How to formulate the following problem?
The salesman gains a profit $p_{i}$ when visiting a city i, trip between city i and city j costs $c_{ij}$ and takes $t_{ij}$ time. The trip must not exceed a time limit T. The difference between profit and costs must be maximized.
I've formulated this problem as follows:
maximize $\sum _{i=1}^{n} \sum _{j=1}^{n}p_{ij}x_{ij}- \sum _{i=1}^{n} \sum _{j=1}^{n}c_{ij}x_{ij}$
can i formulate trip time as $\sum _{i=1}^{n} \sum _{j=1}^{n}t_{ij}x_{ij}$ and add the constraint $\sum _{i=1}^{n} \sum _{j=1}^{n}t_{ij}x_{ij} \leqslant T$?
I've read also about the Time Dependent TSP (TDTSP), but i'm not sure it's my case...