The second matrix B D (bjk ) is a pair-wise comparison
matrix to determine weights for the criteria, where bjk is the
relative importance of criterion j over criterion k. Their values
are derived from the same survey as discussed earlier in this
section. The weights (wj) are calculated using the geomet-
ric mean [39] for each of the ve criteria. The attractions
(Table 6) are ranked according to
P5
jD1
aijwj, for Jane's trip to
New York City, the attraction `Times Square' is ranked
the highest (0.3 miles from the hotel, 24 hours open time,
`Culture, history' activities that are the highest match to her
preferred activities, 6 min walking time, and free admis-
sion fee). Other attractions that receive high ranks and that
can be visited within the preferred time and budget constraints
are the Empire State Building, American Museum of Nature,
Metropolitan Museum of Art, Central Park, and Statue of
Liberty. This arrangement results in a total tour time of
16 hours in two days and a total budget of $88 that satises
the preferred two-day visit and preferred budget of $150,
respectively. Using Dijkstra's shortest path algorithm, the
2-day tour is arranged as following: Day 1: Time square,
Empire State Building, and Statue of Liberty;
Day 2: Metropolitan Museum of Art, American Museum of
Nature, and Central Park.