher 3. Caballero R, Francico Ruiz M, Victoria U, Carlo R, 2006, Interactive meta Goal Programming, European ournal of Operational Reearch, 175, pp Caballero, R. Golache T. Gomez T., Molina and Torrico A. (2001). Efficient Aignment of Financial Reource within a univerity ytem: caetudyog univerity of Malage, European ournal of Operation Reearch, Vol D. one, M. Tamiz,(2010), Practical Goal Programming, International Serie in Operation Reearch & Management Science 141, DOI / _1,Springer Science Buine Media,, PP DME.(2010), Development of Education Denmark Minitry of Education 7. EW Publication, (2003), Eatern Wahington univerity trategic reource allocation model, pp Entezari, Y. (2010); Analyi of Funding Performance of Public Univeritie ; Quarterly ournal of Reearch and Planning in Higher Education, Vol.16, No. 57, pp EW Publication,( 2003), Eatern Wahington univerity trategic reource allocation model, pp G.P. White.(1987). The implementation of management cience in higher education adminitration. Omega 15, Vol.4, pp H. William.(2005). Planning for Effective Reource Allocation in Univeritie.American Council on Education, Wahington, D.C. 12. one. Dylan, (2011). A practical Weight enitivity algorithm for goal and multiple obective programming, European ournal of operational Reearch, vol 213, pp M. Bau, & B. Pal,(2006) A goal programming model for long-range reource planning peronnel management in univerity. Advance in Management Studie 2, Vol.3 & 4, 1985, pp MU publication,( 2005), Maryland Univerity budgeting Proce, pp Nopiah, Z. M. kamaruddin, A. H. Imail, W. R. Abdullai, S. Ahmad, I.(2007). Modeling Univerity a a Production indutry: A Quantitative Approach. Proceeding of the 11th WSEAS International Conference on COMPUTERS, AgioNikolao, Crete Iland, Greece, pp NU Publication, (1998)., State univerity of New York Report pp Ogunlade.Akin.L.,(2008). Reource Allocation: a multi-model, a multi-goal approach, Economic of Education Review, Vol.27, No.1,pp. 18. Pal, BiayBaran, &en, Shymal.(2008). a linear goal programming procedure for Academic peronnel management problem in univerity ytem,ieee region 10 colloquium and the third international conference on indutrial ytem. Kharagpur, India, December pp S, Safari,. A, Sardari,. H, Sabzian.(2012), "Deigning a Mathematical Model for Allocating Budget to Univerity Reearch and Educational Goal: A Cae Studey in Shahed Univerity". Iranian ournal of Management Studie, Vol.5, No.2, pp: