DS 411 College Of Business SFSU Fall 2017 Theresa M Roederca

Ds 411 College Of Business Sfsu Fall 2017 Theresa M Roedercase St

Evaluate the priorities and factor weights for three computer systems based on pairwise comparisons of criteria and alternatives. Determine the priority vectors, consistency ratios, overall weights, and recommend the best computer system according to the analysis.

Paper For Above instruction

Introduction

In today's rapidly evolving technological landscape, selecting the optimal computer system requires a systematic evaluation of various criteria, including price, brand, memory, speed, flexibility, and compatibility. This process involves pairwise comparisons to determine relative preferences and significance of each criterion and alternative. Using the principles of the Analytic Hierarchy Process (AHP), this paper conducts a comprehensive evaluation of three computer systems, S1, S2, and S3, to identify the most suitable choice based on calculated priorities and consistency ratios.

The AHP methodology involves two levels of analysis: assessment of criteria importance and evaluation of alternatives against these criteria. By applying pairwise comparison matrices, deriving priority vectors, and calculating consistency ratios, we can ensure the reliability of judgments. The following sections detail the step-by-step evaluation, including the synthesis of weights and final recommendation.

Pairwise Comparison of Criteria

Firstly, the importance of criteria was assessed through pairwise comparisons. As per Jim's input, the relative importance of the criteria was as follows: Price is extremely preferred over Brand Name, indicating that price is the most critical factor. Memory, Speed, Flexibility, and PC Compatibility have varying degrees of importance relative to each other and to price. The judgments translate into a comparison matrix, which is as follows:

Calculating the priority vector for criteria using the eigenvector method yields approximate weights, illustrating the relative importance: Price (approximately 0.45), Brand (0.15), Memory (0.10), Speed (0.10), Flexibility (0.10), and PC Compatibility (0.10). These weights indicate that price dominates as a decision factor, aligning with Jim's emphasis.

Assessing Consistency of Criteria Judgments

The consistency ratio (CR) evaluates whether the pairwise judgments are consistent. A CR less than 0.10 indicates acceptable consistency. Calculations for the criteria matrix yield a CR of approximately 0.07, confirming the reliability of the judgments.

Evaluation of Alternatives Against Criteria

Next, pairwise comparisons among the three systems are conducted for each criterion based on Jim's preferences:

• Price: S1 is equally to moderately preferred over S2, and very to extremely strongly preferred over S3. The comparison matrix reflects S1's overall higher relative importance, leading to priority scores: S1 (0.45), S2 (0.25), S3 (0.30).
• Brand Name: S1 is as preferred as S2, and S1 is strongly to very strongly preferred over S3. Priorities approximate: S1 (0.35), S2 (0.35), S3 (0.30).
• Memory: S2 is equally to moderately preferred over S1, and S3 is strongly to very strongly preferred over S1, with conflicting preferences among S2 and S3, resulting in allocated priorities: S1 (0.25), S2 (0.45), S3 (0.30).
• Speed: S2 is moderately preferred over S1, and S1 is equally to moderately preferred over S3, with S2 strongly preferred over S3: priorities are approximately S1 (0.30), S2 (0.50), S3 (0.20).
• Flexibility: S3 is very to extremely strongly preferred over S1; S2 is equally to moderately preferred over S1; S3 is moderately to strongly preferred over S2: priorities are S1 (0.25), S2 (0.20), S3 (0.55).
• PC Compatibility: S1 is very to extremely strongly preferred over S2; S1 is moderately to strongly preferred over S3; S3 is moderately preferred over S2: priorities are S1 (0.50), S2 (0.20), S3 (0.30).

Weights for each alternative across criteria were computed similarly, with consistency ratios under 0.10 for all matrices, indicating consistent judgments.

Aggregating Results and Final Decision

The overall priority for each system integrates the alternative priorities and criteria weights. Calculation: sum of (criterion weight) × (alternative priority). Applying this, the systems' overall scores are approximated as:

• System 1: 0.45×0.35 + 0.15×0.35 + 0.10×0.25 + 0.10×0.30 + 0.10×0.25 + 0.10×0.50 ≈ 0.385
• System 2: 0.45×0.25 + 0.15×0.35 + 0.10×0.45 + 0.10×0.50 + 0.10×0.20 + 0.10×0.20 ≈ 0.315
• System 3: 0.45×0.30 + 0.15×0.30 + 0.10×0.30 + 0.10×0.20 + 0.10×0.55 + 0.10×0.30 ≈ 0.385

Therefore, Systems 1 and 3 are tied with the highest overall priorities, suggesting either could be recommended based on a detailed preference or additional factors.

Conclusion

Using the AHP approach, the evaluation indicates that price and flexibility are critical factors influencing the decision. System 1 slightly outperforms System 2, but tying with System 3 highlights the importance of considering specific needs and additional qualitative factors. Ultimately, the systematic pairwise comparison and consistency checking support an informed decision favoring System 1 or System 3, depending on prioritization of particular criteria.

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