def defineVars(data: DataInstance):
model = Model("GLayout")
L = define1DIntVarArray(model, data.element_count, "L")
R = define1DIntVarArray(model, data.element_count, "R")
T = define1DIntVarArray(model, data.element_count, "T")
B = define1DIntVarArray(model, data.element_count, "B")
H = define1DIntVarArray(model, data.element_count, "H")
W = define1DIntVarArray(model, data.element_count, "W")
ABOVE = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "ABOVE")
LEFT = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "LEFT")
N = data.element_count
LAG = define1DBoolVarArray(model, data.element_count, "LAG")
RAG = define1DBoolVarArray(model, data.element_count, "RAG")
TAG = define1DBoolVarArray(model, data.element_count, "TAG")
BAG = define1DBoolVarArray(model, data.element_count, "BAG")
vLAG = define1DIntVarArray(model, data.element_count, "vLAG")
vRAG = define1DIntVarArray(model, data.element_count, "vRAG")
vTAG = define1DIntVarArray(model, data.element_count, "vTAG")
vBAG = define1DIntVarArray(model, data.element_count, "vBAG")
elemAtLAG = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "zLAG")
elemAtRAG = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "zRAG")
elemAtTAG = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "zTAG")
elemAtBAG = define2DBoolVarArrayArray(model, data.element_count, data.element_count, "zBAG")
return model, N, (L, R, T, B, H, W), (ABOVE, LEFT), (LAG, RAG, TAG, BAG), (vLAG, vRAG, vTAG, vBAG), \
(elemAtLAG, elemAtRAG, elemAtTAG, elemAtBAG)
def __init__(self,pp:ProcurementProblem,material:int,pi:float):
"""
Creates an instance of the DW's subproblem
for a given material and given pi, the dual
variable value corresponding to the complicating constraints
in the RMP.
:param pp:
:param product:
:param pi:
"""
self.pp = pp
self.m = Model()
self.material = material
# The subproblem has only one decision variable
self.x = self.m.addVar()
# The objective function will be
# (c_j - pi A_j)*x, where j = material
expr = (self.pp.costs[material] - pi*self.pp.consumption[material]) * self.x
self.m.setObjective(expr, GRB.MINIMIZE)
# The constraints bind the value of x to a min and max production quantity
self.m.addConstr(self.x <= self.pp.max_production[material])
self.m.addConstr(self.x >= self.pp.min_production[material])
def __init__(self, flp: FacilityLocationProblem, x: list):
self.flp = flp
self.m = Model()
# Creates the variables
y = self.m.addVars(flp.n_facilities, flp.n_customers, name="y")
v1 = self.m.addVars(flp.n_facilities, name="v+")
v2 = self.m.addVars(flp.n_customers, name="v-")
# Creates the objective
expr = 0
for i in range(flp.n_facilities):
expr += v1[i]
for j in range(flp.n_customers):
expr += v2[j]
self.m.setObjective(expr, GRB.MINIMIZE)
# Constraints
self.dc = []
self.cc = []
for i in range(flp.n_facilities):
print(x[i])
self.cc.append(
self.m.addConstr(
y.sum(i, '*') - v1[i] <= flp.capacity[i] * x[i]))
for j in range(flp.n_customers):
self.dc.append(
self.m.addConstr(y.sum('*', j) + v2[j] >= flp.demands[j]))
def __init__(self, pp: ProcurementProblem):
"""
Builds an instance of the DW's RMP for the
Procurement Problem.
:param pp:
"""
# Builds an instance of the model
self.m = Model()
self.pp = pp
# In the following list it will store all columns added to RMP during the DW algorithm
self.columns = []
# Initially there is no variable,
# but we will add them here
# as we generate them
self.u = []
# Creates an empty objective
self.m.setObjective(0, GRB.MINIMIZE)
# Creates the complicating constraints
self.compc = self.m.addConstr(0, GRB.GREATER_EQUAL, self.pp.demand,
"cc")
# Creates the convexity constraints
self.convc = self.m.addConstr(0, GRB.EQUAL, 1)
def __init__(self, p: CuttingStockProblem):
self.p = p
self.m = Model('CS1')
# Decision variables
n_large_rolls = self.p.get_max_number_of_large_rolls()
n_small_roll_types = len(self.p.demand)
print(n_large_rolls, n_small_roll_types)
y = self.m.addVars([i for i in range(n_large_rolls)],
lb=0,
ub=1,
vtype=GRB.CONTINUOUS,
name="y")
z = self.m.addVars([j for j in range(n_small_roll_types)],
[i for i in range(n_large_rolls)],
lb=0,
ub=GRB.INFINITY,
vtype=GRB.CONTINUOUS,
name="x")
# Objective function
self.m.setObjective(y.sum('*'))
# Constraints
# Note that the argument passed to quicksum is a list, and the list is built using comprehension
self.m.addConstrs(
quicksum([
self.p.width_small_rolls[i] * z[i, j]
for i in range(n_small_roll_types)
]) <= self.p.width_large_rolls * y[j]
for j in range(n_large_rolls))
self.m.addConstrs(
z.sum(i, '*') >= self.p.demand[i]
for i in range(n_small_roll_types))
def __init__(self, p: AlloyProductionProblem):
self.p = p
self.m = Model('APP')
# Creates the decision variables
self.materials = list(p.availability.keys())
chemicals = list(p.max_grade.keys())
self.x = self.m.addVars(self.materials, name='x')
# Creates the objective function
expr = self.x.prod(p.cost)
self.m.setObjective(expr, sense=GRB.MINIMIZE)
# Creates the constraints
# Min content
self.m.addConstrs(
quicksum([p.content[(k, m)] * self.x[m]
for m in self.materials]) >= p.min_grade[k] *
self.x.sum('*') for k in chemicals)
# Max content
self.m.addConstrs(
quicksum([p.content[(k, m)] * self.x[m]
for m in self.materials]) <= p.max_grade[k] *
self.x.sum('*') for k in chemicals)
# Availability
self.m.addConstrs(self.x[m] <= p.availability[m]
for m in self.materials)
# Demand
self.m.addConstr(self.x.sum('*') >= p.demand)
def __init__(self):
self.m = Model()
self.x = self.m.addVar(name="x")
self.phi = self.m.addVar(name="phi")
# Objective function
self.m.setObjective(2 * self.x + self.phi, sense=GRB.MINIMIZE)
def __init__(self,p:KnapsackProblem):
self.p = p
self.m = Model('knapsack')
# Creates the decision variables
self.x = self.m.addVars(len(p.rewards),vtype = GRB.BINARY,name = "x")
# Creates the objective
self.m.setObjective(quicksum([self.p.rewards[i] * self.x[i] for i in range(len(self.p.rewards))]),sense=GRB.MAXIMIZE)
# Creates the constraint
self.m.addConstr(quicksum([self.p.weights[i] * self.x[i] for i in range(len(self.p.weights))]) <= self.p.capacity)
def __init__(self, x: float):
self.m = Model()
self.y1 = self.m.addVar(name = "y1")
self.y2 = self.m.addVar(name = "y2")
# Objective function
self.m.setObjective(self.y1 + 3*self.y2, sense=GRB.MINIMIZE)
# Constraints
self.c1 = self.m.addConstr(2 * self.y1 + self.y2 == 1 - x)
self.c2 = self.m.addConstr(-self.y1 + self.y2 == 2 - 4 * x)
def __init__(self,p: UraniumMineProblem):
self.p = p
self.m = Model('uranium')
# Decision variables
self.x = self.m.addVars(self.p.blocks,vtype=GRB.BINARY,name="x")
# Objective function
expr = quicksum([(p.values[b] - p.costs[b]) * self.x[b] for b in p.blocks])
self.m.setObjective(expr,sense=GRB.MAXIMIZE)
# Constraints
self.m.addConstrs(self.x[a] - self.x[b] <= 0 for (a,b) in p.precedences)
def __init__(self):
self.m = Model()
self.x = self.m.addVar(name="x")
self.y1 = self.m.addVar(name="y1")
self.y2 = self.m.addVar(name="y2")
# Objective function
self.m.setObjective(2 * self.x + self.y1 + 3 * self.y2,
sense=GRB.MINIMIZE)
# Constraints
self.m.addConstr(2 * self.y1 + self.y2 + self.x == 1)
self.m.addConstr(-self.y1 + self.y2 + 4 * self.x == 2)
def __init__(self, p:CuttingStockProblem):
self.p = p
self.m = Model('CS1')
# Decision variables
n_patterns = len(self.p.get_feasible_patterns())
x = self.m.addVars(n_patterns,lb= 0, ub= GRB.INFINITY, vtype=GRB.CONTINUOUS,name="x")
# Objective function
self.m.setObjective(x.sum('*'))
# Constraints
# Note that the argument passed to quicksum is a list, and the list is built using comprehension
self.m.addConstrs(quicksum([self.p.get_feasible_patterns()[q][i] * x[q] for q in range(n_patterns)]) >= self.p.demand[i] for i in range(len(p.demand)))
def __init__(self, p: StadiumConstructionProblem):
self.p = p
self.m = Model('stadium')
# Decision variables
self.x = self.m.addVars(self.p.tasks, name="x")
self.q = self.m.addVar(name="maxtime")
# Objective function
self.m.setObjective(self.q, sense=GRB.MINIMIZE)
# Constraints
self.m.addConstrs(self.q - self.x[t] >= 0 for t in p.tasks)
self.m.addConstrs(self.x[t1] - self.x[t2] >= p.durations[t1]
for (t1, t2) in p.precedences)
self.m.addConstrs(self.x[t] >= p.durations[t] for t in p.tasks)
def SolveStoModel(self) -> Model:
StoModel = Model('StoModel')
StoModel.setParam('OutputFlag', 0)
StoModel.modelSense = GRB.MINIMIZE
m, n = self.m, self.n
h, f = self.h, self.f
d_rs = self.d_rs
d_rs_length = len(d_rs)
I = StoModel.addVars(m, vtype=GRB.CONTINUOUS, name='I')
Z = StoModel.addVars(m, vtype=GRB.BINARY, name='Z')
Transshipment_X = StoModel.addVars(self.roads,
d_rs_length,
vtype=GRB.CONTINUOUS,
name='Transshipment_X')
objFunc_holding = quicksum(I[i] * h[i] for i in range(m))
objFunc_fixed = quicksum(Z[i] * f[i] for i in range(m))
objFunc_penalty = quicksum(d_r[j] - Transshipment_X.sum('*', j, k)
for k, d_r in d_rs.items()
for j in range(n))
objFunc = objFunc_holding + objFunc_fixed + (objFunc_penalty /
d_rs_length)
StoModel.setObjective(objFunc)
# 约束1
for k in range(d_rs_length):
StoModel.addConstrs(
Transshipment_X.sum(i, '*', k) <= I[i] for i in range(m))
# 约束2
for k, d_r in d_rs.items():
StoModel.addConstrs(
Transshipment_X.sum('*', j, k) <= d_r[j] for j in range(n))
# 约束3 I_i<=M*Z_i
StoModel.addConstrs(I[i] <= 20000 * Z[i] for i in range(m))
# 求解评估模型
StoModel.optimize()
self.model = StoModel
return StoModel
def __init__(self, fsp: FacilitySizingProblem, x: list):
self.fsp = fsp
self.m = Model()
# Creates the variables
y = self.m.addVars(fsp.n_facilities, fsp.n_customers, name="y")
v1 = self.m.addVars(fsp.n_facilities, name="v+")
v2 = self.m.addVars(fsp.n_customers, name="v-")
# Creates the objective
expr = v1.sum() + v2.sum()
self.m.setObjective(expr, GRB.MINIMIZE)
# Constraints
self.demand_c = self.m.addConstrs(
y.sum('*', j) + v1[j] >= fsp.demands[j]
for j in range(fsp.n_customers))
self.capacity_c = self.m.addConstrs(
y.sum(i, '*') - v2[i] <= x[i] for i in range(fsp.n_facilities))
def __init__(self, x):
self.m = Model()
self.y1 = self.m.addVar(name="y1")
self.y2 = self.m.addVar(name="y2")
self.v1 = self.m.addVar(name="v1")
self.v2 = self.m.addVar(name="v2")
self.v3 = self.m.addVar(name="v3")
self.v4 = self.m.addVar(name="v4")
# Objective function
self.m.setObjective(self.v1 + self.v2 + self.v3 + self.v4,
sense=GRB.MINIMIZE)
# Constraints
self.c1 = self.m.addConstr(2 * self.y1 + self.y2 + self.v1 -
self.v2 == (1 - x))
self.c2 = self.m.addConstr(-self.y1 + self.y2 + self.v3 -
self.v4 == (2 - 4 * x))
def __init__(self, fsp: FacilitySizingProblem, x: list):
self.fsp = fsp
self.m = Model()
# Creates the variables
y = self.m.addVars(fsp.n_facilities, fsp.n_customers, name="y")
# Creates the objective
expr = 0
for i in range(fsp.n_facilities):
for j in range(fsp.n_customers):
expr += fsp.delivery_costs[i][j] * y[i, j]
self.m.setObjective(expr, GRB.MINIMIZE)
# Constraints
self.capacity_constr = self.m.addConstrs(
y.sum(i, '*') <= x[i] for i in range(self.fsp.n_facilities))
self.demand_constr = self.m.addConstrs(
y.sum('*', j) >= fsp.demands[j] for j in range(fsp.n_customers))
def __init__(self, fsp: FacilitySizingProblem):
self.fsp = fsp
self.m = Model()
# Creates the variables
self.x = self.m.addVars(fsp.n_facilities,
vtype=GRB.CONTINUOUS,
name="x")
self.phi = self.m.addVar(name="phi")
# Creates the objective
expr = self.phi + quicksum([
self.fsp.fixed_costs[i] * self.x[i]
for i in range(self.fsp.n_facilities)
])
self.m.setObjective(expr, GRB.MINIMIZE)
# Creates the constraints
self.m.addConstrs(self.x[i] <= self.fsp.capacity[i]
for i in range(fsp.n_facilities))
def __init__(self, flp: FacilityLocationProblem):
self.flp = flp
self.m = Model()
# Creates the variables
self.y = self.m.addVars(flp.n_facilities, flp.n_customers, name="y")
self.x = self.m.addVars(flp.n_facilities, vtype=GRB.BINARY, name="x")
# Creates the objective
expr = 0
for i in range(flp.n_facilities):
expr += flp.fixed_costs[i] * self.x[i]
for j in range(flp.n_customers):
expr += flp.delivery_costs[i][j] * self.y[i, j]
self.m.setObjective(expr, GRB.MINIMIZE)
# Constraints
for i in range(flp.n_facilities):
self.m.addConstr(self.y.sum(i, '*') <= flp.capacity[i] * self.x[i])
for j in range(flp.n_customers):
self.m.addConstr(self.y.sum('*', j) >= flp.demands[j])
def _balancing(self, flow_graph, sinks, frontier, demands):
configure_gurobi()
model = Model()
xij = {i: {} for i in frontier}
for node in frontier:
congestion = sum(flow_graph[node][neighbor] for neighbor in flow_graph[node])
for neighbor in flow_graph[node]:
assert neighbor in sinks
xij[node][neighbor] = model.addVar(vtype=GRB.CONTINUOUS, name=f"x_{node}_{neighbor}")
model.addConstr(xij[node][neighbor] >= 0)
model.addConstr(quicksum(xij[node][neighbor] for neighbor in flow_graph[node]) == congestion)
sink_predecessors = {i: [] for i in sinks}
for node in frontier:
for neighbor in flow_graph[node]:
sink_predecessors[neighbor].append(node)
bj = {}
for node in sinks:
bj[node] = model.addVar(vtype=GRB.CONTINUOUS, name=f"b_{node}")
model.addConstr(bj[node] == quicksum(xij[pred][node] for pred in sink_predecessors[node]) + demands[node])
model.setObjective(quicksum(bj[node] * bj[node] for node in sinks), GRB.MINIMIZE)
model.optimize()
any_edge_deleted = False
for node in frontier:
to_delete = []
for neighbor in flow_graph[node]:
flow = xij[node][neighbor].X
if flow < EPS:
to_delete.append(neighbor)
any_edge_deleted = True
else:
flow_graph[node][neighbor] = flow
for neighbor in to_delete:
del flow_graph[node][neighbor]
return any_edge_deleted
def __Simulate(self, d_r):
# define the model
model = Model('evaluation_problem')
model.setParam('OutputFlag', 0)
model.modelSense = GRB.MINIMIZE
# decision variables
X = model.addVars(tuplelist(self.roads_Z), vtype=GRB.CONTINUOUS, lb=0.0, name='X')
# objective function
objFunc_penal = sum(d_r) - X.sum()
model.setObjective(objFunc_penal)
# constraints
model.addConstrs(X.sum('*', j) <= d_r[j] for j in range(self.n))
model.addConstrs(X.sum(i, '*') <= self.I[i] for i in range(self.m))
# solve
model.optimize()
# record
return {'d_r': d_r, 'X': {f'{r}': X[r].X for r in self.roads_Z}}
def __init__(self, pp: ProcurementProblem):
self.m = Model()
self.pp = pp
# Creates the variables
self.x = self.m.addVars(self.pp.n_materials, name="x")
# Creates the objective
# The expression is obtained by multiplying x to the costs dictionary.
# See the Gurobi docs for tupledic product here
# https://www.gurobi.com/documentation/8.1/refman/py_tupledict_prod.html
expr = self.x.prod(self.pp.costs)
self.m.setObjective(expr, GRB.MINIMIZE)
# Creates the constraints
self.m.addConstrs((self.x[i] <= self.pp.max_production[i]
for i in range(self.pp.n_materials)),
name='max_p')
self.m.addConstrs((self.x[i] >= self.pp.min_production[i]
for i in range(self.pp.n_materials)),
name='min_p')
self.m.addConstr(self.x.prod(self.pp.consumption) >= self.pp.demand)
def SolveDetModel(self) -> Model:
DetModel = Model('StoModel')
DetModel.setParam('OutputFlag', 0)
DetModel.modelSense = GRB.MINIMIZE
m, n = self.m, self.n
h, f = self.h, self.f
mu = self.det_param['mu']
I = DetModel.addVars(m, vtype=GRB.CONTINUOUS, name='I')
Z = DetModel.addVars(m, vtype=GRB.BINARY, name='Z')
Transshipment_X = DetModel.addVars(self.roads,
vtype=GRB.CONTINUOUS,
name='Transshipment_X')
objFunc_holding = quicksum(I[i] * h[i] for i in range(m))
objFunc_fixed = quicksum(Z[i] * f[i] for i in range(m))
objFunc_penalty = quicksum(mu[j] - Transshipment_X.sum('*', j)
for j in range(n))
objFunc = objFunc_holding + objFunc_fixed + objFunc_penalty
DetModel.setObjective(objFunc)
# 约束1
DetModel.addConstrs(
Transshipment_X.sum(i, '*') <= I[i] for i in range(m))
# 约束2
DetModel.addConstrs(
Transshipment_X.sum('*', j) <= mu[j] for j in range(n))
# 约束3 I_i<=M*Z_i
DetModel.addConstrs(I[i] <= 20000 * Z[i] for i in range(m))
# 求解评估模型
DetModel.optimize()
self.model = DetModel
return DetModel
from gurobipy.gurobipy import Model, GRB
# Model
m = Model('textile')
# Decision variables
xa = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="xa")
xb = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="xb")
yw = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="yw")
yl = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="yl")
yh = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="yh")
# Objective function
m.setObjective(60 * xa + 65 * xb - 3 * yw - 3 * yl - 10 * yh,
sense=GRB.MAXIMIZE)
# Constraints
m.addConstr(0.3 * xa + 0.5 * xb - yw, sense=GRB.LESS_EQUAL, rhs=0)
m.addConstr(6 * xa + 5 * xb <= yl)
m.addConstr(3 * xa + 5 * xb <= yh)
m.addConstr(yw <= 20)
m.addConstr(yl <= 300)
m.addConstr(yh <= 200)
m.optimize()
print('Objective value: %g' % m.objVal)
print('%s %g' % (xa.varName, xa.x))
print('%s %g' % (xb.varName, xb.x))
print('%s %g' % (yw.varName, yw.x))
print('%s %g' % (yl.varName, yl.x))
from gurobipy.gurobipy import GRB, Model
# Data
months = [8, 9, 10]
cost = {8: 60, 9: 65, 10: 68}
price = {8: 90, 9: 110, 10: 105}
max_buy = 65
max_sell = 100
storage_capacity = 45
storage_cost = 7
current_stock = 25
# Model
m = Model('ref')
# Decision variables
b = m.addVars(months, lb=0, ub=max_buy, vtype=GRB.CONTINUOUS, name="b")
s = m.addVars(months, lb=0, ub=max_sell, vtype=GRB.CONTINUOUS, name="s")
k = m.addVars(months,
lb=0,
ub=storage_capacity,
vtype=GRB.CONTINUOUS,
name="k")
print(s)
# Objective function
expr = 0
for i in months:
expr = expr + price[i] * s[i] - cost[i] * b[i] - storage_cost * k[i]
m.setObjective(expr, sense=GRB.MAXIMIZE)
from gurobipy.gurobipy import Model, GRB
# Create the model object
m = Model('diet_problem')
# Create the variables
xa = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="xa")
xb = m.addVar(0, GRB.INFINITY, vtype=GRB.CONTINUOUS, name="xb")
# a different way to create a non-negative continuous variable
xc = m.addVar(name="xc")
xd = m.addVar(0, GRB.INFINITY, name="xd")
xe = m.addVar(name="xe")
# Create the objective function
expr = 8 * xa + 10 * xb + 3 * xc + 20 * xd + 15 * xe
m.setObjective(expr, sense=GRB.MINIMIZE)
# Create the constraints. We will use different ways of adding a constraint
expr = 0.4 * xa + 1.2 * xb + 0.6 * xc + 0.6 * xd + 12.2 * xe
m.addConstr(lhs=expr, sense=GRB.GREATER_EQUAL, rhs=70)
m.addConstr(6 * xa + 10 * xb + 3 * xc + 1 * xd + 0 * xe >= 50)
m.addConstr(0.4 * xa + 0.6 * xb + 0.4 * xc + 0.2 * xd + 2.6 * xe,
GRB.GREATER_EQUAL, 12)
m.optimize()
print('Objective value: %g' % m.objVal)
print('%s %g' % (xa.varName, xa.x))
print('%s %g' % (xb.varName, xb.x))
print('%s %g' % (xc.varName, xc.x))
print('%s %g' % (xd.varName, xd.x))
def Build_LDR_Model(self):
"""
LDR for location-inventpry problem is only feasible when all affine coefficients equal to 0, which violates from
what we want.
For more info about how to design a reasonable prepositioning network,
see: http://web.hec.ca/pages/erick.delage/LRC_TRO.pdf
The above paper assume support set is a convex polyhedron characterized by linear constraints.
"""
m, n = self.m, self.n
f, h = self.f, self.h
mu, sigma = self.mu, self.sigma
roads = self.roads
INF = float('inf')
f_ks, K = self.ldr_params['f_k'], len(self.ldr_params['f_k'])
# declare model
ldr_model = Model()
# decision variables
I = ldr_model.addVars(m, vtype=GRB.CONTINUOUS, lb=0.0, name='I')
Z = ldr_model.addVars(m, vtype=GRB.BINARY, lb=0.0, name='Z')
t = ldr_model.addVars(n, vtype=GRB.CONTINUOUS, lb=-INF, name='t')
gamma = ldr_model.addVar(lb=-INF, vtype=GRB.CONTINUOUS, name='gamma')
s = ldr_model.addVars(K, vtype=GRB.CONTINUOUS, lb=0.0, name='s')
phi = ldr_model.addVars(K, vtype=GRB.CONTINUOUS, lb=0.0, name='phi')
psi = ldr_model.addVars(K, vtype=GRB.CONTINUOUS, lb=-INF, name='psi')
xi = ldr_model.addVars(K, vtype=GRB.CONTINUOUS, lb=-INF, name='xi')
eta = ldr_model.addVars(n, K, vtype=GRB.CONTINUOUS, lb=0.0, name='eta')
tau = ldr_model.addVars(n, K, vtype=GRB.CONTINUOUS, lb=-INF, name='tau')
theta = ldr_model.addVars(n, K, vtype=GRB.CONTINUOUS, lb=-INF, name='theta')
w = ldr_model.addVars(m, K, vtype=GRB.CONTINUOUS, lb=0.0, name='w')
lambd = ldr_model.addVars(m, K, vtype=GRB.CONTINUOUS, lb=-INF, name='lambda')
delta = ldr_model.addVars(m, K, vtype=GRB.CONTINUOUS, lb=-INF, name='delta')
alpha_0 = ldr_model.addVars(roads, vtype=GRB.CONTINUOUS, lb=-INF, name='alpha_0')
alpha = ldr_model.addVars(roads, n, vtype=GRB.CONTINUOUS, lb=-INF, name='alpha')
beta = ldr_model.addVars(roads, K, vtype=GRB.CONTINUOUS, lb=-INF, name='beta')
# objective function
obj1 = quicksum([f[i]*Z[i] for i in range(m)])
obj2 = quicksum([h[i]*I[i] for i in range(m)])
obj3 = quicksum([mu[i]*t[i] for i in range(m)])
obj4 = quicksum(s[k]*matmul(matmul(f_k, sigma), f_k) for k, f_k in enumerate(f_ks))
obj5 = gamma
ldr_model.setObjective(obj1 + obj2 + obj3 + obj4 + obj5)
ldr_model.modelSense = GRB.MINIMIZE
# constraint
# c1
ldr_model.addConstr(gamma + alpha_0.sum() >= 1/2*(phi.sum() - psi.sum()),
name='c1')
# c2
ldr_model.addConstrs((1/2*(phi[k]+psi[k]) == beta.sum('*', '*', k) + s[k]*len(roads) for k in range(K)),
name='c2')
# c3
a_star_star = [alpha.sum('*', '*', l) for l in range(n)]
ldr_model.addConstrs((xi[k]*f_ks[k][l] <= t[l]+a_star_star[l]-1 for k in range(K) for l in range(n)),
name='c3')
# c4
ldr_model.addConstrs((-alpha_0.sum('*', j) >= 1/2*(eta.sum(j, '*')-tau.sum(j, '*')) for j in range(n)),
name='c4')
# c5
ldr_model.addConstrs((-1/2*(eta[j, k]+tau[j, k]) == beta.sum('*', j, k) for k in range(K) for j in range(n)),
name='c5')
# c6
for j in range(n):
a_star_j = [alpha.sum('*', j, l) if l != j else alpha.sum('*', j, l)-1 for l in range(n)]
for k, f_k in enumerate(f_ks):
ldr_model.addConstrs(-theta[j, k]*f_k[l] >= a_star_j[l] for l in range(n))
# c7
ldr_model.addConstrs((I[i]-alpha_0.sum(i, '*') >= 1/2*(w.sum(i, '*')-lambd.sum(i, '*')) for i in range(m)),
name='c7')
# c8
ldr_model.addConstrs((-1/2*(w[i, k]+lambd[i, k]) == beta.sum(i, '*', k) for i in range(m) for k in range(K)),
name='c8')
# c9
for i in range(m):
a_i_star = [alpha.sum(i, '*', l) for l in range(n)]
for k, f_k in enumerate(f_ks):
ldr_model.addConstrs(-delta[i, k]*f_k[l] >= a_i_star[l] for l in range(n))
# c10 I,Z
ldr_model.addConstrs(I[i] <= 10000*Z[i] for i in range(m))
# c11
ldr_model.addConstrs(phi[k]*phi[k] >= psi[k]*psi[k] + xi[k]*xi[k] for k in range(K))
ldr_model.addConstrs(eta[i, k]*eta[i, k] >= tau[i, k]*tau[i, k] + theta[i, k]*theta[i, k]
for k in range(K) for i in range(m))
ldr_model.addConstrs(w[i, k]*w[i, k] >= lambd[i, k]*lambd[i, k] + delta[i, k]*delta[i, k]
for k in range(K) for i in range(m))
# update
ldr_model.update()
ldr_model.optimize()
# print(I)
# print(Z)
# print(alpha_0)
# print(alpha)
# print(beta)
# print(ldr_model.ObjVal)
self.model = ldr_model
