机场安检评价指标

The analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. Rather than prescribing a "correct" decision, the AHP helps decision makers find one that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating alternative solutions. The procedure for using the AHP can be summarized as: 1. Model the problem as a hierarchy containing the decision goal, the alternatives for reaching it, and the criteria for evaluating the alternatives. 2. Establish priorities among the elements of the hierarchy by making a series of judgments based on pairwise comparisons of the elements. For example, when comparing potential purchases of commercial real estate, the investors might say they prefer location over price and price over timing. 3. Synthesize these judgments to yield a set of overall priorities for the hierarchy. This would combine the investors' judgments about price and timing for properties A, B, C, and D into overall priorities for each property. 4. Check the consistency of the judgments. 5. Come to a final decision based on the results of this process. These steps are more fully described below. ● Model the problem: Symbol table: Average wait time T Variance of waiting time V Number of security lines N Average wait time for PreCheck T1 Average wait time for ID Check T2 Average wait time for Baggage and Body Screening T3 Average service time T4 Variance of wait time for PreCheck V1 Variance of wait time for ID Check V2 Variance of wait time for Baggage and Body Screening V3 Variance of service time V4 ● Establish priorities among the elements of the hierarchy: Priority queue: T > N > V T1 > T2 > T3 > T4 V1 > V2 > V3 > V4 ● Synthesize these judgments to yield a set of overall priorities for the hierarchy: M T V N T 1 7 3 V 1/7 1 1/3 N 1/3 3 1 A T1 T2 T3 T4 T1 1 3 5 9 T2 1/3 1 2 6 T3 1/5 1/2 1 4 T4 1/9 1/6 1/4 1 B V1 V2 V3 V4 V1 1 3 5 9 V2 1/3 1 2 6 V3 1/5 1/2 1 4 V4 1/9 1/6 1/4 1 Priorities are numbers associated with the nodes of an AHP hierarchy. They represent the relative weights of the nodes in any group. Matrix M explains the weight of T, V, N for Z. And matrix A, B is similar to M. ● Check the consistency of the judgments. a) Supposing the greatest eigenvalue of M is λ, and the sum of all eigenvalue is n. The coincidence indicator is: b) Random consistency indexes: n 1 2 3 4 5 6 7 8 9 10 11 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51 c) Consistency ratio: , (Qualified when CR is less than 0.1, otherwise you need to adjust the pairwise comparison until it can pass the consistency check.) d) Normalized the characteristic root of λ to get the weight vector of the first level. e) As same as M, check the consistency of A, B and get their weight vectors. f) Create a new matrix C and a new weight vector W with these three weight vectors. Like matrix M, C explains the relative weight of T1-T4, V1-V4 and N for Z. And the vector W is the total weight vector of the model. g) The total weight vector of the model: W = (0.3905, 0.1590, 0.0899, 0.0301, 0.0513, 0.0209, 0.0118, 0.0039, 0.2426) ● Come to a final decision based on the results of this process. h) To make decision between two choices X, Y, we should normalize those nine attributes of A, B: T1-T4, V1-V4 and N. i) Calculate the value Z of X with its attributes and the total weight vector W, and in the same way the value Z of Y calculated. j) Make a final decision with the value Z of X and Y.