Jump to content

A question about mathematical modeling


JYJUM

Recommended Posts

 

This question is about combine the two contraints to become a mathematical modeling: 

(1) If the number of possible routes is less than 4, probability (a) will be used. All the routes will be considered and the travel time for each route will be calculated. However, if there are more or equal than 4 routes, probability (b) will be used in which 50 percent of the number of routes will be considered and calculated. After determining the number of routes to be considered, step (2) will take place.

Probability (a) Pi=number of routes 

Probability (b) Pi=0.5 * number of routes

 

(2) Let T be the set of possible routes. The routes will be randomly chosen based on probability above. X_(k-1) refers to the last route that is randomly chosen. In the statement, we use Xi≤ Xj to compare their traveling time. The route with the lowest traveling time, Xi, will be the candidate for optimal route.

$$T'=  \left\{  \left( X_0,X_1,...,X_ \left( K-1\right)  \right)| X_i \epsilon T,  \forall 0≤i≤K-1, X_i < X_j,  \forall i < j \right\} $$

 

 

How to combine both (1) and (2) into an appropriate mathematical modeling (equation)?

 

 

Edited by JYJUM
equation format
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

This website uses cookies to ensure you get the best experience on our website. See our Privacy Policy and Terms of Use