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Cost_allo_sub_link_systemopt.py
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Cost_allo_sub_link_systemopt.py
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import numpy as np
import math
import sympy as sp
from gurobipy import *
from scipy.optimize import minimize
from scipy.optimize import LinearConstraint
import scipy.optimize
import matplotlib.pyplot as plt
import warnings
import pandas as pd
# import networkx as nx
import timeit
from time import time
import numpy as np
import ctypes
import copy
def intersection(lst1, lst2):
lst3 = [value for value in lst1 if value in lst2]
return lst3
# pre-process
def pre_process_intsol(flows_link, flows_path, y_sol, v_sol, path_set, dual_p,
link, link_fixed, MODnode_ori,MODoper_node_ori, MODnode, MODoper, dummy_link, d):
dual = dict()
for i in link:
dual[link[i]["start"],link[i]["end"]] = 0
for i in link_fixed:
dual[link[i]["start"],link[i]["end"]] = dual_p[i]
y = y_sol
v = v_sol
h_sol_MOD = dict()
for i in MODnode_ori:
h_sol_MOD[i] = 0
for i in range(len(MODnode)):
if v[i] == 1:
nodee = MODnode_ori[MODnode_ori.index(np.floor(MODnode[i]/10))]
h_sol_MOD[nodee] = MODnode[i]%10
h_sol = dict()
for i in MODoper:
h_sol[i] = 0
for i in MODoper:
for j in MODoper_node_ori[i]:
if h_sol_MOD[j] > 0:
h_sol[i] = h_sol_MOD[j]
break
h = []
for i in MODoper:
h.append(h_sol[i])
x_sol=dict()
for i in range(len(link)):
if i not in dummy_link:
for s in range(len(d)):
x_sol[(link[i]['start'],link[i]['end'],s)]=flows_link[s,i]
x_sol_= dict()
for i in range(len(link)):
if i not in dummy_link:
for s in range(len(d)):
x_sol_[(link[i]['start'],link[i]['end'])]=sum(flows_link[s,i] for s in range(len(d)))
out_of_sys = []
for linkk in dummy_link:
# print(sum(flows_link[ddd,linkk] for ddd in range(len(d))))
out_of_sys.append(sum(flows_link[ddd,linkk] for ddd in range(len(d))))
path_set_ = []
flows_path_ = []
count = 0
for s in range(len(d)):
path_set_od = []
for pathh in path_set[s]:
if flows_path[count]>0 and pathh[0] not in dummy_link:
path_set_od.append(pathh)
flows_path_.append(flows_path[count])
count+=1
path_set_.append(path_set_od)
path_set = path_set_
flows_path = flows_path_
lenn=0
for iii in path_set:
lenn+=len(iii)
print("Number of Paths:", lenn)
return path_set, flows_path, dual, y, v, h_sol_MOD, h_sol, h, x_sol, x_sol_, out_of_sys
###################################################################################################
###################################################################################################
###################################################################################################
###### cost allo prep
def cost_allo_prep(path_set, flows_path, dual, y, v, h_sol_MOD, h_sol, h, x_sol, x_sol_, out_of_sys,
link, dummy_link, d, link_Acce, MODoper, oper_list, t_coef, c_coef):
tt={}
cst={}
for i in link:
if i not in dummy_link:
cst[link[i]['start'],link[i]['end']]=link[i]['operating cost']
for s in range(len(d)):
tt[link[i]['start'],link[i]['end'],s]=link[i]['travel cost']
for i in link_Acce:
fs = h[MODoper.index(link_Acce[i]['operator'])]
fs = float(fs)
flow = sum(x_sol[link_Acce[i]['start'],link_Acce[i]['end'],s] for s in range(len(d)))
for s in range(len(d)):
if flow == 0:
tt[link_Acce[i]['start'],link_Acce[i]['end'],s]=0
elif fs == 0:
tt[link_Acce[i]['start'],link_Acce[i]['end'],s]=9999999999999
else:
tt[link_Acce[i]['start'],link_Acce[i]['end'],s]=t_coef[link_Acce[i]['operator']]*(fs)**(-2)*(flow)**1
volume=dict()
for i in link:
if i not in dummy_link:
volume[(link[i]['start'],link[i]['end'])]=sum(x_sol[link[i]['start'],link[i]['end'],s] for s in range(len(d)))
volume
users=dict()
operated=dict()
for i in link:
if i not in dummy_link:
operated[(link[i]['start'],link[i]['end'])]=link[i]['operator']
io=0
for s in range(len(d)):
if x_sol[link[i]['start'],link[i]['end'],s]>0 and io==0:
users[i]=[s]
io=1
elif x_sol[link[i]['start'],link[i]['end'],s]>0 and io==1:
users[i].append(s)
# print("users = ", users)
#Route taken from user s
route=dict()
for s in range(len(d)):
io=0;
for i in link:
if i not in dummy_link:
if i not in users:
users[i]={}
if x_sol[link[i]['start'],link[i]['end'],s]>0 and io==0:
route[s]=[[link[i]['start'],link[i]['end']]]
io=1
elif x_sol[link[i]['start'],link[i]['end'],s]>0 and io==1:
route[s].append([link[i]['start'],link[i]['end']])
# print("route = ", route)
operators=dict()
for i in oper_list:
operators[i]={}
for i in users:
if users[i]!={}:
if operators[link[i]['operator']]=={}:
operators[(link[i]['operator'])]=[i]
else:
operators[(link[i]['operator'])].append(i)
del operators[0]
# print("operators = ", operators)
path_set_node = []
for s in range(len(d)):
path_set_node_od = []
for pp in path_set[s]:
path_node_od = []
for ii in range(len(pp)):
if ii == 0:
path_node_od.append(link[pp[ii]]['start'])
path_node_od.append(link[pp[ii]]['end'])
else:
path_node_od.append(link[pp[ii]]['end'])
path_set_node_od.append(path_node_od)
path_set_node.append(path_set_node_od)
# print("test_routes = ", path_set_node)
import copy
new_routes = copy.deepcopy(path_set_node)
s = 0
count = 0
for ff in range(len(flows_path)):
if count<len(path_set[s]):
pass
else:
s+=1
count = 0
if flows_path[ff] == 0:
new_routes[s].pop(count)
count+=1
# print("new_routes = ", new_routes)
#operators in each user path
oper=dict()
user_paths=dict()
path_flow=dict()
belong=dict()
count=-1
lst=[]
link_to_path={}
operators_in_path={}
operators_vol_path={}
path_hash={}
for s in range(len(d)):
user_paths[s]={}
for path in new_routes[s]:
count+=1
path_hash[count]=path
path_flow[count]=flows_path[count]
operators_in_path[count]={}
if user_paths[s]=={}:
user_paths[s]=[count]
else:
user_paths[s].append(count)
path_edges=list(zip(path,path[1:]))
for edge in path_edges:
if (count,operated[edge]) not in lst:
if operators_in_path[count]=={}:
if operated[edge] != 0:
operators_in_path[count]=[operated[edge]]
else:
if operated[edge] != 0:
operators_in_path[count].append(operated[edge])
lst.append((count,operated[edge]))
if edge not in link_to_path:
link_to_path[edge]=[count]
else:
link_to_path[edge].append(count)
count=-1
for s in range(len(d)):
for path in new_routes[s]:
count+=1
for oper in oper_list:
if oper in operators_in_path[count]:
operators_vol_path[count,oper]=path_flow[count]
else:
operators_vol_path[count,oper]=0
# print('path_hash = ', path_hash)
# print('path_flow = ', path_flow)
return tt, cst, volume, users, operated, route, operators, path_set_node, new_routes, oper, user_paths, path_flow, belong, count, lst, link_to_path, operators_in_path, operators_vol_path, path_hash
###################################################################################################
###################################################################################################
###################################################################################################
def cost_allo(x_sol, path_set, d, out_of_sys, utility, MODoper, MODnode, MODnode_oper, t_coef, c_coef, oper_list, flows_link, operators, link, link_fixed, link_trans, link_MOD, link_Acce, link_Egre, dummy_link, link_from_to,
a_MODlink, a_fixedlink, a_translink, new_routes, V_coef, MODoper_Acce, orig, dest,
user_paths, operators_in_path, nodes, dual, y, v, h, tt):
x = x_sol
used_link_set = []
for iii in path_set:
for jjj in iii:
used_link_set = used_link_set+jjj
used_link_set = list(np.unique(used_link_set))
lst = []
for iii in used_link_set:
aaa = (iii,link[iii]["operator"])
lst.append(aaa)
m1 = Model()
# Model variables
c = m1.addVars(lst,lb = 0,vtype = GRB.CONTINUOUS, name = 'price')
u = m1.addVars(range(len(d)),lb = 0,ub=utility, vtype = GRB.CONTINUOUS, name = 'u')
m1.update()
# (5a) profitability
infra_cost = dict()
for operr in MODoper:
infra_cost[operr] = 0
for nodee in MODnode_oper:
operr = MODnode_oper[nodee]
infra_cost[operr] = infra_cost[operr] + v[MODnode.index(nodee)]*V_coef[nodee]
MODoper_C = dict()
for i in MODoper:
link_ = MODoper_Acce[i]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x_sol[l[0],l[1],ddd]
MODoper_C[i] = c_coef[i]*demand*(h[MODoper.index(i)]**2) + infra_cost[i]
oper_list_ = oper_list.copy()
oper_list_.remove(0)
for oper in oper_list_:
if oper not in MODoper: # fixed operator
m1.addConstr(quicksum(c[linkk,oper]*sum(flows_link)[linkk] for linkk in operators[oper]) >= sum(link[i]['operating cost'] for i in operators[oper]) , name = 'operator_profitable_'+str(np.round(oper)))
else: # MOD operator
ooo = intersection(operators[oper], list(a_MODlink))
m1.addConstr(quicksum(c[linkk,oper]*sum(flows_link)[linkk] for linkk in ooo) >= MODoper_C[oper], name = 'operator_profitable_'+str(np.round(oper)))
m1.update()
# (5b) feasibility (Requiring same payoff for user paths of the same O-D)
count =- 1
for s in range(len(d)):
for path in new_routes[s]:
count += 1
rhs = utility[s]
lhs = 0
ttl_price = 0
path_edges = list(zip(path,path[1:]))
for edge in path_edges:
rhs -= tt[edge[0],edge[1],s]
ttl_price += c[link_from_to[edge[0],edge[1]], link[link_from_to[edge[0],edge[1]]]['operator']]
path_index = new_routes[s].index(path)
m1.addConstr(u[s]+ ttl_price== rhs, name = 'cost_allo_'+str(s)+'_'+str(path_index))
m1.update()
# (5c) stability
capacity = dict()
cost = dict()
#Users on link ij
serves = dict()
for i in link:
if i not in dummy_link:
io = 0
for s in range(len(d)):
if x[link[i]['start'],link[i]['end'],s]>0 and io == 0:
serves[(link[i]['start'],link[i]['end'])] = [s]
io=1
elif x[link[i]['start'],link[i]['end'],s]>0 and io == 1:
serves[(link[i]['start'],link[i]['end'])].append(s)
for i in link:
if i not in dummy_link:
capacity[(link[i]['start'],link[i]['end'])] = link[i]['capacity']
cost[(link[i]['start'],link[i]['end'])] = link[i]['operating cost']
if (link[i]['start'],link[i]['end']) not in serves:
serves[(link[i]['start'],link[i]['end'])] = {}
C_ij = dict()
for i in a_fixedlink:
if serves[(link_fixed[i]['start'],link_fixed[i]['end'])] == {}:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['operating cost']
else:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = 0
for i in a_translink:
C_ij[(link_trans[i]['start'],link_trans[i]['end'])] = 0
for i in link_MOD:
fs = h[MODoper.index(link_MOD[i]['operator'])]
if fs > 0: # the operator is operating
link_ = MODoper_Acce[link_MOD[i]['operator']]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x[l[0],l[1],ddd]
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(fs**2)*((demand+1)**1) - c_coef[link_MOD[i]['operator']]*(fs**2)*((demand)**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
else: # the operator is not operating
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(1**2)*(1**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
for i in link_Acce:
C_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 0
for i in link_Egre:
C_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
T_ij = dict()
for i in link_fixed:
T_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['travel cost']
for i in link_trans:
T_ij[(link_trans[i]['start'],link_trans[i]['end'])] = link_trans[i]['travel cost']
for i in link_MOD:
T_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = link_MOD[i]['travel cost']
for i in link_Acce:
fs = h[MODoper.index(link_Acce[i]['operator'])]
# print(link_Acce[i]['start'],link_Acce[i]['end'], fs)
flow = sum(x[link_Acce[i]['start'],link_Acce[i]['end'],ddd] for ddd in range(len(d)))
if fs == 0:
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 9999999999999
else:
fs = float(fs)
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = t_coef[link_Acce[i]['operator']]*(fs)**(-2)*(flow+1)**1
for i in link_Egre:
T_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
### revise link: remove closed MOD nodes, links, and transfer links
MOD_node_closed = []
for i in range(len(MODnode)):
if v[i] == 0:
MOD_node_closed.append(MODnode[i])
link_used = copy.deepcopy(link)
for i in link:
start_nodee = link_used[i]['start']
end_nodee = link_used[i]['end']
if (start_nodee in MOD_node_closed) or (end_nodee in MOD_node_closed):
del link_used[i]
if i in dummy_link:
del link_used[i]
from itertools import combinations
from MaaS_game_link_fare_systemopt import Dijkstra_cpp
stability_path_set = dict()
for s in range(len(d)):
stability_path_set[s] = []
for s in range(len(d)):
stability_path_set_od = []
oper_set = []
for path_id in user_paths[s]:
if operators_in_path[path_id] == {}:
pass
else:
oper_set = oper_set + operators_in_path[path_id]
oper_set = list(np.unique(oper_set))
oper_comb = []
for numm in range(1,len(oper_set)+1):
comb_ = list(combinations(oper_set, numm))
oper_comb = oper_comb+comb_
# for i in list(oper_comb):
# print (i)
oper_comb_fin = copy.deepcopy(oper_comb)
for path_id in user_paths[s]:
oper_path = operators_in_path[path_id]
for iii in oper_comb:
if all(operr not in iii for operr in oper_path):
if iii in oper_comb_fin:
oper_comb_fin.pop(oper_comb_fin.index(iii))
for pi in oper_comb_fin:
## shortest path - such that no operator is in pi
# graph matrix
graph_omega = np.ones((len(nodes),len(nodes)))*(-1)
for linkk in link:
if linkk not in dummy_link:
if link[linkk]['operator'] not in pi:
start_id = nodes.index(link[linkk]['start'])
end_id = nodes.index(link[linkk]['end'])
graph_omega[start_id, end_id] = T_ij[link[linkk]['start'],link[linkk]['end']]+dual[link[linkk]['start'],link[linkk]['end']]+C_ij[link[linkk]['start'],link[linkk]['end']]
# dijkstra
O = int(orig[s])
D = int(dest[s])
O_id = nodes.index(O)
D_id = nodes.index(D)
path_node_ind_lst, dist = Dijkstra_cpp(nodes, O_id, D_id, graph_omega)
path_node_ind = path_node_ind_lst[D_id]
path_len = dist[D_id]
path_node = []
for node_ind in path_node_ind:
nodee = nodes[node_ind]
path_node.append(nodee)
path_link = []
for nodee_ind in range(len(path_node)-1):
path_link.append(link_from_to[path_node[nodee_ind],path_node[nodee_ind+1]])
r = path_link # link id's
print(r)
if r != []:
stability_path_set_od.append(r)
core = utility[s]
UN=[]
rhs=0
for linkk in r:
core-=T_ij[link[linkk]['start'],link[linkk]['end']]
core-=dual[link[linkk]['start'],link[linkk]['end']]
core-=C_ij[link[linkk]['start'],link[linkk]['end']]
if linkk in used_link_set:
UN.append(c[linkk,link[linkk]['operator']])
rhs+=sum(list(set(UN)))
#adding stability constraints
# path_index = new_routes[s].index(j)
m1.addConstr(rhs+u[s]>=core,
name = 'stability_'+str(r))
m1.update()
stability_path_set[s] = stability_path_set_od
## zeros
for i in c:
if i[0] in link_trans:
m1.addConstr(c[i]==0, name = 'transfer link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
elif i[0] in link_Acce:
m1.addConstr(c[i]==0, name = 'Acce link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
elif i[0] in link_Egre:
m1.addConstr(c[i]==0, name = 'Egre link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
m1.update()
obj = 88
m1.update()
m1.params.outputflag=0
# m1.display()
m1.optimize()
# print(m1.status)
# print(u)
# m1.computeIIS()
# m1.write("model_infea.ilp")
# a = read('model_infea.ilp')
# a.display()
if m1.status == 3 or m1.status == 4:
m1.computeIIS()
m1.write("model_infea.ilp")
a = read('model_infea.ilp')
# a.display()
infea_path = []
for s in range(len(d)):
for path in new_routes[s]:
path_index = new_routes[s].index(path)
if a.getConstrByName('cost_allo_'+str(s)+'_'+str(path_index)) == None:
pass
else:
infea_path.append(path)
unstab_path = []
alter_path = []
for s in range(len(d)):
for path in new_routes[s]:
path_index = new_routes[s].index(path)
for k in range(len(path_set[s][path_index])):
if a.getConstrByName('stability_'+str(s)+'_'+str(path_index)+'_'+str(k)) == None:
pass
else:
unstab_path.append(path)
alter_path.append(path_set[s][path_index])
print('Infeasible path:',infea_path)
print('Unstable path:',unstab_path)
print('Alternative path:',alter_path)
prices = []
p = {}
u_s = []
u = []
return 0, stability_path_set, [], [], [], [], [], []
else:
print('Cost Allocation feasible!')
# ### User optimal
obj = 0
obj+=quicksum(u[s]*(d[s]-out_of_sys[s]) for s in range(len(d)))
m1.setObjective(obj,GRB.MAXIMIZE)
m1.update()
m1.params.outputflag=0
m1.optimize()
x_ = m1.getAttr('X', m1.getVars())
prices = x_[0:len(lst)]
p_user_opt=dict()
for i in range(len(lst)):
p_user_opt[lst[i]]=prices[i]
u_s_user_opt = x_[len(lst) : len(lst)+len(d)]
u_user_opt = dict()
for var in u:
u_user_opt[var]=u[var].x
# ### Operator optimal
obj = 0
for s in range(len(d)):
for linkk in used_link_set:
obj+=c[linkk,link[linkk]['operator']]*sum(flows_link)[linkk]
m1.setObjective(obj,GRB.MAXIMIZE)
m1.update()
m1.params.outputflag=0
m1.optimize()
x_ = m1.getAttr('X', m1.getVars())
prices = x_[0:len(lst)]
p_oper_opt=dict()
for i in range(len(lst)):
p_oper_opt[lst[i]]=prices[i]
u_s_oper_opt = x_[len(lst) : len(lst)+len(d)]
u_oper_opt = dict()
for i in u:
u_oper_opt[var]=u[var].x
return 1, stability_path_set, p_user_opt, u_s_user_opt, u_user_opt, p_oper_opt, u_s_oper_opt, u_oper_opt
###################################################################################################
###################################################################################################
###################################################################################################
def subsidy_stablize(stability_path_set, x_sol, path_set, d, out_of_sys, utility, MODoper, MODnode, MODnode_oper, t_coef, c_coef, oper_list, flows_link, operators, link, link_fixed, link_trans, link_MOD, link_Acce, link_Egre, dummy_link, link_from_to, path_flow,
a_MODlink, a_fixedlink, a_translink, new_routes, V_coef, MODoper_Acce, orig, dest,
user_paths, operators_in_path, nodes, dual, y, v, h, tt):
x = x_sol
used_link_set = []
for iii in path_set:
for jjj in iii:
used_link_set = used_link_set+jjj
used_link_set = list(np.unique(used_link_set))
lst = []
for iii in used_link_set:
aaa = (iii,link[iii]["operator"])
lst.append(aaa)
number_routes = dict()
for i in range(len(d)):
number_routes[i] = len(new_routes[i])
lst_sub = []
for i in number_routes:
for iii in range(number_routes[i]):
lst_sub.append((i,iii))
m1 = Model()
# Model variables
c = m1.addVars(lst,lb = 0,vtype = GRB.CONTINUOUS, name = 'price')
u = m1.addVars(range(len(d)),lb = 0,ub=utility, vtype = GRB.CONTINUOUS, name = 'u')
S_path = m1.addVars(lst_sub, lb = 0, vtype = GRB.CONTINUOUS, name = 'subsidy_user')
m1.update()
# (5a) profitability
infra_cost = dict()
for operr in MODoper:
infra_cost[operr] = 0
for nodee in MODnode_oper:
operr = MODnode_oper[nodee]
infra_cost[operr] = infra_cost[operr] + v[MODnode.index(nodee)]*V_coef[nodee]
MODoper_C = dict()
for i in MODoper:
link_ = MODoper_Acce[i]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x_sol[l[0],l[1],ddd]
MODoper_C[i] = c_coef[i]*demand*(h[MODoper.index(i)]**2) + infra_cost[i]
oper_list_ = oper_list.copy()
oper_list_.remove(0)
for oper in oper_list_:
if oper not in MODoper: # fixed operator
m1.addConstr(quicksum((c[linkk,oper])*sum(flows_link)[linkk] for linkk in operators[oper]) >= sum(link[i]['operating cost'] for i in operators[oper]) , name = 'operator_profitable_'+str(np.round(oper)))
else: # MOD operator
ooo = intersection(operators[oper], list(a_MODlink))
m1.addConstr(quicksum((c[linkk,oper])*sum(flows_link)[linkk] for linkk in ooo) >= MODoper_C[oper], name = 'operator_profitable_'+str(np.round(oper)))
m1.update()
# (5b) feasibility (Requiring same payoff for user paths of the same O-D)
count =- 1
for s in range(len(d)):
for path in new_routes[s]:
count += 1
rhs = utility[s]
lhs = 0
ttl_price = 0
path_edges = list(zip(path,path[1:]))
for edge in path_edges:
rhs -= tt[edge[0],edge[1],s]
ttl_price += c[link_from_to[edge[0],edge[1]], link[link_from_to[edge[0],edge[1]]]['operator']]
path_index = new_routes[s].index(path)
ttl_price -= S_path[s,path_index]
m1.addConstr(u[s]+ ttl_price== rhs, name = 'cost_allo_'+str(s)+'_'+str(path_index))
m1.update()
# (5c) stability
capacity = dict()
cost = dict()
#Users on link ij
serves = dict()
for i in link:
if i not in dummy_link:
io = 0
for s in range(len(d)):
if x[link[i]['start'],link[i]['end'],s]>0 and io == 0:
serves[(link[i]['start'],link[i]['end'])] = [s]
io=1
elif x[link[i]['start'],link[i]['end'],s]>0 and io == 1:
serves[(link[i]['start'],link[i]['end'])].append(s)
for i in link:
if i not in dummy_link:
capacity[(link[i]['start'],link[i]['end'])] = link[i]['capacity']
cost[(link[i]['start'],link[i]['end'])] = link[i]['operating cost']
if (link[i]['start'],link[i]['end']) not in serves:
serves[(link[i]['start'],link[i]['end'])] = {}
C_ij = dict()
for i in a_fixedlink:
if serves[(link_fixed[i]['start'],link_fixed[i]['end'])] == {}:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['operating cost']
else:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = 0
for i in a_translink:
C_ij[(link_trans[i]['start'],link_trans[i]['end'])] = 0
for i in link_MOD:
fs = h[MODoper.index(link_MOD[i]['operator'])]
if fs > 0: # the operator is operating
link_ = MODoper_Acce[link_MOD[i]['operator']]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x[l[0],l[1],ddd]
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(fs**2)*((demand+1)**1) - c_coef[link_MOD[i]['operator']]*(fs**2)*((demand)**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
else: # the operator is not operating
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(1**2)*(1**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
for i in link_Acce:
C_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 0
for i in link_Egre:
C_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
T_ij = dict()
for i in link_fixed:
T_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['travel cost']
for i in link_trans:
T_ij[(link_trans[i]['start'],link_trans[i]['end'])] = link_trans[i]['travel cost']
for i in link_MOD:
T_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = link_MOD[i]['travel cost']
for i in link_Acce:
fs = h[MODoper.index(link_Acce[i]['operator'])]
# print(link_Acce[i]['start'],link_Acce[i]['end'], fs)
flow = sum(x[link_Acce[i]['start'],link_Acce[i]['end'],ddd] for ddd in range(len(d)))
if fs == 0:
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 9999999999999
else:
fs = float(fs)
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = t_coef[link_Acce[i]['operator']]*(fs)**(-2)*(flow+1)**1
for i in link_Egre:
T_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
### revise link: remove closed MOD nodes, links, and transfer links
MOD_node_closed = []
for i in range(len(MODnode)):
if v[i] == 0:
MOD_node_closed.append(MODnode[i])
link_used = copy.deepcopy(link)
for i in link:
start_nodee = link_used[i]['start']
end_nodee = link_used[i]['end']
if (start_nodee in MOD_node_closed) or (end_nodee in MOD_node_closed):
del link_used[i]
if i in dummy_link:
del link_used[i]
for s in range(len(d)):
for r in stability_path_set[s]:
core = utility[s]
UN=[]
rhs=0
for linkk in r:
core-=T_ij[link[linkk]['start'],link[linkk]['end']]
core-=dual[link[linkk]['start'],link[linkk]['end']]
core-=C_ij[link[linkk]['start'],link[linkk]['end']]
if linkk in used_link_set:
UN.append(c[linkk,link[linkk]['operator']])
rhs+=sum(list(set(UN)))
#adding stability constraints
# path_index = new_routes[s].index(j)
m1.addConstr(rhs+u[s]>=core,
name = 'stability_'+str(r))
m1.update()
## zeros
for i in c:
if i[0] in link_trans:
m1.addConstr(c[i]==0, name = 'transfer link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
elif i[0] in link_Acce:
m1.addConstr(c[i]==0, name = 'Acce link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
elif i[0] in link_Egre:
m1.addConstr(c[i]==0, name = 'Egre link'+str(link[i[0]]['start'])+str(link[i[0]]['end']))
m1.update()
################## Total Subsidies ##################
obj = 0
count = -1
for s in range(len(d)):
for path in new_routes[s]:
count += 1
path_index = new_routes[s].index(path)
obj += path_flow[count]*S_path[s,path_index]
m1.setObjective(obj,GRB.MINIMIZE)
m1.update()
# m1.display()
m1.params.outputflag=0
m1.optimize()
if m1.status == 2:
subsidy_feasi = 1
subsidy_obj = m1.getObjective()
subsidy_obj = subsidy_obj.getValue()
for ii in S_path:
S_path[ii] = S_path[ii].x
else:
subsidy_feasi = 0
subsidy_obj = []
S_path = []
return subsidy_feasi, subsidy_obj, S_path
###################################################################################################
###################################################################################################
###################################################################################################
def cost_allo_sub(stability_path_set, x_sol, path_set, d, out_of_sys, utility, MODoper, MODnode, MODnode_oper, t_coef, c_coef, oper_list, flows_link, operators, link, link_fixed, link_trans, link_MOD, link_Acce, link_Egre, dummy_link, link_from_to, path_flow, a_MODlink, a_fixedlink, a_translink, new_routes, V_coef, MODoper_Acce, orig, dest, user_paths, operators_in_path, nodes, dual, y, v, h, tt, S_path):
x = x_sol
used_link_set = []
for iii in path_set:
for jjj in iii:
used_link_set = used_link_set+jjj
used_link_set = list(np.unique(used_link_set))
lst = []
for iii in used_link_set:
aaa = (iii,link[iii]["operator"])
lst.append(aaa)
m1 = Model()
# Model variables
c = m1.addVars(lst,lb = 0,vtype = GRB.CONTINUOUS, name = 'price')
u = m1.addVars(range(len(d)),lb = 0,ub=utility, vtype = GRB.CONTINUOUS, name = 'u')
m1.update()
# (5a) profitability
infra_cost = dict()
for operr in MODoper:
infra_cost[operr] = 0
for nodee in MODnode_oper:
operr = MODnode_oper[nodee]
infra_cost[operr] = infra_cost[operr] + v[MODnode.index(nodee)]*V_coef[nodee]
MODoper_C = dict()
for i in MODoper:
link_ = MODoper_Acce[i]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x_sol[l[0],l[1],ddd]
MODoper_C[i] = c_coef[i]*demand*(h[MODoper.index(i)]**2) + infra_cost[i]
oper_list_ = oper_list.copy()
oper_list_.remove(0)
for oper in oper_list_:
if oper not in MODoper: # fixed operator
m1.addConstr(quicksum((c[linkk,oper])*sum(flows_link)[linkk] for linkk in operators[oper]) >= sum(link[i]['operating cost'] for i in operators[oper]) , name = 'operator_profitable_'+str(np.round(oper)))
else: # MOD operator
ooo = intersection(operators[oper], list(a_MODlink))
m1.addConstr(quicksum((c[linkk,oper])*sum(flows_link)[linkk] for linkk in ooo) >= MODoper_C[oper], name = 'operator_profitable_'+str(np.round(oper)))
m1.update()
# (5b) feasibility (Requiring same payoff for user paths of the same O-D)
count =- 1
for s in range(len(d)):
for path in new_routes[s]:
count += 1
rhs = utility[s]
lhs = 0
ttl_price = 0
path_edges = list(zip(path,path[1:]))
for edge in path_edges:
rhs -= tt[edge[0],edge[1],s]
ttl_price += c[link_from_to[edge[0],edge[1]], link[link_from_to[edge[0],edge[1]]]['operator']]
path_index = new_routes[s].index(path)
ttl_price -= S_path[s,path_index]
m1.addConstr(u[s]+ ttl_price== rhs, name = 'cost_allo_'+str(s)+'_'+str(path_index))
m1.update()
# (5c) stability
capacity = dict()
cost = dict()
#Users on link ij
serves = dict()
for i in link:
if i not in dummy_link:
io = 0
for s in range(len(d)):
if x[link[i]['start'],link[i]['end'],s]>0 and io == 0:
serves[(link[i]['start'],link[i]['end'])] = [s]
io=1
elif x[link[i]['start'],link[i]['end'],s]>0 and io == 1:
serves[(link[i]['start'],link[i]['end'])].append(s)
for i in link:
if i not in dummy_link:
capacity[(link[i]['start'],link[i]['end'])] = link[i]['capacity']
cost[(link[i]['start'],link[i]['end'])] = link[i]['operating cost']
if (link[i]['start'],link[i]['end']) not in serves:
serves[(link[i]['start'],link[i]['end'])] = {}
C_ij = dict()
for i in a_fixedlink:
if serves[(link_fixed[i]['start'],link_fixed[i]['end'])] == {}:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['operating cost']
else:
C_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = 0
for i in a_translink:
C_ij[(link_trans[i]['start'],link_trans[i]['end'])] = 0
for i in link_MOD:
fs = h[MODoper.index(link_MOD[i]['operator'])]
if fs > 0: # the operator is operating
link_ = MODoper_Acce[link_MOD[i]['operator']]
demand = 0
for ddd in range(len(d)):
for l in link_:
demand += x[l[0],l[1],ddd]
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(fs**2)*((demand+1)**1) - c_coef[link_MOD[i]['operator']]*(fs**2)*((demand)**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
else: # the operator is not operating
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = c_coef[link_MOD[i]['operator']]*(1**2)*(1**1)
if v[MODnode.index(link_MOD[i]['start'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['start']]
if v[MODnode.index(link_MOD[i]['end'])] == 0:
C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = C_ij[(link_MOD[i]['start'],link_MOD[i]['end'])]+V_coef[link_MOD[i]['end']]
for i in link_Acce:
C_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 0
for i in link_Egre:
C_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
T_ij = dict()
for i in link_fixed:
T_ij[(link_fixed[i]['start'],link_fixed[i]['end'])] = link_fixed[i]['travel cost']
for i in link_trans:
T_ij[(link_trans[i]['start'],link_trans[i]['end'])] = link_trans[i]['travel cost']
for i in link_MOD:
T_ij[(link_MOD[i]['start'],link_MOD[i]['end'])] = link_MOD[i]['travel cost']
for i in link_Acce:
fs = h[MODoper.index(link_Acce[i]['operator'])]
# print(link_Acce[i]['start'],link_Acce[i]['end'], fs)
flow = sum(x[link_Acce[i]['start'],link_Acce[i]['end'],ddd] for ddd in range(len(d)))
if fs == 0:
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = 9999999999999
else:
fs = float(fs)
T_ij[(link_Acce[i]['start'],link_Acce[i]['end'])] = t_coef[link_Acce[i]['operator']]*(fs)**(-2)*(flow+1)**1
for i in link_Egre:
T_ij[(link_Egre[i]['start'],link_Egre[i]['end'])] = 0
### revise link: remove closed MOD nodes, links, and transfer links
MOD_node_closed = []
for i in range(len(MODnode)):
if v[i] == 0:
MOD_node_closed.append(MODnode[i])
link_used = copy.deepcopy(link)
for i in link:
start_nodee = link_used[i]['start']
end_nodee = link_used[i]['end']
if (start_nodee in MOD_node_closed) or (end_nodee in MOD_node_closed):
del link_used[i]
if i in dummy_link:
del link_used[i]
for s in range(len(d)):
for r in stability_path_set[s]:
core = utility[s]
UN=[]
rhs=0
for linkk in r:
core-=T_ij[link[linkk]['start'],link[linkk]['end']]
core-=dual[link[linkk]['start'],link[linkk]['end']]
core-=C_ij[link[linkk]['start'],link[linkk]['end']]
if linkk in used_link_set:
UN.append(c[linkk,link[linkk]['operator']])
rhs+=sum(list(set(UN)))
#adding stability constraints