Akshit gupta management_science
- 1. BIRLA INSTITUTE OF MANAGEMENT TECHNOLOGY MANAGMENT SCIENCE ASSIGNMENT ANALYTICAL HIERARCHICAL PROCESS Submitted by: Akshit Gupta Submitted to : 19DM024 Kuldeep Lamba
- 2. Contents Problem Statement...................................................................................................................... 3 Introduction.................................................................................................................................3 AHP……………………………………………………………………………….......................................................................4 How AHP Works.......................................................................................................................4 Questionnare............................................................................................................................... 5 Questions: ...............................................................................................................................6 Criteria.................................................................................................................................6 Analysis.......................................................................................................................................8 Consistency Analysis.................................................................................................................8 Summary................................................................................................................................... 14 References............................................................................................................................. 14
- 3. Problem Statement India is the world’s largesttwo-wheeler market and despite the losses suffered by bikemakersin Indiaduringthe shiftto BS-IV,theindustryrecoveredwellwith a massivegrowthof 14.80percent.Overallthe two-wheeler industrysaw a total sales of over 2.01 cr. units sold in the Indian domestic market and exports from the country also shotup by over 20 percent. Within the Two Wheelers segment, Motorcycles grew by 13.69 percent respectively.(Financial Express). From that report we can conclude that every 5th person owns a 2-wheeler and it is a vast market. So we try to understand the decision making part which done before buy a bike. We took five criteria to which helps customers to take decision and five alternative choice from which customer can choose their final product. Introduction AHP AHP is a decision-making method developed by Prof. Thomas L. Saaty in 1970s that is used to solvecomplex MCDMproblems. Itrequires a decision maker to offer judgments about each criterion’s relative importance and specify a predilection for each decision alternative using each criterion. It is highly
- 4. efficient in identifying the selected criteria, their weighting, and analysis, and it allows a logical data combination, which could be quantitative, qualitative, experience, insight, and intuition in its algorithmic framework. AHP enables decision makers to determine each criterion’s weight. Features of AHP AHP isa very flexibleand powerfultoolbecausethescores, andthereforethe final ranking,areobtained on thebasisof thepairwiserelative evaluationsof both the criteriaandtheoptionsprovided bytheuser.ThecomputationsmadebytheAHP are always guided by the decision maker’s experience, and the AHP can thus be consideredas a toolthatis ableto translatetheevaluations(both qualitativeand quantitative) madebythedecisionmakerinto a multicriteria ranking. In addition, the AHP is simple because there is no need of building a complex expert system with the decision maker’s knowledge embedded in it How AHP Works AHPconsiders a setof evaluation criteria, and a setof alternative options among which the best decision is to be made. It is important to note that, since some of the criteria could be contrasting, it is not true in general that the best option is the one which optimizes each single criterion, rather the one which achieves the most suitable trade-off among the different criteria. AHP generates a weight for each evaluation criterion according to the decision maker’s pairwise comparisons of the criteria. The higher the weight, the more important the corresponding criterion. Next, for a fixed criterion, the AHP assigns a score to each option according to the decision maker’s pairwise comparisons of the options based on that criterion. The higher the score, the better the performanceof the option with respect to the considered criterion. Finally, the AHP combines the criteria weights and the options scores, thus determining a global scoreforeach option, and a consequentranking.Theglobal scorefor a given option is a weighted sum of the scores itobtained with respect to all the criteria.
- 5. Questionnare After the completion of the structure, the second step of the AHP process is to make a questionnaire to determine the preference of the respondents. The questionnaire for a 4 criteria, 3 alternative process would require at least some questions to be answered in order to make the right decision so as to choose a preference of car The questionnaireis madeon the basisof pairwisescaling method, Theselection criteria is shown the table for reference. Criteria 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Criteria Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Price 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Mileage 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Looks 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Weightage Scale Value Extremely Important 8, 9 Very Important 6, 7 Moderately Important 4, 5 Important 2, 3 Equally Important 1 Explanation:
- 6. i. If you choose 1,when comparing Appearance over comfort that means you give equal importance to both the criteria ii. If you choose 9 towards the left, It means that Appearance on the left hand side is 9 times more important than criteria n the right which is comfort iii. If you choose 6 towards the right, it means that you give very strong importance to cost over Appearance Questions: Criteria Questions 1 to 3: what is the relative importance of “PRICE” with respect to others? Questions 4 to 5 : whatis the relative importance of “MILEAGE” with respect to others? Questions6 : whatis therelative importanceof “LOOKS”with respectto others? 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 PRICE LOOKS PRICE COLOR PRICE MILEAGE 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 MILEAGE COLOR MILEAGE LOOKS 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 LOOKS COLOR
- 7. Questions 7 to 9 (PRICE): Relative importance of brands APACHE, ENFIELD, R15 with respect to PRICE? Questions10to 12(MILEAGE):Relative importanceof brandsAPACHE,ENFIELD, R15 with respect to MILEAGE? 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 APACHE R15 ENFIELD R15 ALTERNATIVESCOMPAREDWITHRESPECTTOPRICE APACHE ENFIELD 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 APACHE R15 ENFIELD R15 APACHE ENFIELD ALTERNATIVESCOMPAREDWITHRESPECTTOMILEAGE
- 8. Questions 13 to 15 (LOOKS): Relative importance of brands APACHE, ENFIELD, R15 with respect to LOOKS? Questions 13 to 15 (COLOR): Relative importance of brands APACHE, ENFIELD, R15 with respect to COLOR? Analysis Consistency Analysis STEP 1: The first step of the process is to check for the consistency of the criteria. The consistency of the data is expected to be within the range of 1% to 10%. Before this the important step is to answer the questionnaire with utmost sincerity in 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 ENFIELD R15 APACHE R15 ALTERNATIVESCOMPAREDWITHRESPECTTOLOOKS APACHE ENFIELD 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 ENFIELD R15 APACHE R15 APACHE ENFIELD
- 9. order to get a consistent output. The data from the respondent is as shown below. STEP 2: After finding out the summation of all criteria, we normalize the entire matrix my dividing each value of the column with its sum. Then the weighted average of each row is also taken. The Sum of each column shall be 1. STEP 3: The Vales of Lambdamax, Consistency Index(CI), Random Consistency Index(RI) and the ratio of CI/RI are calculated to find out the consistency of the data collected. N=4 From the calculations we can infer that the data is quite consistent and can be observed that the consistency index is less than 10% as prescribed in the process. Since the data is consistent, there is no need to repeat the entire Criteria PRICE MILEAGE LOOKS COLOR PRICE 1 3.63 5.43 5.24 MILEAGE 0.28 1 0.40 2.00 LOOKS 0.18 2.50 1 4.16 COLOR 0.19 0.50 0.24 1 SUM 1.65 7.63 7 12.4 PairWise Matrix of CRITERIA by synthesing using Geometric Mean Criteria PRICE MILEAGE LOOKS COLOR Criteria Weights PRICE 0.61 0.48 0.77 0.42 0.57 MILEAGE 0.17 0.13 0.06 0.16 0.13 LOOKS 0.11 0.33 0.14 0.34 0.23 COLOR 0.12 0.07 0.03 0.08 0.07 4.26 0.0881 0.90 9.79% ACCEPTABLE Constant Consistency Ratio (CR) ƛ max Consistency Index (CI)
- 10. process to get the consistency indexless than 10%. Wecan now moveon to the next step of calculation of alternatives. Main inference from STEP 3: Price is given the utmost importance by the respondent whichis placedat 57% of the total share, It is thenfollowedby the Looks which is given the second importance at 23% followedby Colour, Price accordingly. STEP 4 (PRICEto Alternatives): From hereonwards each criterion of selecting a Bike is rated with respect to all the alternatives which are Apache, Enfield, R15 .All the above three steps are repeated for each criterion. First Criterion of the Appearance is chosen and compared against all the other brands. PRICE APACHE ENFIELD R15 APACHE 1 0.24 5.19 ENFIELD 4.16 1 7.56 R15 0.19 0.13 1 Sum 5.35 1.37 13.75 Pairwise Matrix of PRICE by using Geometric Mean PRICE APACHE ENFIELD R15 Criteria Weights APACHE 0.19 0.18 0.38 0.25 ENFIELD 0.78 0.73 0.55 0.69 R15 0.04 0.10 0.07 0.07 Normalised Matrix Criteria Weights 0.25 0.69 0.07 PRICE APACHE ENFIELD R15 Sum Sum/Weight APACHE 0.25 0.16 0.35 0.77 3.11 ENFIELD 1.03 0.69 0.52 2.23 3.25 R15 0.05 0.09 0.07 0.21 3.02 Weighted Normalised Matrix
- 11. Main inference: Price wise ENFIELD is given the utmost importance by then followed by the APACHE which is given the second importance followed by R15 accordingly. STEP 5 (MILEAGE to Alternatives): Second Criterion of the Comfort is chosen and compared against all the other brands alternatives APACHE, ENFIELD, R15 Main inference: MILEAGE wise R15 is given the utmost importance by then followed by the APACHE which is given the second importance followed by ENFIELD accordingly. STEP 6 (LOOKS to Alternatives): Second Criterion of the Comfort is chosen and compared against all the other brands alternatives APACHE, ENFIELD, R15. MILEAGE APACHE ENFIELD R15 APACHE 1 3.30 0.23 ENFIELD 0.30 1 0.17 R15 4.35 5.77 1 Sum 5.65 10.07 1.40 MILEAGE APACHE ENFIELD R15 Criteria Weights APACHE 0.18 0.33 0.16 0.22 ENFIELD 0.05 0.10 0.12 0.09 R15 0.77 0.57 0.71 0.69 Criteria Weights 0.22 0.09 0.69 MILEAGE APACHE ENFIELD R15 Sum Sum/Weight APACHE 0.22 0.30 0.16 0.68 3.06 ENFIELD 0.07 0.09 0.12 0.28 3.01 R15 0.97 0.53 0.69 2.18 3.18 3.09 0.0431 0.58 7.43% ACCEPTABLE Pairwise Matrix of MILEAGE by using Geometric Mean Normalised Matrix Weighted Normalised Matrix ƛ max Consistency Index (CI) Constant Consistency Ratio (CR) 3.13 0.0632 0.90 7.03% ACCEPTABLE ƛ max Consistency Index (CI) Constant Consistency Ratio (CR)
- 12. Main inference:LOOKS wise APACHE is given the utmost importance by then followed by the ENFIELD which is given the second importance followed by R15 accordingly. STEP 7 (COLOR to Alternatives): Second Criterion of the Comfort is chosen and compared against all the other brands alternatives APACHE, ENFIELD, R15. LOOKS APACHE ENFIELD R15 APACHE 1 2.71 6.46 ENFIELD 0.37 1 5.77 R15 0.15 0.17 1 SUM 1.52 3.89 13.23 LOOKS APACHE ENFIELD R15 Criteria Weights APACHE 0.66 0.70 0.49 0.61 ENFIELD 0.24 0.26 0.44 0.31 R15 0.10 0.04 0.08 0.07 Criteria Weights 0.61 0.31 0.07 LOOKS APACHE ENFIELD R15 Sum Sum/Weight APACHE 0.61 0.85 0.48 1.94 3.15 ENFIELD 0.23 0.31 0.43 0.96 3.09 R15 0.10 0.05 0.07 0.22 3.02 3.09 0.0443 0.58 7.64% ACCEPTABLE Pairwise Matrix of LOOKS by using Geometric Mean Normalised Matrix Weighted Normalised Matrix ƛ max Consistency Index (CI) Constant Consistency Ratio (CR)
- 13. Maininference:COLORS wise ENFIELDis giventhe utmostimportance by then followed by the APACHE which is given the second importance followed by R15 accordingly. STEP 8: In the last and final step to find out the global weighted average we multiply the weighted average of each criteria against the weighted average given to each criteria of each brand. Once each of these are multiplied the final preference of the respondents can be derived using the table. Main inference: It is observed from the survey that ENFIELD is the most preferred bike with criteria such as Price, Mileage, Color, Looks. The observations show that 53% of the respondents have chosen over the other COLOR APACHE ENFIELD R15 APACHE 1 0.14 2.62 ENFIELD 6.95 1 6.95 R15 0.38 0.14 1 Sum 8.33 1.29 10.57 COLOR APACHE ENFIELD R15 Criteria Weights APACHE 0.12 0.11 0.25 0.16 ENFIELD 0.83 0.78 0.66 0.76 R15 0.05 0.11 0.09 0.08 Criteria Weights 0.16 0.76 0.08 Age APACHE ENFIELD R15 Sum Sum/Weight APACHE 0.16 0.11 0.22 0.49 3.06 ENFIELD 1.11 0.76 0.58 2.45 3.24 R15 0.06 0.11 0.08 0.25 3.02 3.11 0.0534 0.58 9.21% Pairwise Matrix of COLOR by using Geometric Mean Normalised Matrix Weighted Normalised Matrix ƛ max Consistency Index (CI) Constant Consistency Ratio (CR) Criteria Weights APACHE ENFIELD R15 APACHE ENFIELD R15 PRICE 0.57 0.25 0.69 0.07 0.14 0.39 0.04 MILEAGE 0.13 0.22 0.09 0.69 0.03 0.01 0.09 LOOKS 0.23 0.61 0.31 0.07 0.14 0.07 0.02 COLOR 0.07 0.16 0.76 0.08 0.01 0.06 0.01 0.32 0.53 0.15SUM ORIGINAL SCORE WEIGHTED SCORE
- 14. brands, while the other two brands i.e. APACHE and R15 are very low compared to the choice of Enfield. Summary The following table shows the ranking order of each criteria against along each alternative for a better understanding and interpretation of the report. In nutshell, the most preferred Bike among all criteria and among all the alternatives, Enfield is the clear winner and is the most preferred bike brand by the chosen 3 respondents. References Introduction to management science. Sweeney, Anderson Wikipedia https://www.pmi.org/learning https://cran.r-project.org/web/packages/ahp/ Criteria Weights APACHE ENFIELD R15 APACHE ENFIELD R15 PRICE 0.57 0.25 0.69 0.07 0.14 0.39 0.04 MILEAGE 0.13 0.22 0.09 0.69 0.03 0.01 0.09 LOOKS 0.23 0.61 0.31 0.07 0.14 0.07 0.02 COLOR 0.07 0.16 0.76 0.08 0.01 0.06 0.01 0.32 0.53 0.15 RANK 2 1 3 SUM ORIGINAL SCORE WEIGHTED SCORE