python - What tools to use to implement a graph network -

i'm working on hospital network optimization involves optimizing overall cost of patients visits.

i want changing segment of hospitals in network. there 5 segments: - segment n°1 / basic correlated high patients volume - segment n°5 / luxury correlated low patients volume

the higher segment patient paies more hospitals gets into.

the segment not correlated cost nor quality.

my hospitals geographically clustered, because i'm not going apply optimization replaces hospital 1 located 100km away.

i want able select hospital downgrade or upgrade , see consequence in terms of volume movement in sub-network inside cluster.

there 2 phenomenon: - downgrade => vaccum effect, hospital brings new patients had no access in previous segment. - upgrade => deployment effect, hospital loses lower segment , patients go other hospitals in sub-network

constraint: - geographic - speciality of hospital / distribution of medical acts

each hospital has "id card": - speciality of hospital / distribution of medical acts - current volume per segment - current segment - normalized cost / average cost - patient satisfaction score

example:

hospital h1 has "id card" s1 , segment 3 (which means can accept patients paid segment 3, 4 or 5)

patients come h1 medical centers mc , diagnostic center dc

vol = volume of patients

vol(mc1—>h1) = vol(mc1—>h1){segment 3} + vol(mc1—>hop1){segment 4} + vol(mc1—>h1){segment 5}

if downgrade h1, there vaccum effect:

vol(mc1—>h1) = vol(mc1—>h1){segment 2} + vol(mc1—>h1){segment 3} + vol(mc1—>h1){segment 4} + vol(mc1—>h1){segment 5} 

if upgrade h1, there deployment effect:

vol(mc1—>h1) = vol(mc1—>h1){segment 4} + vol(mc1—>h1){segment 5} 

i want make simulate scenario can find best configuration using current volume maximizes cost efficiency of network.

this seems linear programmation problem might solved using metaheuristics tabu search. though maximum flow problem... domains not specialty , wondering how can start build using maybe python libraries networkx or graphilion. guidance helpful.

objectif

the objective limit healthcare costs.

• by downgrading segment of less expansive hospitals because of patients have paid segment 1, 2, 3, more downgrade more patient flock hospital.

• by upgrading segment of expansive hospitals penalize them being expansive , divert volume similar hospitals in cluster less expansive.

patient satisfaction rating used weight @ point, didn't think part yet.

there no entry volume constraint hospitals.