beevabeeva
commented
3 years ago I received an answer on math.stackexchange that clears this up. See https://math.stackexchange.com/questions/4028209/weird-indexing-in-the-milp-literature
Closing, since it is not a typo, but my inexperience.
Hi there, thanks for this great example which I am following - it is really good!
In the model formulation, we have:
I see that we have: d∈D={n+1,n+2,...,n+m}: Index and set of depots (service centers), where m is the number of depots. I am confused as to how there can be n+m depots. I am also confused as to why the set starts from n+1 instead of 1. In the example there are two depots, not 9 i.e 2+7.
I have run into something similar when studying the literature (Ramkumar et al 2012, their formulation also has confusing indices for the number of depots:
)
This makes me think I am missing some key concept in the formulation (as opposed to a typo).
Any enlightenment would be greatly appreciated.
Edit: Indeed, the paper referenced in the notebook also notes "(1,..,n+m) where the m depots are represented by n+1,...,n+m" but does not state their reasoning for doing so. (S. Salhi, A. Imran, N. A. Wassan. The multi-depot vehicle routing problem with heterogeneous vehicle fleet: Formulation and a variable neighborhood search implementation. Computers & Operations Research 52 (2014) 315-325.)
Edit 2: However, in the Supply Network I example, we have something that makes more sense (to me).:
Here there is no (n+1...n+m) indexing.