Project selection by using AHP and Bernardo Techniques

Transcription

1 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN Project selection by using AHP and Bernardo Techniques Aza Keshavarz Haddadha, Ali Naazian, Siaak Haji Yakhchali 3 Abstract Selection of an optial project portfolio is an iportant and strategic decision in project-based organizations. In order to select the optial project portfolio, organizations encountered with different constraints.this paper focuses on developing a odel based on Bernardo and AHP ethods for solving the project portfolio selection proble, consists of these basic stages: at first, the criteria and sub criteria to be used in the odel are identified, then, AHP ethod is perfored for deterining the weights of criteria, at the end based on AHP results and by Bernardo odel which considers soe constraints such as resource constraints the optial projects would be selected. Keywords Project selection; Expert judgent; AHP; Bernardo E I. INTRODUCTION very project begins with a proposal, but soe of the can becoe a project. In a world of liited resources, choices have to be ade. Not every project has viability and aongst those that do, liited resources (people, tie, oney and equipent), ust be applied judiciously. The goal of the project selection process is to analyze project viability and to approve or reject project proposals based on established criteria, following a set of structured steps and checkpoints. In recent years, any ulti criteria decision aking (MCDM) ethods have been developed for handling Project Selection probles. [] used The Technique for Order of Preference by Siilarity to Ideal Solution (TOPSIS) approach, as an MCDM technique, for the project selection proble.[0] applied fuzzy AHP and TOPSIS ethod for project selection proble. [] eployed AHP and fuzzy TOPSIS ethods for project selection in oil-field developent. [6] presented Vikor and AHP ethods for project selection proble.[7] proposed a ethodology based on Hybrid algoriths for evaluating projects. [] in other work, proposed a fuzzy analytical network process (ANP) - based approach to project selection.[3] applies MCDM techniques in project selection proble, it was based on AHP and TOPSIS ethods. There are various ethods on project selection in the different fields. The ajority of accoplished works often yield coplicated atheatical prograing such as ixed integer or nonlinear prograing. For,4: Alaodoleh Senani Institute of Higher Education, Iran. Eail addresses: aza.keshavaez369@gail.co (aza keshavarz Haddadha); (Hassan Taheri Nejad),3 Departent of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran. Eail addresses:a.naazian@ut.ac.ir (Ali Naazian); yakhchali@ut.ac.ir (Siaak Haji Yakhchali) exaple, [5] applied a 0- goal prograing for project selection proble.[] used a goal prograing odel for inforation syste project selection,[3] introduced a coprehensive odel for the portfolio of several objectives. [4] prepared a ulti objective integer optiization odel with distributions of costs probability, and any other researches (e.g. [8],[6], [7], [9], [4], [4], [8],[9]) This paper focuses on developing a odel based on Bernardo and AHP ethods for solving optial project portfolio selection proble. To achieve this purpose, the rest of this paper is organized as follows: In section, soe criteria of project selection that are ore coon in each field are introduced.section 3 discusses AHP approach for ranking and weighting criteria, In section4, by a results of AHP and also by using Bernardo odel the optial projects are selected, for this purpose the developed ethodology is executive in an Case Study. II. CRITERIA OF PROJECT SELECTION PROBLEM In this section, at first the Criteria of Project selection are introduced. For identification of criteria, soe books, thesis, papers and also libraries are used. The listed criteria are shown in table. TABLE I IDENTIFICATED CRITERIA IN PROJECT PORTFOLIO SELECTION Project Selection Criteria NPV(Net Present Value) Strategic Plan Projects constraint Copetency and Skills of anagers and staffs Organizational experience Risks of projects Acquire technology Tie delays Copetitive advantage Organizations iage Marketing plan Huan resources Costs IRR(Investent Return Rate) III. ANALYTIC HIERARCHY PROCESS (AHP) AHP is a coprehensive odel that is appropriate for aking ulti-objective, ulti criteria and ulti-actor decision for any nuber of alternatives in both certain and uncertain environent. In order to quantify the iportance of a set of criteria, AHP was developed in a ulti criteria 69

2 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN decision aking proble. Since AHP is based on easy to understand value rankings, it has been used and applied by organizations in the real world whereas ore atheatically coplex odels ay not be easily transferred fro advancing research theory into real world practice. Additionally, AHP odels have been used effectively to optiize project selection in the research and developent settings and other kinds of projects []. A classical AHP can be constructed as follows. The goal, criteria, and alternatives for at least three levels of a linear hierarchy tree. At first the overall goal and the criteria and alternatives have to be deterined. Then the pairwise coparisons can be obtained. This pairwise coparisons are often based on a -9 scale of iportance [5] These values and their concepts are shown in Table. Let denote the coparison of the strength of criterion i to j criterion. Based on a priority vector for the overall goal, criteria and alternatives are deterined by the decision aker, the pairwise coparison of criterion i to j criterion is coputed by siilarly, And thus,. Then, for the set of decision criteria the pairwise coparisons of n criteria can be suarized in the atrix: []. A= Where every eleent is the quotient of the weights of the criteria. The priority vector, or relative weights, of the set of criteria are deterined by the right eigenvector w of atrix A which corresponds to the largest eigenvalue λ ax, i.e., AW= λ ax w.this is necessary because the atrix is fored based on huan value judgents which are intrinsically inconsistent and this ethod can provide validity of the priorities of a decision.a pairwise coparison and subsequent eigenvalue calculation is copleted by the decision-aker for each criteria and set of sub criteria. The final score of for each alternative is obtained by suing each alternative s relative weight with respect to each criteria ultiplied by the criteria s priority with respect to the goal. TABLE II CONCEPTS OF JUDGMENT VALUES Verbal eaning Extreely ore iportant Very strongly ore iportant More iportant Moderately ore iportant Equally iportant Reciprocal for inverse coparison level of iportance ,4,6,8 IV. PROBLEM MODELING BY BERNARDO METHOD Bernardo Method is a ulti-criteria and group decision ethod for decision aking, in which the group of decision akers also use the ranking ethod in order to prioritize the nuber of options based on n criteria. This odel in addition to ranking the options by eans of group agreeent, is able to select a subset of options. This selection can also take resource constraints into consideration when perforing options which could be the selected projects. In Bernardo Method, the following atters ust be considered: The first step is to show each option according to the different criteria. This process can be obtained by eans of ranking, pricing, polling, or sapling. In order to collect views of the group ebers, an agreeent atrix is fored which indicates views of the group ebers about each option for each criteria. 4.. Group Agreeent Matrix and Unit Perutation Matrix Group Agreeent atrix (Q) is a non-negative and square (*) atrix in which any eber indicates individual rankings, so that i th option have been designated by the ranking of t. Soe of the criteria ight be ore iportant than others; therefore, a decision aker considers higher weights for those criteria. For this purpose, a weight vector,, has been defined in which is the weight designated to the j th criteria. A unit perutation atrix (P) is a non-negative atrix whose rows and coluns include a coefficient equal to one and the rest equal to zero. Decision aker s favor is to select an especial atrix of P which atches the atrix of Q profusely. In other words, the goal is to put nubers in a unit perutation atrix, so that will be axiu. ( = eleents of atrix P.) 4.. Bernardo Method Types Bernardo Model according to its atter will be used in two fors. In this odel, the properties of ranking and prioritizing can be used; however, it is possible that not only prioritizing options will not be the only purpose, but also ranking a subset of options and considering resource constraints can also be iportant goals, which in this case the Bernardo Model is used, in other word, this odel can be used for two purposes of ranking and options prioritizing and ranking and prioritizing a subset of options. In the defined proble if the goal is only to rank and prioritize the options, the following forulas are used, so that 70

3 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN the non-negative atrix of is a unit perutation atrix. (Each row and colun have an eleent which is equal to one and the rest equal to zero, in which the oneaounts indicate the rank of the option aong other options.) The odeling of this case will be atched in the equation (): n ax q p i j i s. t : p i,,..., j p p j,,..., 0or Also, according to what entioned above, the purpose of ranking and prioritizing a subset of options ight be accopanied with soe resource constraints, the Bernardo Model needs atheatical expansion in order to consider the resource constraints when perforing projects (options) and selecting a subset of the so that the resource constraints will be satisfied. Perforing soe of the options ight not be the provider of resource constraints and therefore could not be selected. I.e. the options will not be ranked. Also the entire options are not included in a selected subset, so soe of the are not included in the ranking. This fact causes the rank of the unit perutation atrix of to be less than and therefore the constraints in the atrix will be in fors of equations () and (3): p i p 3 j In ters of designating approach, the selected eleents need to start sequentially and consecutively fro the rank of one. The constraint that includes this case is like equation (4): p p 0, k j 4 ik Due to the resource constraints, soe of the ranks ight prevent a set of options fro being placed in the feasible solution. If the be the aount of s th resource which used by i th option, and be the total aount of s th resource, then the related constraint could be expressed as equation (5): d p T is s i j 5 The decision aker ight not be interested in identifying the rankings of each option, but he ight be interested in identifying rankings for a set of options which can be selected, without attention to the within-set ranking. He also ight be not interested in axiizing the ranking agreeent which has been shown with Q, but rather prefer the axiizing of group agreeent. This case can be expressed by equation (6): R [ r ik ] r ik Q j 6 r ik indicates the nuber of ties in which the option i is ranked in the position of one to k. Therefore, the objective function can be expressed in fors of equation (7): ax : r. p 7 i i Now in order to judge between the different option subsets, the objective function is odified as follows: ax : r. p kn In this case the objective function is coparable with the entire values fro n=, and k (the nuber of experts). Considering the entioned points, the total forula of Bernardo Method will be as follows: i j p j,,..., p i,,..., p p ( j ) 0 j,,..., i i is s i j i d p T s,,..., S 0or p {ax : r. p } n,,..., kn ax n V. THE PROPOSED MODEL The proposed odel for the project selection proble, based on AHP and Bernardo ethods, consists of these basic stages: at first, the criteria and sub criteria to be used in the odel are identified, then, AHP ethod is perfored for deterining the weights of criteria, at the end based on AHP results and by Bernardo odel which considers soe constraints such as resource constraints the optial projects will be selected. Flowchart of the proposed odel is shown in figure. 5.. The Criteria Weighting In the first stage, alternative projects and the criteria are deterined. AHP odel is structured such that the objective is placed in the first level, criteria are in the second level and alternative projects are on the third level and after that the decision hierarchy is approved by decision-aking tea. After the approval of decision hierarchy, criteria used in selection projects are assigned weights using AHP. In this phase, pairwise coparison atrixes are fored to deterine the weights of criteria. These weights are calculated based on final coparison atrix. The selected criteria are shown in table 3. The criteria to be used in the odel were deterined by the expert tea fro project anagers in a consultant 7

4 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN organization. Also the obtained weights of criteria are shown in table Prioritizing and Selecting Projects by Bernardo Model In this stage, firstly we will discuss deterining projects under the study (the elected engineering copany). In the first stage, the following projects will be identified through interviewing the experts and collecting their views. The projects on which experts ephasized are as follow in table 5. (According to the confidential issues inside the copany, the identified projects will be shown paraetrical and we will skip giving the exact naes of the projects according to the copany s request.) Project X X X 3 X 4 X 5 TABLE V IDENTIFIED PROJECTS LIST Budget Duration(Month) Foring of the Expert judgent Matrix: In this stage, expert judgent atrix were fored for each responder, related to the rank of each of the entioned projects in the previous stage and the ranks were given fro one to five, which are atched with atrixes of D to D 6 : Fig..Proposed Model Flowchart Criterion Index TABLE III IDENTIFIED CRITERIA IN THE PROPOSED MODEL Criterion Type Criterion C Financial NPV C Financial cost C 3 Risk Risk C 4 Risk Tie delays C 5 Profitability Copetitive advantage C 6 Profitability Organizations iage C 7 Feasibility required technology C 8 Feasibility Manageent C 9 Feasibility Experience in siilar projects TABLE IV THE WEIGHTS OF CRITERIA Criterion Index Criterion Weight C NPV 0.76 C cost C 3 Risk 0.6 C 4 Tie delays C 5 Copetitive advantage 0.6 C 6 Organizations iage 0.3 C 7 required technology 0.3 C 8 Manageent C 9 Experiences in siilar projects Foring of Group Agreeent Matrix After foring atrixes, a group agreeent atrix was fored by eans of fored atrixes in previous stages for each of the responders as follows. = 7

5 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN j 5, j 5, 5, ( P P P P P ) ( P P P P P ) 0,, 3, 4, 5,,, 3, 4, 5, = Therefore, we will have according to the equation (6): ax{.5 P,.093 P, P3,.57 P4,.5590 P5, (5) st. i i 3.04P.3P.07P.899P.68 P },, 3, 4, 5, P P P P P P,, 3, 4, 5, P P P P P P,, 3, 4, 5, And since the copany faces budget constraints and lack of the necessary tie in order to perfor the projects, we have: (It is assued that the perforance of projects coincidently is not possible, in other words, projects are conducted consecutively and not parallel.) P, P, 4P, P, 8P3, P3, 0P4, P4, P5, P5, 0 5 P, P, P, P, 7P3, P3, P4, P4, P5, P5, After solving the odel by Gas Software the optial solution of the proble indicates the selection of the first and fifth projects in order to be placed in the project portfolio of copany to be conducted. The optial value of the objective function of the proble in this case is Other cases of the project are also shown in table 6. Proble Nuber 3 4 Maxiu Mebers of Sub-Set 3 4 TABLE VI OPTIMAL SOLUTIONS Objective Function Value Selected Projects X 5 X,X 5 X,X 5 X,X 5 According to the above table, optial solution of the proble includes selecting first and fifth projects; and it has the ost atching with group agreeent atrix. According to the objective function of Bernardo s general forula, in order to select a one-option subset, only the first colun of atrix R will be used and also in order to select a two-option subset, two left colun of atrix R will be used. So the designated odel ust be solved four ties with four different objective functions. As a saple, in case of selecting a subset of two projects, the odeling ust be as follows: j j j j, j,,, j,, 3, j 3, 3, 4, j 4, 4, VI. SUMMARY AND CONCLUSION The atter of selecting appropriate projects aong the identified projects includes iportant decisions and strategies in alost every copanies especially the project-based organizations in which the lack of planning and enough precision could have unpleasant influences on the organization. On the other hand, organizational constraints such as resource constraints, geographical constraints and so on, are issues which cause organizations to face serious challenges when selecting and conducting projects. Therefore, selecting the project according to the real constraints sees to be inevitably necessary. In this regard in the paper, attepts were in order to develop a structure by selecting an optial portfolio of projects by ulti criteria decision aking ethods, so that it can regard the existing real situations like organizational constraints when having the ost atching with the expert views. Despite the presented structure in this paper, in order to ake it ore applicable it can be suggested to take the uncertainty about 73

6 International Journal of Huanities and Applied Sciences (IJHAS) Vol. 5, No., 06 ISSN resources aounts or even expert s views into consideration for further studies due to the lack of certainty of the estiated values. VII. REFERENCES [] Airi, M.P, (00). "Project selection for oil-fields developent by using AHP and fuzzy TOPSIS ethod, Expert systes with applications, 37(9), [] Badri, M. A., Davis, D., & Davis, D. (00). A coprehensive 0 goal prograing odel for project selection. International Journal of Project Manageent, 9(4), [3] F. Carazo, T. Góez, J. Molina, A. G. Hernández-Díaz, F. M. Guerrero, and R. Caballero, Solving a coprehensive odel for ultiobjective project portfolio selection, Coputers & Operations Research, vol. 37, no. 4, pp , Apr. 00. [4] Gabriel, S. A., Kuar, S., Ordonez, J., & Nasserian, A. "A ultiobjective optiization odel for project selection with probabilistic considerations." Socio-Econoic Planning Sciences, 40(4),, 006: pp [5] Ghasezadeh, F., Archer, N., & Iyogun, P. (999). A zero-one odel for project portfolio selection and scheduling. Journal of the Operational Research Society, 50(7), [6] Hall, N. G., Hershey, J. C., Kessler, L. G., & Stotts, R. C. "A odel for aking project funding decisions at the National Cancer Institute." Operations Research, 40(6),, 99: pp [7] Hawkins, C. A., & Adas, R. A. "A goal prograing odel for capital budgeting." Financial Manageent,, 974: pp [8] Khalili-Daghani, K., Tavana, M., & Sadi-Nezhad, S. (0). An integrated ulti-objective fraework for solving ulti-period project selection probles. Applied Matheatics and Coputation, 9, [9] Kaveh Khalili-Daghania, Soheil Sadi-Nezhad," A hybrid fuzzy ultiple criteria group decision aking approach for sustainable project selection", Applied Soft Coputing 3 (03) [0] Mahoodzadeh. S, Shahrabi. J, Parizar. M, Zaeri. M. S, "Project selection by using fuzzy AHP & TOPSIS technique, World Acadey of science, Engineering and Technology: 30. [] Mohanty, R. P. "Project selection by a ultiple-criteria decision-aking ethod: an exaple." International Journal of Project Manageent, 0(),, 99: pp [] Mohanty, R. P., Agarwal, R., Choudhury, A. K., & Tiwari, M. K. "A fuzzy ANP-based approach to R&D project selection: a case study." International Journal of Production Research 43(4), 005: pp [3] Pangsri, P., (05).Application of the Multi Criteria Decision Making Methods for Project Selection.Universal Journal of Manageent 3(,) pp. pp.5-0. [4] Rabbani, M., Araoon Bajestani, M., & Baharian Khoshkhou, G. "A ulti-objective particle swar optiization for project selection proble." Expert Systes with Applications 37(), 00: pp [5] Saaty, T.L., "Axioatic foundations of analytic hierarchy process", Manageent Science, vol. 3 no.7, [6] Salehi, Kayvan,. "A hybrid fuzzy MCDM approach for project selection proble." Decision Science Letters,4, 05: pp [7] Singh, " Resource Constrained Multi-Project Scheduling with Priority Rules & Analytic Hierarchy Process", Procedia Engineering, vol 69, pp [8] Weingartner, H. M. "Capital budgeting of interrelated projects: survey and synthesis." Manageent Science, (7),, 996: pp [9] Yavuz, S., & Captain, T. A. "Making project selection decisions: a ultiperiod capital budgeting proble." International Journal of Industrial Engineering, 9(3),, 00: pp