Suppose we have a transportation problem similar to pickup and delivery problems. So, we have a set of drivers and a set of passengers. each passenger has predefined origins and destinations. I'd like to know if we could compute the distance between a passenger's destinations and the drop-off nodes without having access to the solver's output.
Every riders could be picked-up and drooped-off by multiple drivers. And there's no particular order on nodes of the graph which is denoted by $N$.
We have a binary variables of $ x_{i,j}^{d,r}$ if driver $d$ drives $r$ on edge $(i,j)$ and we already know for each $r$ their start's $s_r$ and their destination's $d_r$ points ($s_r \in N$ and $d_r in N$). I'm wondering without knowing the path and values of variables from the solver how to minimize the objective as a distance between the last drop-off point and the destinations of each rider. Is this possible to compute this value implicitly and have it as an objective function or do we simply need more information?