Spatiotemporal Critical Opportunity and Link Identification for Joint Participation Scheduling - Space-Time Integration in Geography and GIScience - page 112

Fig. 7.3 Joint activity opportunities

U. opp k ; G.t // D max ( X
i 2 STP j

CI .e i ;Œ0;t/ ! = linknum STP j ˇ ˇ ˇ

2 ST P.k; kst / ) STP j (7.12)

where linknum ( STP j ) represents the link number of the j th shortest space-time path
for op portunity k , STP j is a space-time path in the shortest space-time path set
STP.k;kst/,and kst is a user-defined constant which indicates the number of
the kst shortest space-time paths for opportunity k .
An opportunity with a utility index value within the fi rst kst maximum utility
index values U ( opp k , G ( t )) of its corresponding path set STP.k;kst/is referred to
here as a critical activity opportunity.
Therefore, two steps are required to identify critical activity opportunities for
scheduling joint participation. The first step is to identify the first kst shortest
space-time paths for each opportunity in the TVNBP. The second step is to
find the critical activity opportunity by finding the activity with the highest ratio
U ( opp k , G ( t ))/ criterion ( STP j ) among all available activity opportunities, where
criterion ( STP j ) is the value of the specific evaluation criterion (e.g., travel distance,
travel time) for opportunity k 's critical activity.