Multi Criteria DSS on Mobile Phone Selection With AHP & TOPSIS

Multi Criteria DSS onMobile Phone SelectionWith AHP & TOPSIS

Electronic & Computer DepartmentIsfahan University Of TechnologyTo: Dr M.A.Montazeri , By: Reza Ramezani1In The Name Of AllahOutlineMulti-Criteria Decision Making (MCDM)

Analytic Hierarchy Process (AHP)

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)2Mobile PhonesBy the late 1980s, launch of the first GSM phone.

Swift evolution as the generations develop.

Additional value-added services and high computing capabilities on 3G.3Mobile producerBy Mobile Development:The producers had started to develop their sale strategies based on consumer preferences over time.

To achieve maximum number of consumer:They throw different types of handsets every so often on the market.4Is Mobile Phone Selection Important?The number of published papers on mobile phones.The rapid evolution of the mobile phone has produced a proliferation of models and features.Selecting a mobile phone is now a complex multi-criteria problem (MCDM).Customers may find online decision support useful.5Lecture aimPropose a multi-criteria decision making (MCDM) approach.Show the most important mobile phone features.Evaluating the mobile phone options in respect to the users' preferences order.Finally, ranking mobile phone alternatives by AHP and TOPSIS methods.6MCDMMCDM is a powerful tool used widely for evaluating and ranking problems containing multiple, usually conflicting criteria.MCDM refers to find the best opinion from all of the feasible alternatives in the presence of multiple decision criteria.MCDM helps offer recommendations when decisions involve trade-offs among different decision criteria.The MCDM generally enable to structure the problem clearly and systematically.7MCDM MethodsSome MCDM methods: Priority based, outranking, distance-based and mixed methods.One of the most outstanding MCDM approaches is the Analytic Hierarchy Process (AHP)8The Evaluation ProcedureStep 1. Identifying the mobile phone selection (evaluation) criteria that are considered the most important for the users.

Step 2. Calculating the criteria weights by applying AHP method.

Step 3. Conducting TOPSIS method to achieve the final ranking results.9

The Evaluation Procedure10Evaluation CriteriaMain objective: Select the best alternative among a number of mobile phone options in respect to the users' preferences order.

Criteria list resources:A literature research in depthA survey conducted among the target groupThe experiences of the telecommunication sector experts11Evaluation CriteriaSome Examples from two groups:The Product-related criteria.The User-friendly criteria.

Basic Requirements - MarketabilityUsability - StyleCustomer Excitement - LuxuriousnessSimplicity - AttractivenessColorfulness - TextureDesign Standards - AcceptabilityReliability - Harmoniousness.12

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By collected data, the essential criteria are decided to be into two Class: product-related and user-related.15

By interview, the essential criteria are decided to be into two Class: product-related and user-related.16Analytical Hierarchy Process (AHP)Formulated way to structure decision problem.The best-known and most widely used model in decision making.Powerful Methodology in order to determine the priorities among different criteria.Attempts to mirror human decision process.Easy to use.Well accepted by decision makers.Can be used for multiple decision makers.17AHP Procedure Build the HierarchyVery similar to hierarchical value structure Goal on top (Fundamental Objective) Decompose into sub-goals (Means objectives) Further decomposition as necessary Identify criteria (attributes) to measure achievement of goals (attributes and objectives) Alternatives added to bottom Different from decision tree Alternatives show up in decision nodes Alternatives affected by uncertain events Alternatives connected to all criteria18Categories of ElementsObjective

Criteria

Alternatives

Goals19

20AHP Procedure Judgments and Comparisons21AHP Steps (Step 1)Step 1:AHP uses several small sub problems to present a complex decision problem.Thus, the first act is to decompose the decision problem into a hierarchy with:a goal at the topcriteria and sub-criteria at sub-levelsand alternatives at the bottom22

Building the Hierarchy23Our Study Hierarchically24

Another Example25

AHP Steps (Step 2)Step 2:The Decision Matrix, Decision Vector (Saaty's nine-point scale), must constructed.Use the fundamental 19 scale defined by Saaty to assess the priority score.The decision matrix involves the assessments of each alternative in respect to the decision criteria.The decision vector involves the criteria's preferences. 261 -9 Scale

27Decision Matrix28Normalized Decision Matrix For Mobile PhoneMotorola V80Sony Ericsson K700iNokia 7260Decision Matrix0.3330.3330.333Basic Requirements0.3820.3820.235Physical characteristics0.2720.4560.272Technical features0.2730.4540.273Functionality0.1100.3350.555Brand choice0.2300.3850.385Customer excitement29Decision Vector30AHP Steps (Step 3)Step 3:Pairwise Comparison Matrix

Compare the pairs of the elements of the constructed hierarchy.

The aim is to set their relative priorities with respect to each of the elements at the next higher level.31Pairwise Comparison Matrix32Pairwise Comparison MatrixWays to build pairwise comparison matrix:Build From Decision VectorBuild Directly with solicit from user

Weight determination of criteria is more reliable when using pairwise comparisons than obtaining them directly.33Decision Vector:

Will Become:

Surly this is consistence.Pairwise Comparison Matrix (Direct)ABCABC1115/353/51/531/3ABC53134Pairwise Comparison Matrix (Solicit)Purchase CostMaintenance CostGas Mileage Want to find weights on these criteria AHP compares everything two at a time(1) ComparePurchase CosttoMaintenance Cost Which is more important?Say purchase cost By how much? Say moderately 335P = 3M(2) ComparePurchase Costto Which is more important?Say purchase cost By how much? Say more important 5Gas Mileage(3) Compareto Which is more important?Say maintenance cost By how much? Say more important 3Gas MileageMaintenance Cost36Pairwise Comparison Matrix (Solicit)P = 5GM = 3GThis set of comparisons gives the following matrix:PMGPMG111351/31/531/3 Ratings mean that P is 3 times more important than Mand P is 5 times more important than G Whats wrong with this matrix?The ratings are inconsistent (Step 4)!37Pairwise Comparison Matrix (Solicit)P = 3M, P=5M 3M = 5G M = (5/3)G But here M = 3G

Pairwise Comparison Matrix38AHP Steps (Step 4)Step 4:

CalculateIs Pairwise Comparison Matrix Consistent?Consistency Ratio

Reflect the consistency of decision maker's judgments during the evaluation phase.39ConsistencyRatings should be consistent in two ways: (1) Ratings should be transitive That means that If A is better than B and B is better than C then A must be better than C (2) Ratings should be numerically consistent In car example we made 1 more comparison than we needed We know that P = 3M and P = 5G 3M = 5G M = (5/3)G40ConsistencyWays to understand whether a matrix is consistent or not?

Matrix Rank

Eigenvalue

Consistency Ratio41Consistent Matrix (Rank)Consistent matrix for the car example would look like:PMGPMG111351/31/55/33/5 Note that matrix has Rank = 1 That means that all rows are multiples of each other and matrix can build from one row.

4243Consistent Matrix (Eigenvalue)87654321n1.41.351.251.110.890.5200R.I.44Consistent Matrix (Consistency Ratio)45Consistent Matrix (Consistency Ratio)AHP Steps (Step 5)Step 5:Compute Criterias' Weight

Compute Weights in 2 different situation:

Consistent Pairwise Comparison MatrixNormalization

Inconsistent Pairwise Comparison MatrixEigenvectorGeometric Mean46Criterias' Weight (Consistent)Each pairwise comparison matrix column has to be divided by the sum of entries of the corresponding column.

A normalized matrix is obtained in which the sum of the elements of each column vector is 1.47PMGPMG111351/31/55/33/5PMGPMG15/235/233/2315/2315/235/233/235/233/23=Sum = 1 1 1Sum = 23/15 23/5 23/3W(P) = 15/23, W(M)= 5/23, W(G) = 3/2348Criterias' Weight (Consistent)Normalization:Criterias' Weight (Inconsistent)Eigenvalue/Eigenvector Method:

Eigenvalues are important tools in several math, science and engineering applications Compute by solving the characteristic equation: det(I A) = | A I | = 0 Use the largest , for the computation. Defined as follows: for matrix A and vector x, = Eigenvalue of A when Aw = w, w is nonzero w is then the eigenvector associated with 49Compute the Eigenvalues for the inconsistent matrix:PMGPMG111351/31/531/3w = vector of weights Must solve: Aw = w by solving det(I A) = 0 We get:

Different than before!max= 3.039 Find the eigenvector for 3.039 and normalize50Criterias' Weight (Inconsistent)51Criterias' Weight (Inconsistent)Car example with geometric meansPMGPMG111351/31/531/3NormalizedPMGPMG.65.23.11.69.56.22.13.33.08wwwpMG= [(.65)(.69)(.56)]1/3= [(.22)(.23)(.33)]1/3= [(.13)(.08)(.11)]1/3= 0.63= 0.26= 0.05Normalized= 0.67= 0.28= 0.05wwwpMG52Criterias' Weight (Inconsistent)ComputeAHP Steps (Step 6)Step 6:Calculate weight vector!Multiply weight vector by weight coefficients of the elements at the higher levels, until the top of the hierarchy is reached.53

Normalized Weights of the Criterias54

Normalized Weights of the Criterias55TOPSISTechnique for Order Preference by Similarity to Ideal Solution (TOPSIS)TOPSIS is based on positive and negative ideal solutions.Solutions are determined in respect to the distance of each alternative to the best and the worst performing alternative.The alternative ratings and criterion weights, must pass from AHP phase to TOPSIS phase.56Evaluating Alternatives by TOPSISTOPSIS method, which is based on choosing the best alternative having the:Shortest distance to the ideal solutionFarthest distance from the negative-ideal solutionThe ideal solution is the solution that maximizes the benefit and also minimizes the total cost.The negative-ideal solution is the solution that minimizes the benefit and also maximizes the total cost.57Topsis Steps (Step 1)58C1C2C3A1A2A3131357335NormalizedC1C2C3A1A2A30.160.360.160.500.840.850.500.360.8459ExampleCalculate the normalized decision matrix.Topsis Steps (Step 2)60WNDM Mobile PhoneMotorola V80Sony Ericsson K700iNokia 7260WeightWeighted Decision Matrix0.0210.0210.0210.064Basic Requirements0.0360.0360.0220.094Physical characteristics0.0480.0800.0480.175Technical features0.1120.1860.1120.409Functionality0.0190.0580.0960.173Brand choice0.0190.0320.0320.84Customer excitement61Topsis Steps (Step 3)62Ideal and Negative-ideal Solutions63Topsis Steps (Step 4)64Alternatives Distances65The distance of each alternative to the ideal solution and the non-ideal solution:Topsis Steps (Step 5)66

Relative Closeness To The Ideal Solution67Topsis Steps (Step 6)68The End

Thanks For Your Regard69Intensity of ImportanceDefinition

1Equal Importance

3Moderate Importance

5Strong Importance

7Very Strong Importance

9Extreme Importance

2, 4, 6, 8For compromises between the above

Reciprocals of aboveIn comparing elements i and j

- if i is 3 compared to j

- then j is 1/3 compared to i

RationalsForce consistency

Measured values available