### Analytical Hierarchy Process Example

Objective:
• There are 3 restaurants; the objective is to choose the most favorable one.
• There are 3 perspectives of the criteria:
• Price Level
• Interior Decoration
• Kinds of Dishes
• Analytical Hierarchy Process:
• C.I.: Consistency Index
• R.I.: Random Index
• C.R.: C.I. / R.I.
Pairwise Comparison Tables:
• Criteria Perspective Comparison Table:

 Criteria Price Level Interior Decoration Kinds of Dishes Price Level 1 1/3 1/5 Interior Decoration 3 1 1/4 Kinds of Dishes 5 4 1
• Price vs Restaurant Perspective Comparison Table:

 Price Level Restaurant - A Restaurant - B Restaurant - C Restaurant - A 1 1/3 1/4 Restaurant - B 3 1 1 Restaurant - C 4 1 1
• Interior Decoration vs Restaurant Perspective Comparison Table:

 Interior Decoration Restaurant - A Restaurant - B Restaurant - C Restaurant - A 1 1/4 1/4 Restaurant - B 4 1 1/2 Restaurant - C 4 2 1
• Kinds of Dishes vs Restaurant Perspective Comparison Table:

 Kinds of Dishes Restaurant - A Restaurant - B Restaurant - C Restaurant - A 1 1/2 1/5 Restaurant - B 2 1 1/3 Restaurant - C 5 3 1
Calculation:
• R.I. Reference Table:

 n (K1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 R.I. (L1) 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.48 1.49 1.51 1.56 1.57 1.59
• Criteria Perspective Comparison Table:

 Criteria (A1) Price Level (B1) Interior Decoration (C1) Kinds of Dishes (D1) Criterion (E1) Priority Weight (F1) Matrix Dot (G1) λ (H1) C.I. (I1) C.R. (J1) Price Level (A2) 1 1/3 1/5 =(B2*C2*D2)^(1/n) n=3 Perspectives 0.4055 =E2/E5 0.1007 =B2*F2+C2*F3+D2*F4 0.3106 =G2/F2 3.0858 =(H5-n)/(n-1) n=3 Perspectives 0.0429 =I2/L4 0.0739 Interior Decoration (A3) 3 1 1/4 0.9086 0.2255 0.6959 3.0858 < 0.1 -> Valid Kinds of Dishes (A4) 5 4 1 2.7144 0.6738 2.0792 3.0858 (A5) =SUM(E2..E4) 4.0285 λ-max =AVERAGE(H2:H4) 3.0858
• Price vs Restaurant Perspective Comparison Table:

 Price Level (A1) Restaurant A (B1) Restaurant B (C1) Restaurant C (D1) Criterion (E1) Priority Weight (F1) Matrix Dot (G1) λ (H1) C.I. (I1) C.R. (J1) Restaurant - A (A2) 1 1/3 1/4 =(B2*C2*D2)^(1/n) n=3 Perspectives 0.4368 =E2/E5 0.1084 =B2*F2+C2*F3+D2*F4 0.3263 =G2/F2 3.0092 =(H5-n)/(n-1) n=3 Perspectives 0.0046 =I2/L4 0.0079 Restaurant - B (A3) 3 1 1 1.4422 0.3580 1.0773 3.0092 < 0.1 -> Valid Restaurant - C (A4) 4 1 1 1.5874 0.3940 1.1858 3.0092 (A5) =SUM(E2..E4) 3.4664 λ-max =AVERAGE(H2:H4) 3.0092
• Interior Decoration vs Restaurant Perspective Comparison Table:

 Interior Decoration (A1) Restaurant A (B1) Restaurant B (C1) Restaurant C (D1) Criterion (E1) Priority Weight (F1) Matrix Dot (G1) λ (H1) C.I. (I1) C.R. (J1) Restaurant - A (A2) 1 1/4 1/4 =(B2*C2*D2)^(1/n) n=3 Perspectives 0.3969 =E2/E5 0.0985 =B2*F2+C2*F3+D2*F4 0.3008 =G2/F2 3.0536 =(H5-n)/(n-1) n=3 Perspectives 0.0268 =I2/L4 0.0462 Restaurant - B (A3) 4 1 1/2 1.2599 0.3128 0.9550 3.0536 < 0.1 -> Valid Restaurant - C (A4) 4 2 1 2.0000 0.4965 1.5160 3.0536 (A5) =SUM(E2..E4) 3.6568 λ-max =AVERAGE(H2:H4) 3.0536
• Kinds of Dishes vs Restaurant Perspective Comparison Table:

 Kinds of Dishes (A1) Restaurant A (B1) Restaurant B (C1) Restaurant C (D1) Criterion (E1) Priority Weight (F1) Matrix Dot (G1) λ (H1) C.I. (I1) C.R. (J1) Restaurant - A (A2) 1 1/2 1/5 =(B2*C2*D2)^(1/n) n=3 Perspectives 0.4642 =E2/E5 0.1152 =B2*F2+C2*F3+D2*F4 0.3461 =G2/F2 3.0037 =(H5-n)/(n-1) n=3 Perspectives 0.0018 =I2/L4 0.0032 Restaurant - B (A3) 2 1 1/3 0.8736 0.2169 0.6514 3.0037 < 0.1 -> Valid Restaurant - C (A4) 5 3 1 2.4662 0.6122 1.8389 3.0037 (A5) =SUM(E2..E4) 3.8040 λ-max =AVERAGE(H2:H4) 3.0037

Decision Table:

 Decision (A1) Price Level (B1) Interior Decoration (C1) Kinds of Dishes (D1) Decision Weight (E1) Order (F1) Priority Weight (A2) 0.1007 0.2255 0.6738 Restaurant - A (A3) 0.1084 0.0985 0.1152 =B2*B3+C2*C3+D2*D3 0.11 3 Restaurant - B (A4) 0.3580 0.3128 0.2169 0.25 2 Restaurant - C (A5) 0.3940 0.4965 0.6122 0.56 1

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2010年11月3日 上午5:01
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2010年11月3日 上午3:49
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2010年11月3日 上午3:47