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