A Novel Model of JOURNAL OF STRATEGY & …jspm.firstpromethean.com/documents/2-2-79-106.pdf1979/02/02 · Journal of Strategy and Performance Management, Volume 2, Issue 2, April

79 Journal of Strategy and Performance Management, Volume 2, Issue 2, April 2014.

Faisal Masood Center for Advanced Studies in Engineering, Islamabad.

[email protected]

ABSTRACT

Problem Statement: In recent era of competition, the organizations have minimum resources and excessive projects; therefore, the organizations have to optimize the portfolio according to their budget and capacity. During the optimization of portfolio, organizations face problem in taking best possible decisions for competitive advantage in order to gain market direction and readi1ly developing competencies for maintaining market leadership position. The organizations have problem in assessment of projects with respect to Marketing, Finance, IT, Legal, Sales and related sub criteria. This problem leads towards the difficulty in prioritization of projects. Finally if not managed these aspects effectively, affects the strategy of the organization.

Methodology: Primary data has been collected by the judgments of the five experts’ opinion through participant observation in meetings. For credibility the unanimous decisions of experts were taken and also used data in the form of documents.

Results: The results outline that the Marketing is the dominant criteria in portfolio optimization where as finance criteria has also its pace as far as results are concerned The project of Campaign Management system is found to be the best in portfolio as well as with respect to strategic Alignment.

Originality/ Value: Portfolio optimization is one of the critical decision milestones in the business. The main idea is to structure a possible decision support model on guaranteeing different criteria of portfolio. Fuzzy AHP methodology, in view of Chang's extended analysis, is applied in portfolio optimization. In the wake of organizing the crucial progression, the model is performed with an application on IT industry to have the ability to get illustrative outcomes. The projects of Portfolio were assessed with respect to criteria (Marketing, Finance, IT, Legal and Sales) and sub criteria. Resource alignment, project costs, infrastructure growth, skill set development and process improvement are the proposed objectives for strategic alignment that are achieved by applying TOPSIS method.

Keywords: Portfolio optimization, Fuzzy AHP, Chang's extended analysis, Strategic Alignment, TOPSIS method.

A Novel Model of Strategically Aligned Portfolio Optimization through Fuzzy project prioritization.

JOURNAL OF STRATEGY & PERFORMANCE MANAGEMENT

April 2014. Volume 2, Issue 2, 79-106. Article Type: Original Research.

Citation: Masood, F. (2014). A novel model of portfolio optimization through fuzzy based prioritization for increased strategic alignment, Journal of Strategy and Performance Management, 2(2), 79-106.

Journal of Strategy and Performance Management, Volume 2, Issue 2, April 2014. 80

INTRODUCTION

Organizations today face a remarkably intense environment described by fast progressions, expanding many-sided quality, and dangers from worldwide rivalry. In their endeavors to secure their own position and all the more basically to enhance their intensity, satisfactory systems must be produced and actualized in the companies. From the corporate level, system could be conveyed by portfolio optimization utilizing programs and projects of diverse sorts and sizes as compelling devices. The purpose of this research is to present a model for portfolio optimization, helping the organizations in effective decision making, project balancing and prioritization. This model is aligned with the defined objectives of the strategy i.e. resource alignment, project costs, infrastructure growth, skill set development and process improvement. Research questions

1. What are the most important criteria and sub criteria in portfolio management? 2. How can the organizations optimize portfolio by using fuzzy Logic approach? 3. How the portfolio is strategically aligned and congruent with the defined criteria? 4. What are the proposed recommendations for the organizations?

Research Limitations This research is conducted by a single student which was just fit to perform limited research in the time given, predetermined number of organizations and resources. In any case, the effort was made to gather sensible information and get opinions of various experts.

The exploration includes a little scale study. The point was to follow how fuzziness is associated with the useful world with an emphasis on portfolio optimization. The way that the idea of portfolio optimization is definitely not institutionalized in limited no of organizations, is a major limitation to this study.

RESEARCH METHODOLOGY

This section portrays the research methodology for this study. This part starts with research purpose and approach used for the research. In addition, a discussion about research strategy is carried out. Moreover, this part summarizes how data was collected and settles with a theoretical discussion in concurrence to our role in science. ResearchPurposeThe point when directing research it is imperative to work in an orderly way to make dependable replies to research questions, also to help others in comprehension the rationale and consequence of work. (Ghauri & Grønhaug, 2005). Cognizant Choices of methodology and methods make this deliberate way. Research Methodology is defined as Depiction of how research ought to be attempted; further, characterizing research methods as the systems and methodology used to gather and break down information. (Saunders et al, 2009) Research comprises of exploratory, descriptive or explanatory reason for the study, or a blend of these. Research questions and how they will be addressed focus the choice of research reason. According to (Saunders et al, 2009) a researcher utilizes an exploratory reason when the research inquiries expect to addition further data and comprehension of the chose theme. The researcher normally details these inquiries in an open way, which prompts the exploratory design being extremely adaptable and versatile to change. This adaptability is preference as it gives the researcher the chance to begin with a wide


center, which can be limit down later all the while. Saunders keeps on explaining the spellbinding reason, which the researcher utilizes when necessities to get a right perspective of a circumstance, occasion or individual. Saunders states that the engaging research reason could be utilized as a pre study or a growth to exploratory research; then again it is all the more frequently utilized as a piece of logical research.

The research is to give further information about criteria and sub criteria in portfolio optimization as well as understanding of how can the organizations optimize portfolio by using fuzzy logic approach and how portfolio is strategically aligned and congruent with the defined criteria. This research makes use of both an exploratory as well as descriptive purpose. Research Approach A research study might be dependent upon two separate methodologies, or a blending of the two. One regular first venture of a task is to outline a hypothesis -‐ based research system. A researcher then tests this hypothesis inside the study, and the effects of this test either affirm the existing hypothesis or give include on pertinent deviations. This methodology is known as a deductive methodology. Saunders portrays an alternate approach in which the study starts with gathering information so as to investigate a subject. From that information, new hypothesis is created. This methodology is called an inductive methodology. Additionally, researchers frequently discover a blending of the methodologies to be worthwhile. This mix is recognized as an abductive methodology, where the researcher behaviors consistent circles between utilizing a deductive methodology and an inductive methodology. The research approach of this study can best be expressed as being abductive.

Research Strategy Five research strategies according to Yin are Experiment, Survey, Archival analysis, History and Case study. In order to choose strategy the variables that guide the researcher are research questions types, degree of control over behavioral activities and relative focus on contemporary v/s historical events. The focus of this study is on contemporary events and not has control over behavioral events therefore case study is opted. The case study is suitable with respect to viewpoint, having the methodology in center and proposes to give a comprehension of the entire.

(Saunders et al, 2009) defined that research strategy is characterized as an arrangement for how the study will address the expressed research questions. The authors additionally characterize the most paramount part of picking a research strategy as the capability to empower a sensible level of consistency in the research, onto which the research inquiries might be addressed and the targets could be met. The destinations of the study and the research addresses along these lines impact the improvement of the strategy; on the other hand, pre- existing information and the measure of time and different assets required to direct the study take a part in molding the strategy.

According to Yin (2009) case study research has been characterized as a method for examining an exact point by taking after a set of pre-specified strategies . Yin is recognized as the best known example of case technique in social science. Detailed analysis as a research strategy is used in numerous circumstance to help our information of singular, gathering, organizational, social, political and related phenomena. Despite the fact that this kind of detail is not basic in principle building, it is significant since it allows researchers to measure contracts all the more correctly and detailed analysis is advantageous for diverse purposes; give portrayal, create hypothesis or test existing theory (Eisenhardt, 1989). (Flyvbjerg, 2006) suggests that decision of research method ought to unmistakably hinge on upon the issue under study and its circumstances, that research endeavor method is not dependably suitable and significant as a research method. There are few reasons that case study as a research strategy is criticized. According to Yin three common objections are: Case studies need careful research implying that the researcher may exhibit dubious information or predisposition perspectives to impact


direction of conclusions. The second objection is about little support for scientific generalization and the time consuming represents the last objection point. In this thesis I tried to clarify the assessments of projects with respect to criteria and sub criteria and present this study without biasness. Moreover unique case has been taken and holistic as focus is on the entire organization.

Data collectionResearchers utilize two sorts of data, primary & secondary data. New data gathered with the end goal of the specific study is the primary data. Secondary data will be data, that as of recently has been gathered for some different past purpose yet could be utilized for new study. Primary data has been collected by the judgments of the five experts’ opinion through participant observation in meetings. For credibility the unanimous decisions of experts were taken and also used data in the form of documents.

Research StagesThe research stages are presented in Figure 1. First of all author identified problem, designed

research questions that directed towards the literature review and research methodology defined. The concepts of portfolio management, project selection and prioritization, balancing and strategic alignment reviewed in literature. Then concepts of Fuzzy Analytic Hierarchy process, Chang’s Extended analysis method and TOPSIS method reviewed. From there, a portfolio optimization model developed that guided the entire research process. The model was applied in IT industry by Case study approach. Portfolio optimization is achieved by Chang’s Extended analysis Method where as Strategic Alignment is achieved by using TOPSIS method. Finding and Results were presented. Finally conclusion summarizes research and Recommendations leave suggestions.

Figure 2: Research stages

PORTFOLIO MANAGEMENT

The standard of portfolio 2006 defines portfolio as a group of projects and programs and other efforts that are planned to make conceivable the successful supervision of that work to achieve strategic business objectives. The investments made or planned should be in accordance with the goals and


objectives of strategy of the organization. The main concerns are identified, decisions of investments are taken and resources are assigned in portfolio. (Cooper et al. 2001) proposed that in Portfolio management process, new projects may be assessed, chosen and prioritized. Existing projects may be quickened, executed, or deprioritized and resources are designated and reallocated to the dynamic projects. According to (Cooper et al. 1997) portfolio management has particularly picked up good fame in Research and Development to decide the correct projects to a great degree critical for the organizations in this area. (Engwall et al. 2003) proposed that Multi-project management is an element of portfolio management, as it’s a further extensive and additional intricate methodology that incorporates procedures and strategies for the different parts of portfolio. Multi-project management might be actualized as a part of methodology, yet regularly Multi-project management rises without it to be a part of a specific usage method. Methods, for example Gantt diagrams, PERT and CPM was created around then of the World War II and gradually acclimates by commercial enterprises. In the last part of the twentieth century advancement of methods and techniques started to assess and select projects inside firms. Throughout previous 50 years, many studies have been distributed portraying these methods and techniques and this might be seen as the start of portfolio management as we know it today.( Henriksen & Traynor, 1999)

According to (Crawford et al.2006) projects are of varied nature contingent upon the necessities they serve. They could be sorted dependent upon sort or importance of the project, the engineering questionable matter, or on some configuration that fits the particular organizational undertakings and character .Moreover, a variety in imperativeness, direness, and finish phase of projects exists. (Fricke& Shenbar, 2009) (Patanakul & Milosevic, 2009). (Cooper, 2009) suggests that numerous mulls over in the control of portfolio management affirm the significance of project arrangement alluding to project determination, prioritization and asset distribution dependent upon necessity. In a multi nature's domain, single projects could be created to portfolios and projects to accelerate their management. According to Elonen & Artto, 2003) portfolio management is about 'doing the projects that are right, making a connection from the projects to organization's technique and, synchronously embracing the enduring view.

Prioritization (Gareis, 1991) suggests that numerous studies stress the importance of project determination for portfolio selection. A choice to begin a project needs to be refined in a categorization of the system of projects instead of acknowledging projects in segregation. This view is imparted by Chien (2002) who contends that selecting of singular solid project does not accelerate an optimal portfolio blend. Additionally the generally targets of the portfolio have to be recognized in the choice prepare. The author further notes that existing determination instruments don't address the issue of interrelationships around projects and are lacking to assess nonmonetary variables like project assorted qualities. Chien (2002) separates between four sorts of interrelation: result or specialized, take and asset use, sway and profit, and serial. His exploration is restricted to R&D projects. Müller in participation with Martinsuo and Blomquist (2008) check a positive correspondence of portfolio determination with accomplishing portfolio results and attaining project furthermore program reason. Accordingly, portfolio choice is about arranging projects with system and prioritizing them. Firms distinguished as best entertainers have a tendency to depend on system when selecting projects as opposed to on unimportant monetary strategies. This approach incorporates dispensing assets to distinctive sorts of projects and accelerates expanded portfolio execution. Organizations have by and large two plans B when choosing which projects to begin Firstly, treating all projects similarly the choice could be arranged to a scoring framework. Besides, making classifications and assembling projects in a significant manner. According to (Archer & Ghasemzadeh, 1999) the second choice is supported and inferred that more elevated amount management is required to designate assets to certain project classifications preferably before determination of projects. Five criteria were also defined by (Mikkola, 2001) to rank R&D


projects: vital fit, capability to expand income, capability to make piece of the pie, level of item separation, and engineering headway.

Portfolio Balancing A project portfolio is decently equalized in the event that that it 'empowers an organization to attain the development and benefit targets connected with business technique, without uncovering the organization to excessive risks. (Hill & Jones, 1992). Cooper in (2000) also suggested that high performing portfolios comprise of the right blend of projects while the objective of quality amplification is subordinate. This angle keeps tabs on non-money related variables identified with project determination and choice to equalize the portfolio with respects to project sort, risk stage, and asset ampleness. Meskendahl in (2010) also explained that these measurements may be common subordinate e.g. enduring projects are connected with huge project measure while a higher degree in improvement includes more dangers. An adjusted portfolio might limit the amount of projects in a compelling manner, with the goal that the asset bottleneck might be maintained a strategic distance.

Portfolio Monetary valueThis part will display the objectives of Portfolio management. Much like in money markets, portfolio in R&D needs to streamline their speculations and decide on the appealing novel item plan that provides the generally greatest budgetary quality of the portfolio. (Cooper & Edgett (2008). In place to have the ability to accomplish that, according to Levine (2005) it is crucial that both current and proposed activities are always assessed and surveyed. That will give the portfolio management the chances to drop or delay projects that are not helping the monetary quality of the portfolio and bring in different ones with additional worth potential. There are two stages that should be recognized in the Portfolio optimization. The foremost stage is to select the true project for portfolio and second stage is to manage the portfolio and determine that planned profits will be acknowledged. For stage one, the most well-known methods are the money related ones, for example the (ROI), (NPV) and (IRR). According to Ross (2008) in the connection of portfolio management, the venture with the most elevated NPV might as well under typical circumstances be stacked up the most noteworthy. It is additionally vital to specify that these monetary methods can't be utilized alone to prioritize the projects. The projects are continually assessed and movements taken provided that not executing at right stage. It is likewise essential that organization put in effort to advance the Portfolio optimization transforming always with a specific end goal to uncover the most ideal approaches to supervise the portfolio. That could be accomplished through lessons studied after every undertaking has been finished. Numerous companies have accompanied guidelines, at the top of the priority list, the firms can characterize their plans important for their functions. (Wheelwright & Clark, 1992) Portfolio Strategic Alignment Portfolio Management builds a plan over the projects inside the portfolio, which is key keeping in mind the end goal to verify association with strategy of business. This plan likewise makes it less demanding to update and straighten projects to another system, by disposing or presenting new project, reassigning assets and so forth. Business procedures are continually changing inside organizations and proficient Portfolio management can determine, projects are assessed as well as modified in place general portfolio to be adjusted to the business method at every time. Portfolio management is resolving the issues between the working and project management by aligning the projects to the strategy and verifying that the true projects are accomplished.

In organizations a project is acknowledged firmly, provided that it meets the prerequisites of time, money and quality. At the same time that is insufficient, since provided that it is not arranged to the business procedure it will most likely not conveyed the planned profits to the organization that should empower the organization to make use of the chances and benefit available (Levine, 2005). By taking advantage of techniques introduced for adjusting the projects in portfolio, organizations can fulfill the key necessities.


The point where business and improvement methodologies have been built, the organization needs to think about what activities must be hold keeping in mind the end goal to succeed in the businesses. By this technique, firms can determine that the projects are totally determined. By using techniques in portfolio optimization, it might be guaranteed that the organizations in general are working in accordance with the vital destinations implemented by the higher management. This is vital for the organization to support or pick up focused point of interest available. Organizational Capacity

In today's world usually firms have excessive projects on-striving for the low number of assets. This is an important portfolio where projects are balanced to achieve the businesses. This includes extensive expenses, since a few projects that are started may never have the assets to have the capacity to complete. This is significant that the portfolio has the true number of projects keeping in mind the end goal to have the ability to enhance the quality of the portfolio, and guarantee that the portfolio reflects the business strategy.

FUZZY LOGIC BASED PROJECT PRIORITIZATION Analytic hierarchy process (AHP) AHP is a standout amongst the most generally utilized MADM techniques. Dealing with the multi-criteria choice analysis, the fuzzy set hypothesis could be the very well-known strategy in managing uncertain problems. AHP make the most of "pair-wise relationship" and priority weights criteria. According to Saaty selection is made by developing weights and assessing criteria.

Numerous fuzzy AHP techniques are proposed by different authors. According to Zadeh (1968) the techniques are logical methodologies to possible choice and by using ideas of fuzzy set hypothesis as well as progressive structure analysis. The work was presented in fuzzy AHP, in which fuzzy degrees depicted by triangular fuzzy concepts.( Van Laarhoven & & Pedrycz, 1983). Buckley (1985) confirmed fuzzy requirements of assessment degrees participation capability trapezoidal. Stam et al. (1996) investigated method to confirm or expect the tendency evaluations in AHP. Chang (1996) presented another approach by fuzzy AHP, using triangular fuzzy numbers. Cheng (1997) proposed another calculation for assessing maritime strategic rocket frameworks by FAHP. Another system was presented to assess diverse generation cycle options including the arithmetic fuzzy extended AHP method. (Weck et al.1997). Any generation cycle assessed by this way results a fuzzy set. The conclusion of the investigation can at long last be defuzzified by structuring the surface focus of significance of any fuzzy set. A fuzzy objective as well as subjective system was proposed acquiring the weights from AHP building a fuzzy weighted assessment.(Kahraman et al, 2003). Cheng et al. (1999) proposed another system for assessing weapon frameworks by analytical hierarchy process in view of phonetic variable weight. Zhu et al. (1999) make an assessment on degree analysis strategy and provisions of fuzzy AHP. Another framework of AHP-GP was proposed for quality control by Badri in (2001). Fuzzy AHP model was proposed to measure supplier fulfillment of catering running organization by Cebeci (2003). Yu (2002) incorporates an absolute term linearization technique and a fuzzy rating expression into a GP-AHP model for solving group decision-making fuzzy AHP problem. Another approach that provides an analytical tool to select the best Turkish catering firm providing the better customer satisfaction was proposed by (Kahraman et al (2003). Failure of AHP to manage the imprecision and subjectiveness in the pair-wise comparison process has been enhanced in fuzzy AHP. According to Kuswandari (2004) rather than a fresh worth, fuzzy AHP attain quality to consolidate the choice creator's doubt. A calculation was also offered that is the immediate growth of Saaty's AHP strategy by Van Laarhoven & Pedrycz (1983). They distinguished the weights through the AHP procedure. In that study, Laarhoven and Pedrycz used the triangular fuzzy numbers. The Lootsma's logarithmic minimum squares strategy is utilized to determine fuzzy weights and fuzzy execution


scores (Chen et al., 1992). Buckley additionally developed Saaty's AHP technique to combine fuzzy correlation degrees. He called attention to that Van Laarhoven and Pedrycz's (1983) strategy was liable to two issues. Initially, the direct comparisons of obtained mathematical statements don't dependably have a novel result. Second, they demanded getting triangular fuzzy numbers for their weights.

Choices are made today in even more unpredictable situations. The fuzzy AHP gives a planned technique for assessment and weighting of the different criteria and options. Numerous possible fuzzy AHP systems exist in literature. The issue that one is better than any possible has not yet been settled. Furthermore it is likely to meet new fuzzy AHP strategies within a limited period of time. Generally, these strategies couldn't be called AHP-based multi-criteria decision making strategies.

A Multi-Attribute Evaluation Method The AHP has been applied within several diverse fields as a multi-attribute evaluation method with different options and criteria. A far reaching literary works survey on AHP might be discovered by Vaidya &Kumar (2006). AHP make the most of "pair-wise comparisons" and framework to weigh criteria. The choice is made by utilizing the inferred weights of the evaluative criteria (Saaty, 1980). After the hierarchy of the issue is built, the frameworks of pair wise correlations are acquired. CaseStudyThe papers on portfolio management in literature are so important and the outcomes of the literature review are expected to provide contributions by using fuzzy approach and structuring the hierarchic criterion on portfolio optimization. Table 1 illustrates the criterion structure, referred from expert opinions and previous studies, on portfolio management as the outcomes of the literature review. As the original taxonomies on optimization of portfolio, the main element can be divided into five main criteria such as Marketing, Finance, IT, Legal and Sales. Market Segmentation, Consumer Buying Behavior and Market Trends are the sub criteria of Marketing while ROI, NPV and IRR are the sub criteria of Finance. Information Technology includes Technology, Services and Licenses and Legal has sub criteria Laws and Regulations, Consistency with Government policies and Agreements/ Contracts. Action of suppliers, Revenue and profit margin is taken in Sales. The illustrative application is performed on the case of IT industry. A multiple criteria decision-making methodology, FAHP is determined to ensure the judgments of the related experts in an efficient manner. The description about alternatives/projects is given below: Projects Enterprise Data Warehouse Project (EDWP) Modern day organizations have multiple applications and databases to manage their daily operations and organizational flows. Applications include CRM, ERP, Call Centre and many more. Data and Information of all these sources is mostly scattered, and it is a cumbersome process to take decisions based on this scattered information. Enterprise data warehouse project allows organizations to consolidate all the information in a single structure and give them a single version of truth. EDW project includes extracting all the information from different sources and consolidating it in a single source. EDW acts as a Decision supports system as well as analytical reporting system. Advanced Analytics (AA) Advanced analytics gives a deep analysis on all aspects of data. Advanced analytics is mostly used for predictive analysis. Data mining also uses machine learning algorithms to train model and then use them to predict future events that can affect the business. Churn prediction, revenue drop predictions are some of the applications of advanced analytics. Revenue Assurance (RA) Revenue assurance is used for auditing of all revenues in an enterprise. Controls are developed to compare data at different levels to detect and flag any unexpected discrepancies. Revenue assurance is also used to maintain an audit trail to detect fraud.


Campaign Management System (CMS) Campaign management system is used to design and offer customers with most suited campaigns. Campaign management system reduces the target audience for any campaign by selecting the most suitable customers. Campaign management system helps in increasing the effectiveness of campaigns which results in increasing the revenues. Locational Intelligence (LI) Locational intelligence gives a picture of different KPI’s including revenue, traffic on a map. Interactive maps enable the users to drill down into different areas and detect any unusual dropage of revenue or traffic. Strategic placement of ATM’s in banking and cell sites in telecom organizations are some of the applications of Locational intelligence.

Table 16: Structure of Hierarchy

Structure of Hierarchy problem on portfolio optimization Criterias C1, C2, ………..Cn Marketing C1

Market Segmentation C11

Consumer Buying Behavior C12

Market Trends C13 Finance C2

Return on Investment C21 Net Present Value C22 Internal Rate of Return C23

Information Technology C3 Technology C31 Services C32 Licenses C33

Legal C4 Laws/Regulations C41 Consistency with Government policies C42 Agreements/ Contracts C43

Sales C5 Action of Suppliers C51 Revenues/ Targets C52 Profit Margin C53

Alternatives (Projects) A1, A2, ………..An Enterprise Data Warehouse Project(EDWP) Advanced Analytics/ Data mining(AA) Revenue Assurance (RA) Campaign Management System (CMS) Locational Intelligence (LI)

FuzzyanalytichierarchyprocessandChang’sextendedanalysis

FAHP methodology is initially dependent upon the idea of fuzzy set hypothesis, presented by Zaddeh (1965). Research of hierarchical structures in nature, at first proposed by Buckley (1985), who was


analyzed representations of leaders with respect to the pair wise comparisons while using fuzzy degrees rather than crisp values. The fundamental attributes of distinctive methodologies on explaining FAHP-based models by communicating their focal points and weaknesses with a few perspectives were presented (Büyüközkan et al,2004). One of the most recent approaches on result techniques of FAHP methodology is taking into account Chang's extent analysis method. In research, core issue is assessed by using FAHP philosophy with the result methodologies of Chang's extent analysis. The Chang's extent analysis is reasonably simple while thinking about alternate approaches on FAHP. Chang (1992, 1996) illustrated the fundamental reasoning behind this hypothesis and the proposed methodology was backed with true case applications. (Zhu et al. 1999) described key points of extent analysis method by using triangular fuzzy numbers in FAHP applications. The principal venture in this system is to utilize triangular fuzzy numbers for pair wise judgment by method of FAHP scale, and then approach of extent analysis method is applied to acquire required weights. The hypothetical essentials of Chang's extent analysis on FAHP were characterized in four steps as accompanies by considering the past papers (Erensal, Oncan, & Demircan, 2005; Kahraman, Cebeci, & Ruan, 2004) in literature.

The two sets, , , … . . , as an object set, and as a goal set, , , …… . could be characterized in beginning stage. Consistent with the standards of Chang's extent analysis, every object is recognized in the same way, and extent analysis for each of the goal, is obtained. It implies that it is conceivable to acquire the values of m extent analyses that could be exhibited as

, , …… . . , , 1,2, …… . . , Where 1,2, … . . , are triangular fuzzy numbers. Once we identified the first assumptions, Chang’s extent analyses could be analyzed in these main steps. Step 1: The value of fuzzy synthetic extent in accordance with ith object is shown as

& fuzzy addition function of m extent analysis values can be achieved for specific matrix by

∑ ∑ ,∑ , ∑ in order to get ∑ , . After this the fuzzy addition

function of (j=1,2,……,m) values i.e.

∑ ∑ ∑ , ∑ , ∑ are carried out to get ∑ ∑ , . Finally the

inverse of determined vector can be shown as follows.

1

∑,

1∑

,1

∑

Step 2: Degree of possibility of , , , , is expressed as min , and it is shown as follows:


∩

=

1, ,0, ,

,

Here d is the ordinate of the highest intersection point between & . In order to compare we require both values of and . Step 3: Degree possibility of a convex fuzzy number should be larger than k convex fuzzy numbers 1,2, … . . , and described as

, , …… , and

… . min

1,2, ……… . , . Suppose that d'(Ai) = min V(Si ≥ Sk) For k = 1,2,….,n; k is not equivalent to i. Therefore the weight vector computed is W' = (d' (A1),d' (A2),…,d' (An) )T, here Ai (I = 1, 2 ,….n) are n elements. Step 4: By the use of normalization, the normalized weight vectors are W= (d(A1), d(A2)…..,d (An))T here W is a non fuzzy number representing priority weights of an alternative over other. A large portion of the FAHP functions on different cases might be found in literature dependent upon Chang's extent analysis. This technique was also used by Kwong, & Bai (2003) to prioritize customer pre requisites in the QFD. Based on Chang's extent analysis, the link between competitiveness and technology management was built by Erensal et al. (2005) utilizing FAHP. In literature work was also done on incorporating a FAHP approach, to assess alternatives of knowledge development tools.( Kreng & Wu, (2007). Also trend of papers with respect to the FAHP applications is increasing. A model was proposed on supplier worldwide development issue by using FAHP as a different criteria choice making approach that was risk based global supplier development model with extended AHP-based methodology (Nagahanumaiah & Mukherjee, 2007). Bozbura, Beskese, and Kahraman (2007) furthermore Bozbura and Beskese (2007) proposed methodology by using an approach dependent upon the extent FAHP in fuzzy environment to confirm the priorities of human capital estimation indicators. FAHP-based ranking structure for semiconductor fabrication was developed by Kang and Lee (2007).The use of FAHP in published papers is in progress in large portion in different fields. Application of fuzzy analytic hierarchy process on portfolio optimization problem In the remaining part of thesis, the proposed decision model is applied for portfolio optimization in order to obtain illustrative results. By discussions with the experts, it is decided to perform the model with five of the portfolio projects. Finally, the hierarchic structure of the proposed model on case analysis is illustrated in Fig. 2. The model can be achieved to extend to cover the whole of the projects by determining the scope of the decision model. However, it is concentrated in this thesis on five of the alternatives as a pilot application. Series of meeting was organized with contribution of sector representatives and professionals for determining the expert opinions on hierarchical model in order to achieve tangible results with higher utility. The experts used the assessment scale showing in Table 2.


Long run discussions were made on pair wise comparisons with the experts to ensure the different projects relating to relevant criteria and comparisons are showing in Tables 9-23.

Figure 3: Model of Portfolio Optimization

Table 17: Fuzzy Analytic Hierarchy Process Scale [45]

Description Scale Equal (1,1,1) Weak (2/3,1,3/2) Fairly Strong (3/2,2,5/2) Very Strong (5/2,3,7/2) Absolute (7/2,4,9/2)

FINDINGS AND RESULTS

Chang’s Method The main criteria and sub criteria on portfolio optimization are compared in tables, 3-8, on the other hand comparative evaluation of alternatives/ projects with respect to relevant attributes are illustrated in Table 9–21 correspondingly.


Table 18 : Assessment of Project Selection Criteria relating to Goal

Marketing Finance IT Legal Sales Marketing 1,1,1 7/2,4,9/2 5/2,3,7/2 5/2,3,7/2 5/2,3,7/2

Finance 2/9,1/4,2/7 1,1,1 3/2,2,5/2 5/2,3,7/2 5/2,3,7/2 IT 2/7,1/3,2/5 2/5,1/2,2/3 1,1,1 3/2,2,5/2 5/2,3,7/2

Legal 2/7,1/3,2/5 2/7,1/3,2/5 2/5,1/2,2/3 1,1,1 7/2,4,9/2 Sales 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 2/9,1/4,2/7 1,1,1

Table 19: Assessment of Sub Criteria of Marketing

Market Segmentation

Consumer Buying Behavior

Market Trends

Market Segmentation 1,1,1 5/2,3,7/2 5/2,3,7/2 Consumer Buying Behavior 2/7,1/3,2/5 1,1,1 5/2,3,7/2

Market Trends 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1

Table 20 : Assessment of Sub Criteria of Finance

ROI NPV IRR ROI 1,1,1 5/2,3,7/2 2/7,1/3,2/5 NPV 2/7,1/3,2/5 1,1,1 2/5,1/2,2/3 IRR 5/2,3,7/2 3/2,2,5/2 1,1,1

Table 21 : Assessment of Sub Criteria of IT

Technology Services Licenses Technology 1,1,1 2/7,1/3,2/5 2/9,1/4,2/7

Services 5/2,3,7/2 1,1,1 2/5,1/2,2/3 Licenses 7/2,4,9/2 3/2,2,5/2 1,1,1

Table 22 : Assessment of Sub Criteria of Legal

Laws and Regulations

Consistency with Govt. policies

Agreements/ Contracts

Laws and Regulations 1,1,1 2/9,1/4,2/7 5/2,3,7/2 Consistency with Govt. policies

7/2,4,9/2 1,1,1 7/2,4,9/2

Agreements/ Contracts 2/7,1/3,2/5 2/9,1/4,2/7 1,1,1

Table 23 : Assessment of Sub Criteria of Sales

Action of Suppliers

Revenue Profit Margin

Action of Suppliers 1,1,1 5/2,3,7/2 2/7,1/3,2/5 Revenue 2/7,1/3,2/5 1,1,1 2/9,1/4,2/7

Profit Margin 5/2,3,7/2 7/2,4,9/2 1,1,1


Table 24 : Assessment of Projects relating to Market Segmentation

EDWP AA RA CMS LI EDWP 1,1,1 5/2,3,7/2 2/7,1/3,2/5 2/9,1/4,2/7 2/9,1/4,2/7

AA 2/7,1/3,2/5 1,1,1 2/3,1,3/2 2/7,1/3,2/5 3/2,2,5/2 RA 5/2,3,7/2 2/3,1,3/2 1,1,1 2/5,1/2,2/3 2/3,1,3/2

CMS 7/2,4,9/2 5/2,3,7/2 3/2,2,5/2 1,1,1 3/2,2,5/2 LI 7/2,4,9/2 2/5,1/2,2/3 2/3,1,3/2 2/5,1/2,2/3 1,1,1

Table 25: Assessment of Projects relating to Consumer Buying Behavior

EDWP AA RA CMS LI EDWP 1,1,1 5/2,3,7/2 5/2,3,7/2 2/9,1/4,2/7 3/2,2,5/2

AA 2/7,1/3,2/5 1,1,1 2/7,1/3,2/5 2/7,1/3,2/5 3/2,2,5/2 RA 2/7,1/3,2/5 5/2,3,7/2 1,1,1 2/5,1/2,2/3 2/5,1/2,2/3

CMS 7/2,4,9/2 5/2,3,7/2 3/2,2,5/2 1,1,1 2/7,1/3,2/5 LI 2/5,1/2,2/3 2/5,1/2,2/3 3/2,2,5/2 5/2,3,7/2 1,1,1

Table 26: Assessment of Projects relating to Market Trends

EDWP AA RA CMS LI EDWP 1,1,1 2/7,1/3,2/5 5/2,3,7/2 2/7,1/3,2/5 2/5,1/2,2/3

AA 5/2,3,7/2 1,1,1 2/7,1/3,2/5 2/7,1/3,2/5 2/5,1/2,2/3 RA 7/2,4,9/2 5/2,3,7/2 1,1,1 2/5,1/2,2/3 2/3,1,3/2

CMS 5/2,3,7/2 5/2,3,7/2 3/2,2,5/2 1,1,1 7/2,4,9/2 LI 3/2,2,5/2 3/2,2,5/2 2/3,1,3/2 2/9,1/4,2/7 1,1,1

Table 27: Assessment of Projects relating to ROI


AA 2/7,1/3,2/5 1,1,1 2/7,1/3,2/5 2/7,1/3,2/5 3/2,2,5/2 RA 2/7,1/3,2/5 5/2,3,7/2 1,1,1 2/7,1/3,2/5 2/3,1,3/2

CMS 7/2,4,9/2 5/2,3,7/2 5/2,3,7/2 1,1,1 2/7,1/3,2/5 LI 2/5,1/2,2/3 2/5,1/2,2/3 2/3,1,3/2 5/2,3,7/2 1,1,1

Table 28 : Assessment of Projects relating to NPV

EDWP AA RA CMS LI EDWP 1,1,1 3/2,2,5/2 5/2,3,7/2 3/2,2,5/2 3/2,2,5/2

AA 2/5,1/2,2/3 1,1,1 2/3,1,3/2 2/7,1/3,2/5 2/3,1,3/2 RA 2/7,1/3,2/5 2/3,1,3/2 1,1,1 3/2,2,5/2 2/3,1,3/2

CMS 2/5,1/2,2/3 5/2,3,7/2 2/5,1/2,2/3 1,1,1 2/3,1,3/2


LI 2/5,1/2,2/3 2/3,1,3/2 2/3,1,3/2 2/3,1,3/2 1,1,1

Table 29: Assessment of Projects relating to IRR

EDWP AA RA CMS LI EDWP 1,1,1 2/3,1,3/2 2/7,1/3,2/5 2/5,1/2,2/3 3/2,2,5/2

AA 2/3,1,3/2 1,1,1 5/2,3,7/2 3/2,2,5/2 2/3,1,3/2 RA 5/2,3,7/2 2/7,1/3,2/5 1,1,1 2/3,1,3/2 2/3,1,3/2

CMS 3/2,2,5/2 2/5,1/2,2/3 2/3,1,3/2 1,1,1 2/3,1,3/2 LI 2/5,1/2,2/3 2/3,1,3/2 2/3,1,3/2 2/3,1,3/2 1,1,1

Table 30 : Assessment of Projects with relating to Technology


AA 2/7,1/3,2/5 1,1,1 2/3,1,3/2 5/2,3,7/2 3/2,2,5/2 RA 2/7,1/3,2/5 2/3,1,3/2 1,1,1 2/3,1,3/2 2/3,1,3/2

CMS 2/7,1/3,2/5 2/7,1/3,2/5 2/3,1,3/2 1,1,1 3/2,2,5/2 LI 2/7,1/3,2/5 2/5,1/2,2/3 2/3,1,3/2 2/5,1/2,2/3 1,1,1

Table 31 : Assessment of Projects relating to Services


AA 2/7,1/3,2/5 1,1,1 3/2,2,5/2 5/2,3,7/2 3/2,2,5/2 RA 2/7,1/3,2/5 2/5,1/2,2/3 1,1,1 3/2,2,5/2 3/2,2,5/2

CMS 2/7,1/3,2/5 2/7,1/3,2/5 2/5,1/2,2/3 1,1,1 3/2,2,5/2 LI 2/7,1/3,2/5 2/5,1/2,2/3 2/5,1/2,2/3 2/5,1/2,2/3 1,1,1

Table 32: Assessment of Projects with relating to Licenses


AA 2/7,1/3,2/5 1,1,1 2/3,1,3/2 5/2,3,7/2 3/2,2,5/2 RA 2/7,1/3,2/5 2/3,1,3/2 1,1,1 2/3,1,3/2 3/2,2,5/2

CMS 2/7,1/3,2/5 2/7,1/3,2/5 2/3,1,3/2 1,1,1 5/2,3,7/2 LI 2/7,1/3,2/5 2/5,1/2,2/3 2/5,1/2,2/3 2/7,1/3,2/5 1,1,1

Table 33 : Assessment of Projects relating to Laws and Regulations


AA 2/7,1/3,2/5 1,1,1 5/2,3,7/2 5/2,3,7/2 5/2,3,7/2


RA 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 2/7,1/3,2/5 5/2,3,7/2 CMS 2/7,1/3,2/5 2/7,1/3,2/5 5/2,3,7/2 1,1,1 5/2,3,7/2

LI 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1

Table 34: Assessment of Projects relating to Consistency with Government policies


AA 2/9,1/4,2/7 1,1,1 5/2,3,7/2 5/2,3,7/2 5/2,3,7/2 RA 2/9,1/4,2/7 2/7,1/3,2/5 1,1,1 5/2,3,7/2 5/2,3,7/2 CMS 2/9,1/4,2/7 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 5/2,3,7/2

LI 2/9,1/4,2/7 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1

Table 35: Assesment of Projects relating to Agreements/ Contracts


AA 2/7,1/3,2/5 1,1,1 5/2,3,7/2 5/2,3,7/2 2/7,1/3,2/5 RA 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 5/2,3,7/2 2/7,1/3,2/5

CMS 5/2,3,7/2 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 5/2,3,7/2 LI 2/7,1/3,2/5 5/2,3,7/2 5/2,3,7/2 2/7,1/3,2/5 1,1,1

Table 36: Assesment of Projects relating to Action of Suppliers


AA 2/7,1/3,2/5 1,1,1 3/2,2,5/2 5/2,3,7/2 5/2,3,7/2 RA 2/7,1/3,2/5 2/5,1/2,2/3 1,1,1 2/3,1,3/2 5/2,3,7/2

CMS 2/7,1/3,2/5 2/7,1/3,2/5 2/3,1,3/2 1,1,1 5/2,3,7/2 LI 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1

Table 37: Assesment of Projects relating to Revenues

EDWP AA RA CMS LI EDWP 1,1,1 3/2,2,5/2 5/2,3,7/2 2/5,1/2,2/3 2/5,1/2,2/3

AA 2/5,1/2,2/3 1,1,1 2/3,1,3/2 5/2,3,7/2 2/7,1/3,2/5 RA 2/7,1/3,2/5 2/3,1,3/2 1,1,1 5/2,3,7/2 2/7,1/3,2/5

CMS 3/2,2,5/2 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 2/3,1,3/2 LI 3/2,2,5/2 2/7,1/3,2/5 5/2,3,7/2 2/3,1,3/2 1,1,1

Table 38: Assessment of Projects relating to Profit Margin

EDWP AA RA CMS LI


EDWP 1,1,1 3/2,2,5/2 5/2,3,7/2 2/5,1/2,2/3 2/5,1/2,2/3

AA 2/5,1/2,2/3 1,1,1 2/3,1,3/2 5/2,3,7/2 2/7,1/3,2/5 RA 2/7,1/3,2/5 2/3,1,3/2 1,1,1 5/2,3,7/2 2/7,1/3,2/5

CMS 3/2,2,5/2 2/7,1/3,2/5 2/7,1/3,2/5 1,1,1 2/3,1,3/2 LI 3/2,2,5/2 5/2,3,7/2 5/2,3,7/2 2/3,1,3/2 1,1,1

For clear identification of computation stages, the pair wise judgments from Table 3 are assessed as follows: From Table 3

SMKT = (12, 14, 16) (1/44.30, 1/38.50, 1/32.96) = (0.27, 0.36, 0.49)

SFIN = (7.72, 9.25, 10.79) (1/44.30, 1/38.50, 1/32.96) = (0.17, 0.24, 0.33)

SIT = (5.69, 6.83, 8.07) (1/44.30, 1/38.50, 1/32.96) = (0.13, 0.18, 0.24)

SLEG= (5.47, 6.17, 6.97) (1/44.30, 1/38.50, 1/32.96) = (0.12, 0.16, 0.21)

SSAL= (2.08, 2.25, 2.49) (1/44.30, 1/38.50, 1/32.96) = (0.047, 0.058, 0.08)

After computing these results

V (SMKT ≥ SFIN ) = 1.00

V (SMKT ≥ SIT ) = 1.00

V (SMKT ≥ SLEG ) = 1.00

V (SMKT ≥ SSAL ) = 1.00

V (SFIN ≥ SMKT) = 0.20

V (SFIN ≥ SIT) = 1.00

V (SFIN ≥ SLEG) = 1.00

V (SFIN ≥ SSAL) = 1.00

V (SIT ≥ SMKT) = 0.00

V (SIT ≥ SFIN) = 0.53

V (SIT ≥ SLEG) = 1.00

V (SIT ≥ SSAL) = 1.00

V (SLEG ≥ SMKT) = 0.00

V (SLEG ≥ SFIN) = 0.32

V (SLEG ≥ SIT) = 0.83

V (SLEG ≥ SSAL) = 1.00


V (SSAL ≥ SMKT) = 0.00

V (SSAL ≥ SFIN) = 0.00

V (SSAL ≥ SIT) = 0.00

V (SSAL ≥ SLEG) = 0.00

are attained. Therefore from Table 3 the weight vector computed is WG = (0.83, 0.17, 0.00, 0.00, 0.00). The other assessments are made by using same approach and priority weights are :

The computation of weight vector of Table 4 is WMKT=(0.91, 0.09, 0.00)

The computation of weight vector of Table 5 is WFIN=(0.31,0.00,0.69)

The computation of weight vector of Table 6 is WIT=(0.00, 0.09, 0.91)

The computation of weight vector of Table 7 is WLEG=(0.00,1.00, 0.00)

The computation of weight vector of Table 8 is WSAL=(0.00,0.00,1.00)

The computation of weight vector of Table 9 is WMS=(0.00, 0.00, 0.00,1.00,0.00)

The computation of weight vector of Table 10 is WCBB=(0.34,0.00, 0.00,0.42, 0.24)

The computation of weight vector of Table 11 is WMT=(0.00, 0.00,0.00,1.00, 0.00)

The computation of weight vector of Table 12 is WROI=(0.39, 0.00,0.00, 0.59, 0.02)

The computation of weight vector of Table 13 is WNPV =(0.51,0.00, 0.17, 0.21, 0.11)

The computation of weight vector of Table 14 is WIRR= (0.14, 0.30, 0.23, 0.19, 0.14)

The computation of weight vector of Table 15 is WT=(0.86, 0.14, 0.00,0.00, 0.00)

The computation of weight vector of Table 16 is WS=(0.81, 0.19, 0.00,0.00,0.00)

The computation of weight vector of Table 17 is WL=(0.88,0.12, 0.00, 0.00, 000)

The computation of weight vector of Table 18 is WL&R=(0.63, 0.30, 0.00, 0.07, 0.00)

The computation of weight vector of Table 19 is WCGP=(0.98,0.02,0.00, 0.00,0.00)

The computation of weight vector of Table 20 is WAC=(0.43,0.15,0.00, 0.21,0.21)

The computation of weight vector of Table 21 is WAS=(0.74,0.26,0.00, 0.00,0.00)

The computation of weight vector of Table 22 is WR=(0.25,0.14,0.12, 0.02,0.47)

The computation of weight vector of Table 23 is WPM=(0.25,0.14,0.12, 0.02,0.47)

Relating to relevant sub-criteria priority weights of projects are showing in Tables 24–28. At last, global priority weights are showing in Table 29. The assessments conclude, CMS is the best project having priority weight of 0.3336. Accordingly, portfolio ranking is showing in Table 30.


Table 39 : Projects Priority weights relating to Marketing Sub Criteria

Market Segmentation

Consumer Buying

Behavior

Market Trends Priority Weight

Sub Criteria of Marketing Projects 0.91 0.09 0.00 EDWP 0.00 0.34 0.00 0.032

AA 0.00 0 0.00 0.000 RA 0.00 0 0.00 0.005

CMS 1.00 0.42 1.00 0.941 LI 0.00 0.24 0.00 0.022

Table 40 : Projects Priority weights relating to Finance Sub Criteria

ROI NPV IRR Priority WeightSub Criteria of Finance

Projects 0.31 0.00 0.69 EDWP 0.39 0.51 0.14 0.219

AA 0.00 0.00 0.30 0.210 RA 0.00 0.17 0.23 0.158

CMS 0.59 0.21 0.19 0.313 LI 0.02 0.11 0.14 0.100

Table 41 : Projects Priority weights relating to Information Technology Sub Criteria

Technology Services Licenses Priority WeightSub Criteria of IT

Projects 0.00 0.09 0.91 EDWP 0.86 0.81 0.88 0.874

AA 0.14 0.19 0.12 0.126 RA 0.00 0.00 0.00 0.000

CMS 0.00 0.00 0.00 0.000 LI 0.00 0.00 0.00 0.000

Table 42 : Projects Priority weights relating to Legal Sub Criteria

Laws and Regulations

Consistency with Govt.

Policies

Agreements/ Contracts

Priority Weight

Sub Criteria of Legal Projects 0.00 1.00 0.00

EDWP 0.63 0.98 0.43 0.979 AA 0.30 0.02 0.15 0.021 RA 0.00 0.00 0.00 0.000


CMS 0.07 0.00 0.21 0.000 LI 0.00 0.00 0.21 0.000

Table 43 : Projects Priority weights relating to Sales Sub Criteria

Action of Suppliers

Revenue Profit Margin Priority Weight

Sub Criteria of Sales Projects 0.00 0.00 1.00

EDWP 0.74 0.25 0.25 0.247 AA 0.26 0.14 0.14 0.142 RA 0.00 0.12 0.12 0.120

CMS 0.00 0.02 0.02 0.023 LI 0.00 0.47 0.47 0.468

Table 44 : Projects priority weights with relating to Goal

Marketing Finance IT Legal Sales Priority Weight

Main Criteria of Goal Projects 0.83 0.17 0.00 0.00 0.00

EDWP 0.032 0.219 0.874 0.979 0.247 0.2559 AA 0.000 0.210 0.126 0.021 0.142 0.1435 RA 0.005 0.158 0.000 0.000 0.120 0.1233

CMS 0.941 0.313. 0.000 0.000 0.023 0.3336 LI 0.022 0.100 0.000 0.000 0.468 0.1437

Table 45: Ranking of Projects

Rank Projects Priority weights 1 CMS 0.3336 2 EDWP 0.2559 3 LI 0.1437 4 AA 0.1435 5 RA 0.1233 Strategic Alignment: In strategic Alignment, five objectives have been finalized after discussion with the experts, which are given below:

Table 46 : Structure of Hierarchy on Strategic Alignment

Structure of Hierarchy on Strategic Alignment Objectives OBJ1, OBJ 2, ………..OBJ n

Resource Alignment OBJ1 Project Costs OBJ2 Infrastructure Growth OBJ3 Skill Set Development OBJ4 Process Improvement OBJ5


Alternatives A1, A2, ………..An Enterprise Data Warehouse Project(EDWP) Advanced Analytics/ Data mining(AA) Revenue Assurance (RA) Campaign Management System (CMS) Locational Intelligence (LI)

Technique for Order Preference by Similarity to Ideal Solution TOPSIS

TOPSIS method was developed by Kwangsun Yoon and Hwang Ching-Lai in 1980. According to (Dodangeh et al, 2009)This approach takes into account three types of aspects or Criteria.

i. Quantitative benefit Criteria ii. Qualitative benefit aspects/criteria

iii. Cost aspects or criteria Two artificial alternatives are hypothesized in TOPSIS method

i. Ideal alternative: the one which has the best level for all aspects considered. ii. Negative ideal alternative: the one which has the worst criteria values.

The basic concept in TOPSIS is to choose the alternative that is the closest to the ideal solution and farthest from negative ideal alternative. (Önüt & Soner, 2008).In TOPSIS method we take m alternatives and n criteria and we have the score of each option with respect to each criterion. The score is assigned on a scale from 1-10, and criteria weight from 0.1 to 1.0 by expert judgments. Suppose xij is score of option i with respect to criterion j and we have a matrix X = (xij) mn matrix. J is the set of benefit aspects or criteria (more is better) and J' is the set of negative aspects or criteria (less is better). (Tsaur et al. (2002).

Step 1: Construct normalized decision matrix. This step converts various aspect dimensions into non-dimensional aspects that help for comparisons across criteria. Normalize scores or data as follows: rij = xij/ (x2

ij) for i = 1… m; j = 1… n

Step 2: Construct the weighted normalized decision matrix.

Suppose we have a set of weights for each criteria wj for j = 1…n. After that we have to multiply

each column of the normalized decision matrix by its associated weight. An element of the new

matrix is:

vij = wj rij Table 47: Decision Matrix

Weights 0.3 0.2 0.2 0.1 0.2

Resource Alignment

Project costs

Infrastructure Growth

Skill set Development

Process Improvement

EDWP 9 8 6 6 9AA 6 7 9 9 6RA 7 7 7 8 7CMS 8 8 8 9 8LI 6 7 8 8 7


Table 48 : Normalized decision matrix

Weight 0.3 0.2 0.2 0.1 0.2

Resource Alignment

Project costs

Infrastrure Growth


Process Improvement

EDWP 81 64 36 36 81AA 36 49 81 81 36RA 49 49 49 64 49CMS 64 64 64 81 64LI 36 49 64 64 49∑ 266 275 294 326 279√ 16.31 16.58 17.15 18.06 16.70

Table 49 : Weighted normalized decision matrix

Weight 0.3 0.2 0.2 0.1 0.2

Resource Alignment

Project costs

Infrastrure Growth


Process Improvement

EDWP 0.55 0.48 0.35 0.33 0.54AA 0.37 0.42 0.52 0.50 0.36RA 0.43 0.42 0.41 0.44 0.42CMS 0.49 0.48 0.47 0.50 0.48LI 0.37 0.42 0.47 0.44 0.42

Step 3: Determine the ideal and negative ideal solutions

Ideal solution

A* = {v1* … vn

*}, where

vj*

={ max (vij) if j J ; min (vij) if j J' }

Negative ideal solution

A' = {v1’ …

vn'}, where

v' = { min (vij) if j J ; max (vij) if j J' }

Table 50: ideal and negative ideal solutions

Weight 0.3 0.2 0.2 0.1 0.2


Resource

Alignment Project costs

Infrastrure Growth


Process Improvement

EDWP 0.166 0.096 0.070 0.033 0.108 AA 0.110 0.084 0.105 0.050 0.072 RA 0.129 0.084 0.082 0.044 0.084

CMS 0.147 0.096 0.093 0.050 0.096 LI 0.110 0.084 0.093 0.044 0.084

Ideal Solution

A* = {0.166, 0.084, 0.105, 0.050,0.108}

Negative Ideal Solution

A'= {0.110, 0.096, 0.070,0.033,0.072}

Step 4: Calculate the separation measures for each alternative.

The separation from the ideal alternative is: Si

* = [ (vj

*– vij)2 ] ½ i = 1…, m j

Table 51 : separation from the ideal alternative

Resource Alignment

Project costs

Infrastrure Growth


Process Improvement Sum Si*

EDWP 0.000000 0.000145 0.001224 0.000276 0.000000 0.00164

6 0.040571

AA 0.003045 0.000000 0.000000 0.000000 0.001290 0.00433

5 0.065844

RA 0.001353 0.000000 0.000544 0.000031 0.000573 0.00250

2 0.050018

CMS 0.000338 0.000145 0.000136 0.000000 0.000143 0.00076

3 0.027627

LI 0.003045 0.000000 0.000136 0.000031 0.000573 0.00378

5 0.061525 Similarly, the separation from the negative ideal alternative is: S'i = [ (vj' – vij)2 ] ½ i = 1, …, m j

Table 52: separation from the negative ideal alternative


Resource Alignment

Project costs

Infrastrure Growth


Process Improvement Sum Si'

EDWP 0.003045 0.000000 0.000000 0.000000 0.001290 0.00433

5 0.065844

AA 0.000000 0.000145 0.001224 0.000276 0.000000 0.00164

6 0.040571

RA 0.000338 0.000145 0.000136 0.000123 0.000143 0.00088

6 0.029764

CMS 0.001353 0.000000 0.000544 0.000276 0.000573 0.00274

7 0.052413

LI 0.000000 0.000145 0.000544 0.000123 0.000143 0.00095

6 0.030915 Step 5: Calculate the relative closeness to the ideal solution Ci

* Ci*=Si'/(Si*+Si')

Table 53: Relative Closeness

Projects Ci* EDWP 0.62

AA 0.38 RA 0.37

CMS 0.65 LI 0.33

Select the option with Ci

* closest to 1. Table 54: Ranking

Ranking projects Relative Closeness to Ideal

Solution 1 CMS 0.65 2 EDWP 0.62 3 AA 0.38 4 RA 0.37 5 LI 0.33

CONCLUSION AND RECOMMENDATIONS

In this research, MCDM on portfolio optimization in fuzzy environment is constructed and the proposed model is applied on the case of IT industry. The practical contributions of the model are keenly expected in real case applications by concentrating on the existing problems. It is


clearly seemed during portfolio optimization, the FAHP methodology provides significant support to the decision makers for assigning the judgments on related pairwise comparisons.

The first question was to find out the important criteria and sub criteia in portfolio management. Marketing, Finance, IT, Legal and Sales were taken as the criteria and with respect to each criteria, sub criteria were defined based on the expert judgments and literature Review. Finally the summary of results proves that the Marketing is the leading criteria in portfolio optimization (priority weight 0.83) where as criteria of finance also have impact on results (priority weight 0.17). Especially, the sub criteria of market segmentation (priority weight 0.91) and internal rate of return (priority weight 0.69) have unique role in decision making.

In order to answer the second question, Chang’s Extended Analysis Method was applied that provided the priority weights of the projects. The projects were assessed with respect to each criteria and sub criteria. As the overall results of the case application, the campaign management system project is found to be the best in portfolio (priority weight 0.336).

After achieving the priority of projects in portfolio, next step was to find out that how portfolio is strategically aligned and congruent with the defined criteria. In order to achieve this alignment, five objectives were defined. These were Resource Alignment, Projects Costs, Infrastructure growth, Skill set development and Process Improvement. This part was achieved by using the TOPSIS method. The experts again provided the judgments about projects with respect to each objective. With respect to strategic alignment Campaign management system project also found to be the best project having value (0.65) close to 1.

The last question was about providing proposed recommendations for the organizations hence concluding other highlighted results, the projects of Advance Analytics (AA) and Revenue Assurance (RA) are not meeting the expectations of marketing criteria in portfolio optimization. Therefore, there is an urgent need to modify the existing procedures of AA and RA. It can also be concluded from results that profit margin is very important for the organizations to operate their business. Similarly the way in which organizations do their business and procedures should be consistent with Government policies. The results also show each hardware and software should have the proper licenses. So each table represents the significance of each aspect as well information about the project. The scope of the case application can be determined to extent and the structure of the proposed model can be modified by considering the priority weights of attributes. On the other hand, application of the other multiple criteria decision-making methodologies on the same case can be discussed in advance as further research proposals.

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Saunders, M., Lewis, P. & Thornhill, A. (2009). Research methods for business students (Sixth ed.). England: Pearson Education Limited. Yin, R. K. (2009). Case study research: Design and methods (Vol. 5).


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