BUS606: Operations and Supply Chain Management

Analytic Hierarchy Process (AHP) Modeling

The AHP is a weight estimation technique that generates weights or ratio scales from paired comparisons. It is widely used in Multi-Criteria Decision Analysis (MCDA), resource planning, and conflict resolution. AHP-based modeling has been used for forest fire hazard mapping in the south Asian region. The AHP method basically employs a square matrix with ones on the (main) diagonal, weights on one side of the diagonal and reciprocal weights on the reverse side. In such a pair-wise comparison matrix, weightage of one factor over the other is assigned using a fundamental scale with numerical values ranging from 1/9 to 9 in the order of least comparative importance to highest comparative importance. It is during this step that expert knowledge on the subject matter becomes extremely useful. Expert knowledge was gathered from published literature, forest fire managers, field personnel, and field reports of forest fire incidences. Several rounds of consultations were held with forest fire managers to assign weights for an AHP matrix. Consistency of the weight matrix was measured by a Consistency Ratio (CR), which measures divergence of the weights from a principal eigenvalue. Recalibration of the weights was needed whenever the CR was greater than 0.10 (or 10%). Once a consistent matrix was obtained, a vector of relative weights for each factor was produced. In this study, a 7 × 7 AHP matrix was used, as shown in Table 3. A highly consistent CR value of 0.05 was obtained, and the relative weights were subsequently produced, as shown in Table 4. The highest weightage (45%) was assigned to the LULC layer, followed by the settlement layer (19%) and road layer (12%). The lowest weightage (4%) was assigned to the slope layer. These weights were used as the percentages of influence of each layer in the 'weighted overlay' process in ArcGIS to produce a map of forest fire-prone areas.

Table 3. A 7 × 7 Analytic Hierarchy Process (AHP) matrix showing pairwise comparison of forest fire conditioning factors with respect to perceived influence on forest fire susceptibility using expert knowledge in Bhutan. Unity of diagonal represents equality of weights, which range from 1/9 (extremely low importance) to 9 (extremely high importance).

Table 4.The weights for the seven conditioning factors in Bhutan with respect to influence on forest fire susceptibility derived from an Analytical Hierarchy Process with a consistency ratio of 0.05.

Frequency Ratio (FR) Modeling

The FR can be defined as the probability of occurrence of a specific attribute. Higher FR weights illustrate a high relationship among that class and forest fire occurrence. For modeling of forest fire-prone areas, an FR was used to extract the quantitative relationship between forest fire occurrence points and the seven forest fire conditioning factors. The FR-based modeling is a popular approach for computing the probabilistic relationship between a specific phenomenon and a set of contributing factors involved in the creation of a spatial layer of that phenomenon.

The following equation for the FR was used:

$F R_{i}=\left(A_{i} / B_{i}\right) /\left(H_{i} / L\right)=P_{i} / K$

where:

$F R_{i}$ = frequency ratio of a class for the $i^{t h}$ conditioning factor;

$A_{i}$ = area of a class for the $i^{t h}$ conditioning factor;

$B_{i}$ = total area of the $i^{t h}$ conditioning factor;

$H_{i}$= number of pixels in each class of the $i^{t h}$ factor;

$L$ = number of total pixels in the study area;

$P_{i}$ = the percentage for area with respect to a class for $i^{t h}$ factor; and

$K$ = is the percentage for the entire domain.