Objective measurement for attractiveness of sightseeing spots under minimization of maximum error among pairwise comparisons

This paper proposes a minimax problem to determine an attractiveness of each sightseeing spot based on pairwise comparison by the tourist. A tourist can subjectively and qualitatively compare two sightseeing spots, and the ranking of candidate sightseeing spots can be obtained from the standard AHP. However, it is almost impossible to set the numerical values of attractiveness of each sightseeing spot strictly. Furthermore, it is also difficult to evaluate the attractiveness objectively according to the tourist's feelings. On the other hand, by using sightseeing plans which include some popular sightseeing spots, a tourist can simultaneously do a qualitative and quantitative evaluation of multiple sightseeing spots. The main step of the proposed approach is to propose a mathematical programming problem to minimize the maximum error from the tourist's pairwise comparison and to determine the attractiveness of sightseeing spots objectively. Furthermore, the synergy effect among sightseeing spots is also considered.