# fpl and constraints about centers

Does anybody know how we could optimise fpl problems with additional constraints?

• Cross-posted: math.stackexchange.com/questions/4092789/… Apr 7 at 19:17
• @RobPratt Thanks for your mention. I posted the question here because one of the user suggested it. Apr 7 at 19:58
• please don't change the question. Now the program is correct, and the text following the program refers to a fourth and fifth set of constraints which is no longer there. In addition, the answer to the question is no longer correct, as it says that the second set of constraints should be removed, which it no longer should.
– Sune
Apr 8 at 11:54
• @Sune You are right. Sorry about that. I put the question as it was at the beginning Apr 10 at 18:15

Your problem is a so-called single source capacitated facility location problem. Your second constraint is not meaningful and should be removed, otherwise the formulation seems to be correct. Often you see your third and fourth set of constraints combined in $$$$\sum_{i \in I} d_ia_{ij} \leq c_jy_j, \quad \forall j\in J$$$$

There is a ton of literature on this problem.

Edit: apparently I missed the wrong objective function for some reason. You need to measure the total travel cost and add the total fixed costs to that: $$$$\min\text{total travel costs} + \text{total fixed costs}$$$$ Can you take it from there?

• The objective function is not correct. See the linked post. Apr 7 at 19:18
• @Mohammadreza What makes you think there are hidden constraints?
– Sune
Apr 8 at 6:40
• You have formulated that. $a_{ij}=1$ if and only if family $i$ is assigned to centre $j$. And if family $i$ is assigned to centre $j$, the the capacity of that centre is decreased by $d_i$ (or equivalently, family $i$ consumes $d_i$ units of capacity at centre $j$). Given that the assigned vaccine-consumption to the centres cannot exceed the centres' capacity, all families' demands are met at the centre to which they are assigned.
– Sune
Apr 8 at 8:16