def do_pyomo_work(profit_rate_windows):
Products = ['Doors', 'Windows']
ProfitRate = {'Doors': 300, 'Windows': profit_rate_windows}
Plants = ['Door Fab', 'Window Fab', 'Assembly']
HoursAvailable = {'Door Fab': 4, 'Window Fab': 12, 'Assembly': 18}
HoursPerUnit = {
('Doors', 'Door Fab'): 1,
('Windows', 'Window Fab'): 2,
('Doors', 'Assembly'): 3,
('Windows', 'Assembly'): 2,
('Windows', 'Door Fab'): 0,
('Doors', 'Window Fab'): 0
}
#Concrete Model
model = ConcreteModel()
#Decision Variables
model.WeeklyProd = Var(Products, within=NonNegativeReals)
#Objective
model.obj = Objective(expr=sum(ProfitRate[i] * model.WeeklyProd[i]
for i in Products),
sense=maximize)
def CapacityRule(model, p):
"""User Defined Capacity Rule
Accepts a pyomo Concrete Model as the first positional argument,
and a list of Plants as a second positional argument
"""
return sum(HoursPerUnit[i, p] * model.WeeklyProd[i]
for i in Products) <= HoursAvailable[p]
model.Capacity = Constraint(Plants, rule=CapacityRule)
opt = SolverFactory("glpk")
instance = model.create()
results = opt.solve(instance)
#results.write()
return results.Solution()
Constraint)
# Plant data
Products = ['Doors', 'Windows']
ProfitRate = {'Doors':300, 'Windows':500}
Plants = ['Door Fab', 'Window Fab', 'Assembly']
HoursAvailable = {'Door Fab':4, 'Window Fab':12, 'Assembly':18}
HoursPerUnit = {('Doors', 'Door Fab'):1,
('Windows', 'Window Fab'):2,
('Doors', 'Assembly'):3,
('Windows', 'Assembly'):2,
('Windows', 'Door Fab'):0,
('Doors', 'Window Fab'):0}
# Concrete Model
model = ConcreteModel() # instantiates the data of the problem, such as hours available from the plant
# Decision variables
model.WeeklyProd = Var(Products, within=NonNegativeReals)
# Objective
model.obj = Objective(expr = sum(ProfitRate[i] * model.WeeklyProd[i] for i in Products),
sense=maximize)
def CapacityRule(model, p):
"""User defined capacity rule -
Accepts a pyomo Concrete Model as the first positional argument,
and a plant index as a second positional argument
"""
return sum(HoursPerUnit[i,p] * model.WeeklyProd[i] for i in Products) <= HoursAvailable[p]
# Constraint
def __init__(self,
cov,
occ,
groups_4digit,
allele_table,
beta,
t_max_allele=2,
solver="glpk",
threads=1,
verbosity=0):
"""
Constructor
"""
self.__allele_table = allele_table
self.__beta = float(beta)
self.__t_max_allele = t_max_allele
self.__solver = SolverFactory(solver)
self.__threads = threads
self.__verbosity = True if verbosity > 0 else False
self.__changed = True
self.__ks = 1
self.__groups_4digit = groups_4digit
loci_alleles = defaultdict(list)
for type_4digit, group_alleles in groups_4digit.iteritems():
#print type_4digit, group_alleles
loci_alleles[type_4digit.split('*')[0]].extend(group_alleles)
loci = loci_alleles
self.__allele_to_4digit = {
allele: type_4digit
for type_4digit, group in groups_4digit.iteritems()
for allele in group
}
'''
generates the basic ILP model
'''
model = ConcreteModel()
#init Sets
model.LociNames = Set(initialize=loci.keys())
model.Loci = Set(model.LociNames, initialize=lambda m, l: loci[l])
L = list(itertools.chain(*loci.values()))
reconst = {allele_id: 0.01 for allele_id in L if '_' in allele_id}
R = set([r for (r, _) in cov.keys()])
model.L = Set(initialize=L)
model.R = Set(initialize=R)
#init Params
model.cov = Param(model.R,
model.L,
initialize=lambda model, r, a: cov.get((r, a), 0))
model.reconst = Param(model.L,
initialize=lambda model, a: reconst.get(a, 0))
model.occ = Param(model.R, initialize=occ)
model.t_allele = Param(initialize=self.__t_max_allele, mutable=True)
model.beta = Param(
initialize=self.__beta,
validate=lambda val, model: 0.0 <= float(self.__beta) <= 0.999,
mutable=True)
model.nof_loci = Param(initialize=len(loci))
#init variables
model.x = Var(model.L, domain=Binary)
model.y = Var(model.R, domain=Binary)
model.re = Var(model.R, bounds=(0.0, None))
model.hetero = Var(bounds=(0.0, model.nof_loci))
#init objective
model.read_cov = Objective(rule=lambda model: sum(
model.occ[r] * (model.y[r] - model.beta * (model.re[r]))
for r in model.R) - sum(model.reconst[a] * model.x[a]
for a in model.L),
sense=maximize)
#init Constraints
model.max_allel_selection = Constraint(
model.LociNames,
rule=lambda model, l: sum(model.x[a] for a in model.Loci[l]
) <= model.t_allele)
model.min_allel_selection = Constraint(
model.LociNames,
rule=lambda model, l: sum(model.x[a] for a in model.Loci[l]) >= 1)
model.is_read_cov = Constraint(
model.R,
rule=lambda model, r: sum(model.cov[r, a] * model.x[a]
for a in model.L) >= model.y[r])
model.heterozygot_count = Constraint(
rule=lambda model: model.hetero >= sum(model.x[a] for a in model.L
) - model.nof_loci)
#regularization constraints
model.reg1 = Constraint(
model.R,
rule=lambda model, r: model.re[r] <= model.nof_loci * model.y[r])
model.reg2 = Constraint(
model.R, rule=lambda model, r: model.re[r] <= model.hetero)
model.reg3 = Constraint(model.R,
rule=lambda model, r: model.re[r] >= model.
hetero - model.nof_loci * (1 - model.y[r]))
#generate constraint list for solution enumeration
model.c = ConstraintList()
#generate instance
self.__instance = model.create()
def __init__(self, cov, occ, groups_4digit, allele_table, beta, t_max_allele=2, solver="glpk", threads=1,
verbosity=0):
"""
Constructor
"""
self.__allele_table = allele_table
self.__beta = float(beta)
self.__t_max_allele = t_max_allele
self.__solver = SolverFactory(solver)
self.__solver.options["threads"] = threads
self.__verbosity = True if verbosity > 0 else False
self.__changed = True
self.__ks = 1
self.__groups_4digit = groups_4digit
loci_alleles = defaultdict(list)
for type_4digit, group_alleles in groups_4digit.iteritems():
#print type_4digit, group_alleles
loci_alleles[type_4digit.split('*')[0]].extend(group_alleles)
loci = loci_alleles
self.__allele_to_4digit = {allele: type_4digit for type_4digit, group in groups_4digit.iteritems() for allele in
group}
'''
generates the basic ILP model
'''
model = ConcreteModel()
#init Sets
model.LociNames = Set(initialize=loci.keys())
model.Loci = Set(model.LociNames, initialize=lambda m, l: loci[l])
L = list(itertools.chain(*loci.values()))
reconst = {allele_id: 0.01 for allele_id in L if '_' in allele_id}
R = set([r for (r, _) in cov.keys()])
model.L = Set(initialize=L)
model.R = Set(initialize=R)
#init Params
model.cov = Param(model.R, model.L, initialize=lambda model, r, a: cov.get((r, a), 0))
model.reconst = Param(model.L, initialize=lambda model, a: reconst.get(a, 0))
model.occ = Param(model.R, initialize=occ)
model.t_allele = Param(initialize=self.__t_max_allele, mutable=True)
model.beta = Param(initialize=self.__beta,
validate=lambda val, model: 0.0 <= float(self.__beta) <= 0.999,
mutable=True)
model.nof_loci = Param(initialize=len(loci))
#init variables
model.x = Var(model.L, domain=Binary)
model.y = Var(model.R, domain=Binary)
model.re = Var(model.R, bounds=(0.0, None))
model.hetero = Var(bounds=(0.0, model.nof_loci))
#init objective
model.read_cov = Objective(
rule=lambda model: sum(model.occ[r] * (model.y[r] - model.beta * (model.re[r])) for r in model.R) - sum(
model.reconst[a] * model.x[a] for a in model.L), sense=maximize)
#init Constraints
model.max_allel_selection = Constraint(model.LociNames, rule=lambda model, l: sum(
model.x[a] for a in model.Loci[l]) <= model.t_allele)
model.min_allel_selection = Constraint(model.LociNames,
rule=lambda model, l: sum(model.x[a] for a in model.Loci[l]) >= 1)
model.is_read_cov = Constraint(model.R,
rule=lambda model, r: sum(model.cov[r, a] * model.x[a] for a in model.L) >=
model.y[r])
model.heterozygot_count = Constraint(
rule=lambda model: model.hetero >= sum(model.x[a] for a in model.L) - model.nof_loci)
#regularization constraints
model.reg1 = Constraint(model.R, rule=lambda model, r: model.re[r] <= model.nof_loci * model.y[r])
model.reg2 = Constraint(model.R, rule=lambda model, r: model.re[r] <= model.hetero)
model.reg3 = Constraint(model.R,
rule=lambda model, r: model.re[r] >= model.hetero - model.nof_loci * (1 - model.y[r]))
#generate constraint list for solution enumeration
model.c = ConstraintList()
#generate instance
self.__instance = model.create()
def maxRetPortfolio(riskyRetMtx, riskFreeRetVec,
buyTransFeeMtx, sellTransFeeMtx,
allocatedWealth):
'''
-假設有T期的資料, 投資在M個risky assets, 以及1個riskfree asset
-在(T+1)期初結算
goal: 最大化T+1期期初財產
@param riskyRetMtx, numpy.array, size: M * T+1
@param riskFreeRetVec, numpy.array, size: T+1
@param buyTransFeeMtx, numpy.array, size: M * T
@param sellTransFeeMtx, numpy.array, size: M * T
@param allocatedWealth, numpy.array, size: (M+1) (最後一個為cash)
@return (buyMtx, sellMtx), numpy.array, each size: M*T
'''
assert buyTransFeeMtx.shape == sellTransFeeMtx.shape
assert riskyRetMtx.shape[1] == riskFreeRetVec.size
M, T = buyTransFeeMtx.shape
t1 = time.time()
#create model
model = ConcreteModel()
#number of asset and number of periods
model.symbols = range(M)
model.T = range(T)
model.Tp1 = range(T+1)
model.Mp1 = range(M+1)
#decision variables
model.buys = Var(model.symbols, model.T, within=NonNegativeReals)
model.sells = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskyWealth = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskFreeWealth = Var(model.T, within=NonNegativeReals)
#objective
def objective_rule(model):
wealth =sum( (1. + riskyRetMtx[m, T]) * model.riskyWealth[m, T-1]
for m in xrange(M))
wealth += (1.+ riskFreeRetVec[T]) * model.riskFreeWealth[T-1]
return wealth
model.objective = Objective(rule=objective_rule, sense=maximize)
#constraint
def riskyWealth_constraint_rule(model, m, t):
if t>=1:
preWealth = model.riskyWealth[m, t-1]
else:
preWealth = allocatedWealth[m]
return (model.riskyWealth[m, t] ==
(1. + riskyRetMtx[m,t])*preWealth +
model.buys[m,t] - model.sells[m,t])
def riskyFreeWealth_constraint_rule(model, t):
totalSell = sum((1-sellTransFeeMtx[mdx, t])*model.sells[mdx, t]
for mdx in xrange(M))
totalBuy = sum((1+buyTransFeeMtx[mdx, t])*model.buys[mdx, t]
for mdx in xrange(M))
if t >=1:
preWealth = model.riskFreeWealth[t-1]
else:
preWealth = allocatedWealth[-1]
return( model.riskFreeWealth[t] ==
(1. + riskFreeRetVec[t])*preWealth +
totalSell - totalBuy)
model.riskyWeathConstraint = Constraint(model.symbols, model.T,
rule=riskyWealth_constraint_rule)
model.riskFreeWealthConstraint = Constraint(model.T,
rule=riskyFreeWealth_constraint_rule)
#optimizer
opt = SolverFactory('cplex')
# opt.options["threads"] = 4
instance = model.create()
results = opt.solve(instance)
print results
# instance.load(results)
# display(instance)
# instance.load(results)
# for var in instance.active_components(Var):
# varobj = getattr(instance, var)
# for idx in varobj:
# print varobj[idx], varobj[idx].value
#
print "elapsed %.3f secs"%(time.time()-t1)
def big_m_model():
with open('Pickled_Data', 'rb') as f:
rd = pickle.load(f)
model = ConcreteModel()
#-----------------------------------------------------------------------------
# DECLARE MODEL PARAMETERS
#-----------------------------------------------------------------------------
model.STORES = Set(initialize=rd.STORES)
model.PRODUCTS = Set(initialize=rd.PRODUCTS)
model.FASHION = Set(initialize=rd.FASHION)
model.VENDORS_Q = Set(initialize=rd.VENDORS_Q)
model.VENDORS_P = Set(initialize=rd.VENDORS_P)
model.VENDORS = Set(initialize=rd.VENDORS)
model.TIMES = Set(initialize=rd.TIMES)
model.PICKING = Set(initialize=rd.PICKING)
model.PUTAWAY = Set(initialize=rd.PUTAWAY)
model.SP = model.STORES * model.PRODUCTS
model.VP = model.VENDORS * model.PRODUCTS
model.ST = model.STORES * model.TIMES
model.PT = model.PRODUCTS * model.TIMES
model.VT = model.VENDORS * model.TIMES
model.VPT = model.VENDORS * model.PRODUCTS * model.TIMES
model.SPT = model.STORES * model.PRODUCTS * model.TIMES
model.OMEGA_Q = Set(initialize=rd.Omega_q, dimen=2)
model.OMEGA_P = Set(initialize=rd.Omega_p, dimen=2)
model.T_minus_One = Param(model.TIMES, initialize=rd.T_minus_One)
def K_init(model, s): return 10000000
model.K_s = Param(model.STORES, initialize=K_init)
def L_init(model): return 0
model.L = Param(initialize=L_init)
model.Script_Q = Param(initialize=15000)
model.phi_put = Param(initialize=1.0)
model.phi_pick = Param(initialize=1.0)
model.gamma = Param(initialize=0.5)
model.pt = Param(initialize=1)
model.tb = Param(initialize=rd.tb)
model.te = Param(initialize=rd.te)
model.ty = Param(initialize=rd.ty)
model.Demand = Param(model.STORES, model.PRODUCTS, model.TIMES, initialize=rd.Demand)
model.V_p = Param(model.PRODUCTS, initialize=rd.V_p)
model.V_q = Param(model.FASHION, initialize=rd.V_q)
model.W_p = Param(model.PRODUCTS, initialize=rd.W_p)
model.W_q = Param(model.FASHION, initialize=rd.W_q)
X_ivq = {tup:rd.X_ivq[tup] for tup in model.OMEGA_Q}
model.X_ivq = Param(model.OMEGA_Q, initialize=X_ivq)
model.X_osq = Param(model.STORES, model.FASHION, initialize=rd.X_osq)
model.C_alpha = Param(initialize=rd.C_alpha)
model.C_beta = Param(initialize=rd.C_beta)
def C_hp_init(model, p): return .01
model.C_hp = Param(model.PRODUCTS, initialize=C_hp_init)
model.C_hq = Param(model.FASHION, initialize=C_hp_init)
def C_hsp_init(model, s, p): return .05
model.C_hsp = Param(model.STORES, model.PRODUCTS, initialize=C_hsp_init)
model.C_hsq = Param(model.STORES, model.FASHION, initialize=C_hsp_init)
model.C_fv = Param(model.VENDORS, initialize=rd.C_fv)
model.C_fs = Param(model.STORES, initialize=rd.C_fs)
model.C_vv = Param(model.VENDORS, initialize=rd.C_vv)
model.C_vs = Param(model.STORES, initialize=rd.C_vs)
model.Lambda_put = Param(model.PUTAWAY, initialize=rd.lambda_put)
model.MHE = Param(model.PUTAWAY, initialize=rd.MHE)
model.Lambda_pick = Param(model.PICKING, initialize=rd.lambda_pick)
model.Cth_put = Param(model.PUTAWAY, initialize=rd.C_put)
model.Cth_pick = Param(model.PICKING, initialize=rd.C_pick)
#-----------------------------------------------------------------------------
# DECLARE MODEL VARIABLES
#-----------------------------------------------------------------------------
model.alpha_put = Var(bounds=(0.0, 500),
within=NonNegativeIntegers)
model.alpha_pick = Var(bounds=(0.0, 500),
within=NonNegativeIntegers)
model.theta_put = Var(model.PUTAWAY, within=Binary)
model.theta_pick = Var(model.PICKING, within=Binary)
model.MHE_cost = Var(model.PUTAWAY, within=NonNegativeIntegers)
model.beta_put = Var(model.TIMES,
within=NonNegativeIntegers)
model.beta_pick = Var(model.TIMES,
within=NonNegativeIntegers)
model.tau_sq = Var(model.STORES, model.FASHION,
within=NonNegativeIntegers)
model.rho_vqt = Var(model.OMEGA_Q, model.TIMES,
within=Binary)
model.rho_sqt = Var(model.STORES, model.FASHION, model.TIMES,
within=Binary)
model.x_vpt = Var(model.OMEGA_P, model.TIMES,
within=NonNegativeIntegers)
model.x_spt = Var(model.STORES, model.PRODUCTS, model.TIMES,
within=NonNegativeIntegers)
model.y_pt = Var(model.PRODUCTS, model.TIMES,
within=NonNegativeIntegers)
model.y_spt = Var(model.STORES, model.PRODUCTS, model.TIMES,
within=NonNegativeIntegers)
model.y_sqt = Var(model.STORES, model.FASHION, model.TIMES,
within=NonNegativeIntegers)
model.z_spt = Var(model.STORES, model.PRODUCTS, model.TIMES,
within=NonNegativeIntegers)
model.z_sqt = Var(model.STORES, model.FASHION, model.TIMES,
within=NonNegativeIntegers)
model.n_vt = Var(model.VENDORS, model.TIMES,
within=NonNegativeIntegers)
model.n_st = Var(model.STORES, model.TIMES,
within=NonNegativeIntegers)
def objective_rule(model):
Workers_Cost = model.Ca * (model.alpha_put + model.alpha_pick) + \
model.Cb * sum((model.beta_put[t] + model.beta_pick[t])
for t in model.TIMES)
MHE_Cost = summation(model.MHE_cost)
Tech_Cost = summation(model.Cth_put, model.theta_put) + \
summation(model.Cth_pick, model.theta_pick)
Holding_Cost = sum(model.C_hp[p] * model.y_pt[p,t]
for p in model.PRODUCTS for t in model.TIMES)
Holding_Cost += sum(model.C_hq[q] * model.X_osq[s,q] * model.tau_sq[s,q]
for s in model.STORES for q in model.FASHION)
Holding_Cost += sum(model.C_hsp[s,p] * model.y_spt[s,p,t]
for s in model.STORES for p in model.PRODUCTS for t in model.TIMES)
Holding_Cost += sum(model.C_hsq[s,q] * model.y_sqt[s,q,t]
for s in model.STORES for q in model.FASHION for t in model.TIMES)
Fixed_Shipping_Cost = sum(model.C_fv[v] * model.n_vt[v,t]
for v in model.VENDORS for t in model.TIMES)
Fixed_Shipping_Cost += sum(model.C_fs[s] * model.n_st[s,t]
for s in model.STORES for t in model.TIMES)
Var_Shipping_Cost = sum(model.C_vv[v] * model.W_p[p] * model.x_vpt[v,p,t]
for v, p in model.OMEGA_P for t in model.TIMES)
Var_Shipping_Cost += sum(model.C_vv[v] * model.W_q[q] * model.X_ivq[v,q] * model.rho_vqt[v,q,t]
for v, q in model.OMEGA_Q for t in model.TIMES)
Var_Shipping_Cost += sum(model.C_vs[s] * model.W_p[p] * model.x_spt[s,p,t]
for s in model.STORES for p in model.PRODUCTS for t in model.TIMES)
Var_Shipping_Cost += sum(model.C_vs[s] * model.W_q[q] * model.X_osq[s,q] * model.rho_sqt[s,q,t]
for s in model.STORES for q in model.FASHION for t in model.TIMES)
FS_Expr = (Workers_Cost + MHE_Cost + Tech_Cost + Holding_Cost
+ Fixed_Shipping_Cost + Var_Shipping_Cost)
return FS_Expr
model.objective = Objective(sense=minimize)
def BigM_MHE_LOWER_rule(model, i):
expr = model.MHE_COST[i]
expr -= sum(model.MHE[i] * (model.alpha_put + model.beta_put[t])
for t in model.TIMES)
return (-model.M_MHE * (1 - model.theta_put[i]), expr, None)
model.BigM_MHE_LOWER = Constraint(model.PUTAWAY, model.TIMES)
def BigM_MHE_UPPER_rule(model, i):
expr = model.MHE_COST[i]
expr -= sum(model.MHE[i] * (model.alpha_put + model.beta_put[t])
for t in model.TIMES)
return (None, expr, model.M_MHE * (1 - model.theta_put[i]))
model.BigM_MHE_UPPER = Constraint(model.PUTAWAY, model.TIMES)
def ConstraintFour_rule(model, i, t):
Four_expr1 = sum(model.x_vpt[v,p,t] for v, p in model.OMEGA_P)
Four_expr1 += sum(model.X_ivq[v,q] * model.rho_vqt[v,q,t] for v, q in model.OMEGA_Q)
Four_expr2 = model.Lambda_put[i] * (model.alpha_put + model.phi_put * model.beta_put[t])
return (Four_expr1 - Four_expr2 <= model.BigM * (1 - model.theta_put[i]))
model.ConstraintFour = Constraint(model.PUTAWAY, model.TIMES)
def ConstraintFive_rule(model, j, t):
Five_expr1 = sum(model.x_spt[s,p,t] for s in model.STORES for p in model.PRODUCTS)
Five_expr1 += sum(model.X_osq[s,q] * model.rho_sqt[s,q,t] for s in model.STORES for q in model.FASHION)
Five_expr2 = model.Lambda_pick[j] * (model.alpha_pick + model.phi_pick * model.beta_pick[t])
return (Five_expr1 - Five_expr2 <= model.BigM * (1 - model.theta_pick[j]))
model.ConstraintFive = Constraint(model.PICKING, model.TIMES)
# Constraint Six
def ConstraintSixPutaway_rule(model, t):
Six_expr1 = model.beta_put[t]
Six_expr2 = model.gamma * model.alpha_put
return (Six_expr1 - Six_expr2 <= 0)
model.ConstraintSixPutaway = Constraint(model.TIMES)
def ConstraintSixPicking_rule(model, t):
Six_expr1 = model.beta_pick[t]
Six_expr2 = model.gamma * model.alpha_pick
return (Six_expr1 - Six_expr2 <= 0)
model.ConstraintSixPicking = Constraint(model.TIMES)
# Constraint Seven
def ConstraintSeven_rule(model, v, q, s):
Seven_expr1 = model.tau_sq[s,q]
Seven_expr2 = sum(t * model.rho_sqt[s, q, t] for t in model.TIMES)
Seven_expr2 -= sum(t * model.rho_vqt[v, q, t] for t in model.TIMES)
return (Seven_expr1 - Seven_expr2 == 0)
model.ConstraintSeven = Constraint(model.OMEGA_Q, model.STORES)
# Constraint Eight
def ConstraintEight_rule(model, s, q):
Eight_expr1 = model.tau_sq[s,q]
return (model.pt - Eight_expr1 <= 0)
model.ConstraintEight = Constraint(model.STORES, model.FASHION)
# Constraint Nine
def ConstraintNine_rule(model, s, q):
Nine_expr1 = sum(t * model.rho_sqt[s, q, t] for t in model.TIMES)
Nine_expr2 = model.ty - model.L
return (Nine_expr1 - Nine_expr2 <= 0)
model.ConstraintNine = Constraint(model.STORES, model.FASHION)
# Constraint Ten
def ConstraintTenVendor_rule(model, v, q):
Ten_expr1 = sum(model.rho_vqt[v, q, t] for t in model.TIMES if model.tb <= t <= model.te)
return (Ten_expr1 - 1 == 0)
model.ConstraintTenVendor = Constraint(model.OMEGA_Q)
def ConstraintTenStore_rule(model, s, q):
Ten_expr1 = sum(model.rho_sqt[s, q, t] for t in model.TIMES if model.tb <= t <= model.ty)
return (Ten_expr1 - 1 == 0)
model.ConstraintTenStore = Constraint(model.STORES, model.FASHION)
# Constraint Ten Prime
def ConstraintTenPrimeVendor_rule(model, v, q, t):
if not model.tb <= t <= model.ty:
return model.rho_vqt[v, q, t] == 0
else:
return Constraint.Skip
model.ConstraintTenPrimeVendor = Constraint(model.OMEGA_Q, model.TIMES)
def ConstraintTenPrimeStore_rule(model, s, q, t):
if not model.tb <= t <= model.ty:
return model.rho_sqt[s, q, t] == 0
else:
return Constraint.Skip
model.ConstraintTenPrimeStore = Constraint(model.STORES, model.FASHION, model.TIMES)
# Constraint Eleven and Twelve
def ConstraintEleven_rule(model, s, p, t):
assert model.L == 0
Eleven_expr1 = model.z_spt[s,p,t]
Eleven_expr2 = model.x_spt[s,p,t]
return (Eleven_expr1 - Eleven_expr2 == 0)
model.ConstraintEleven = Constraint(model.STORES, model.PRODUCTS, model.TIMES)
# Constraint Thirteen
def ConstraintThirteen_rule(model, s, q, t):
assert model.L== 0
if model.tb <= t <= model.ty:
Thirteen_expr1 = model.z_sqt[s,q,t]
Thirteen_expr2 = model.X_osq[s,q] * model.rho_sqt[s,q,t]
return (Thirteen_expr1 - Thirteen_expr2 == 0)
else:
return Constraint.Skip
model.ConstraintThirteen = Constraint(model.STORES, model.FASHION, model.TIMES)
# Constraint Fourteen and Fifteen
def ConstraintFourteen_rule(model, p, t):
Fourteen_expr1 = sum(model.x_vpt[v, p, t] for v, pee in model.OMEGA_P if pee == p)
Fourteen_expr1 -= sum(model.x_spt[s, p, t] for s in model.STORES)
Fourteen_expr2 = model.y_pt[p,t] - model.y_pt[p,model.T_minus_One[t]]
return (Fourteen_expr1 - Fourteen_expr2 == 0)
model.ConstraintFourteen = Constraint(model.PRODUCTS, model.TIMES)
# Constraint Sixteen and Seventeen
def ConstraintSixteen_rule(model,s,p,t):
Sixteen_expr1 = model.z_spt[s, p, t]
Sixteen_expr1 -= model.Demand[s,p,t]
Sixteen_expr2 = model.y_spt[s,p,t] - model.y_spt[s,p,model.T_minus_One[t]]
return (Sixteen_expr1 - Sixteen_expr2 == 0)
model.ConstraintSixteen = Constraint(model.STORES, model.PRODUCTS, model.TIMES)
# Constraint Eighteen
def ConstraintEighteen_rule(model,s,q,t):
if model.tb <= t <= model.ty:
if t == 1:
Eighteen_expr1 = model.z_sqt[s, q, t]
Eighteen_expr2 = model.y_sqt[s,q,t]
return (Eighteen_expr1 - Eighteen_expr2 == 0)
else:
Eighteen_expr1 = model.z_sqt[s, q, t]
Eighteen_expr2 = model.y_sqt[s,q,t] - model.y_sqt[s,q,model.T_minus_One[t]]
return (Eighteen_expr1 - Eighteen_expr2 == 0)
else:
return Constraint.Skip
model.ConstraintEighteen = Constraint(model.STORES, model.FASHION, model.TIMES)
# Constraints Nineteen
def ConstraintNineteen_rule(model, s, t):
Nineteen_expr1 = sum(model.V_p[p] * model.z_spt[s, p, t] for p in model.PRODUCTS)
Nineteen_expr1 += sum(model.V_q[q] * model.z_sqt[s, q, t] for q in model.FASHION)
Nineteen_expr2 = model.K_s[s]
return (Nineteen_expr1 - Nineteen_expr2 <= 0)
model.ConstraintNineteen = Constraint(model.STORES, model.TIMES)
# Constraints Twenty
def ConstraintTwenty_rule(model, v, t):
if v in model.VENDORS_P:
Twenty_expr1 = sum(model.W_p[p] * model.x_vpt[v,p,t] for ve, p in model.OMEGA_P
if ve == v)
else:
Twenty_expr1 = 0
if v in model.VENDORS_Q:
Twenty_expr1 += sum(model.W_q[q] * model.X_ivq[v,q] * model.rho_vqt[v,q,t]
for ve, q in model.OMEGA_Q if ve == v)
Twenty_expr2 = model.Script_Q * model.n_vt[v,t]
return (Twenty_expr1 - Twenty_expr2 <= 0)
model.ConstraintTwenty = Constraint(model.VENDORS, model.TIMES)
# Constraints TwentyOne
def ConstraintTwentyOne_rule(model, s, t):
TwentyOne_expr1 = sum(model.W_p[p] * model.x_spt[s,p,t] for p in model.PRODUCTS)
TwentyOne_expr1 += sum(model.W_q[q] * model.X_osq[s,q] * model.rho_sqt[s,q,t] for q in model.FASHION)
TwentyOne_expr2 = model.Script_Q * model.n_st[s,t]
return (TwentyOne_expr1 - TwentyOne_expr2 <= 0)
model.ConstraintTwentyOne = Constraint(model.STORES, model.TIMES)
return model
#Explicit importing makes it more clear what a user needs to define
#versus what is included within the pyomo library
from coopr.pyomo import (ConcreteModel, Objective, Var, NonNegativeIntegers, maximize, Constraint)
Products = ['Doors', 'Windows', 'Tables']
ProfitRate = {'Doors':0.300, 'Windows':0.500, 'Tables':0.430}
Plants = ['Door Fab', 'Window Fab', 'Assembly']
HoursAvailable = {'Door Fab':4, 'Window Fab':4, 'Assembly':3}
HoursPerUnit = {('Doors','Door Fab'):0.21, ('Windows', 'Window Fab'):0.52,
('Doors','Assembly'):0.23, ('Windows', 'Assembly'):0.32,
('Windows', 'Door Fab'):0.30,('Doors', 'Window Fab'):0.20,
('Tables','Door Fab'):0.29, ('Tables','Window Fab'):0.34,
('Tables', 'Assembly'):0.41}
#Concrete Model
model = ConcreteModel()
#Decision Variables
model.WeeklyProd = Var(Products, within=NonNegativeIntegers)
#Objective
model.obj = Objective(expr=
sum(ProfitRate[i] * model.WeeklyProd[i] for i in Products),
sense = maximize)
for i in Products:
print model.WeeklyProd[i]
def CapacityRule(model, p):
"""User Defined Capacity Rule
Accepts a pyomo Concrete Model as the first positional argument,
from coopr.pyomo import (ConcreteModel, Objective, Var, NonNegativeReals,
maximize, Constraint)
Activities = ['ActivityOne', 'ActivityTwo'] #Products in other models
UnitProfit = {'ActivityOne':2, 'ActivityTwo':5} #Also called ProfitRate
Resources = ['ResourceOne', 'ResourceTwo']
ResourcesAvailable = {'ResourceOne':10, 'ResourceTwo':12}
ResourcesPerUnit = {('ActivityOne', 'ResourceOne'):1,
('ActivityTwo', 'ResourceOne'):2,
('ActivityOne', 'ResourceTwo'):1,
('ActivityTwo', 'ResourceTwo'):3}
#Concrete Model
model = ConcreteModel()
#Decision Variables
model.Prod = Var(Activities, within=NonNegativeReals)
#Objective
model.obj = Objective(expr=
sum(UnitProfit[i] * model.Prod[i] for i in Activities),
sense = maximize)
def ActivityRule(model, r):
return sum(ResourcesPerUnit[i,r] * model.Prod[i] for i in Activities) <= ResourcesAvailable[r]
model.Utilization = Constraint(Resources, rule = ActivityRule)
#This is an optional code path that allows the script to be run outside of
#pyomo command-line. For example: python wyndor.py
def maxRetPortfolio(riskyRetMtx, riskFreeRetVec, buyTransFeeMtx,
sellTransFeeMtx, allocatedWealth):
'''
-假設有T期的資料, 投資在M個risky assets, 以及1個riskfree asset
-在(T+1)期初結算
goal: 最大化T+1期期初財產
@param riskyRetMtx, numpy.array, size: M * T+1
@param riskFreeRetVec, numpy.array, size: T+1
@param buyTransFeeMtx, numpy.array, size: M * T
@param sellTransFeeMtx, numpy.array, size: M * T
@param allocatedWealth, numpy.array, size: (M+1) (最後一個為cash)
@return (buyMtx, sellMtx), numpy.array, each size: M*T
'''
assert buyTransFeeMtx.shape == sellTransFeeMtx.shape
assert riskyRetMtx.shape[1] == riskFreeRetVec.size
M, T = buyTransFeeMtx.shape
t1 = time.time()
#create model
model = ConcreteModel()
#number of asset and number of periods
model.symbols = range(M)
model.T = range(T)
model.Tp1 = range(T + 1)
model.Mp1 = range(M + 1)
#decision variables
model.buys = Var(model.symbols, model.T, within=NonNegativeReals)
model.sells = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskyWealth = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskFreeWealth = Var(model.T, within=NonNegativeReals)
#objective
def objective_rule(model):
wealth = sum((1. + riskyRetMtx[m, T]) * model.riskyWealth[m, T - 1]
for m in xrange(M))
wealth += (1. + riskFreeRetVec[T]) * model.riskFreeWealth[T - 1]
return wealth
model.objective = Objective(rule=objective_rule, sense=maximize)
#constraint
def riskyWealth_constraint_rule(model, m, t):
if t >= 1:
preWealth = model.riskyWealth[m, t - 1]
else:
preWealth = allocatedWealth[m]
return (model.riskyWealth[m,
t] == (1. + riskyRetMtx[m, t]) * preWealth +
model.buys[m, t] - model.sells[m, t])
def riskyFreeWealth_constraint_rule(model, t):
totalSell = sum((1 - sellTransFeeMtx[mdx, t]) * model.sells[mdx, t]
for mdx in xrange(M))
totalBuy = sum((1 + buyTransFeeMtx[mdx, t]) * model.buys[mdx, t]
for mdx in xrange(M))
if t >= 1:
preWealth = model.riskFreeWealth[t - 1]
else:
preWealth = allocatedWealth[-1]
return (
model.riskFreeWealth[t] == (1. + riskFreeRetVec[t]) * preWealth +
totalSell - totalBuy)
model.riskyWeathConstraint = Constraint(model.symbols,
model.T,
rule=riskyWealth_constraint_rule)
model.riskFreeWealthConstraint = Constraint(
model.T, rule=riskyFreeWealth_constraint_rule)
#optimizer
opt = SolverFactory('cplex')
# opt.options["threads"] = 4
instance = model.create()
results = opt.solve(instance)
print results
# instance.load(results)
# display(instance)
# instance.load(results)
# for var in instance.active_components(Var):
# varobj = getattr(instance, var)
# for idx in varobj:
# print varobj[idx], varobj[idx].value
#
print "elapsed %.3f secs" % (time.time() - t1)
Plants = ['Barley', 'Wheat', 'Rice', 'Maize'] # Plants' area
SellingPrice = {'Barley':300, 'Wheat':200, 'Rice':250, 'Maize':380} # selling price per km2
Resource = ['fertilizer', 'pesticide'] # fertilizer and pesticide are constraints
Resource_available = {'fertilizer':1260, 'pesticide':780} # amount of fertilizer and pesticide available
Resource_required = {('Barley', 'fertilizer'):4,
('Wheat', 'fertilizer'):12,
('Rice', 'fertilizer'):18,
('Maize', 'fertilizer'):19,
('Barley', 'pesticide'):5,
('Wheat', 'pesticide'):4,
('Rice', 'pesticide'):3,
('Maize', 'pesticide'):6}
# Concrete Model instantiates the data of the problem
model = ConcreteModel()
# Decision variables - varying the combination of plant area
model.SeasonProd = Var(Plants, within=NonNegativeReals)
# Objective - to maximize profit
# meaning: for each product, calculate the profit rate * production, sum all these at the end
model.obj = Objective(expr = sum(SellingPrice[i] * model.SeasonProd[i] for i in Plants),
sense=maximize)
# Constraint - uses a Capacity Rule and Land Area function
# meaning: for each plant, the resource used should not exceed the total resource available
def CapacityRule(model, p):
"""User defined capacity rule -
Accepts a pyomo ConcreteModel as the first positional argument,
and a plant index as a second positional argument"""
def maxRetMultiStagePortfolio(riskyRetMtx, riskFreeRetVec, buyTransFeeMtx,
sellTransFeeMtx, allocatedWealth, symbols,
transDates):
'''
-假設資料共T期, 投資在M個risky assets, 以及1個riskfree asset
-求出每個risky asset每一期應該要買進以及賣出的金額
-最後一期結算不投資
@param riskyRetMtx, numpy.array, size: M * T+1
@param riskFreeRetVec, numpy.array, size: T+1
@param buyTransFeeMtx, numpy.array, size: M * T
@param sellTransFeeMtx, numpy.array, size: M * T
@param allocatedWealth, numpy.array, size: (M+1) (最後一個為cash)
@return (buyMtx, sellMtx), numpy.array, each size: M*T
'''
assert buyTransFeeMtx.shape == sellTransFeeMtx.shape
assert riskyRetMtx.shape[1] == riskFreeRetVec.size
M, T = buyTransFeeMtx.shape
t1 = time.time()
#create model
model = ConcreteModel()
#number of asset and number of periods
model.symbols = range(M)
model.T = range(T)
#decision variables
model.buys = Var(model.symbols, model.T, within=NonNegativeReals)
model.sells = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskyWealth = Var(model.symbols, model.T, within=NonNegativeReals)
model.riskFreeWealth = Var(model.T, within=NonNegativeReals)
#objective
def objective_rule(model):
wealth = sum((1. + riskyRetMtx[m, T]) * model.riskyWealth[m, T - 1]
for m in xrange(M))
wealth += (1. + riskFreeRetVec[T]) * model.riskFreeWealth[T - 1]
return wealth
model.objective = Objective(sense=maximize)
#constraint
def riskyWeathConstraint_rule(model, m, t):
if t >= 1:
preWealth = model.riskyWealth[m, t - 1]
else:
preWealth = allocatedWealth[m]
return (model.riskyWealth[m,
t] == (1. + riskyRetMtx[m, t]) * preWealth +
model.buys[m, t] - model.sells[m, t])
def riskFreeWealthConstraint_rule(model, t):
totalSell = sum((1 - sellTransFeeMtx[mdx, t]) * model.sells[mdx, t]
for mdx in xrange(M))
totalBuy = sum((1 + buyTransFeeMtx[mdx, t]) * model.buys[mdx, t]
for mdx in xrange(M))
if t >= 1:
preWealth = model.riskFreeWealth[t - 1]
else:
preWealth = allocatedWealth[-1]
return (
model.riskFreeWealth[t] == (1. + riskFreeRetVec[t]) * preWealth +
totalSell - totalBuy)
model.riskyWeathConstraint = Constraint(model.symbols, model.T)
model.riskFreeWealthConstraint = Constraint(model.T)
#optimizer
opt = SolverFactory('cplex')
instance = model.create()
results = opt.solve(instance)
print type(results)
print results
#load decision variable
instance.load(results)
display(instance)
# instance.load(results)
# for var in instance.active_components(Var):
# varobj = getattr(instance, var)
# for idx in varobj:
# print varobj[idx], varobj[idx].value
#
# print type(results)
#load objective value
finalWealth = results.Solution.Objective.__default_objective__['value']
print "finalWealth:", finalWealth
print "ret: %.3f %%" % ((finalWealth / 1e5 - 1) * 100)
print "elapsed %.3f secs" % (time.time() - t1)
from coopr.pyomo import (ConcreteModel, Objective, Var, NonNegativeReals,
maximize, Constraint)
Activities = ['ActivityOne', 'ActivityTwo'] #Products in other models
UnitProfit = {'ActivityOne': 2, 'ActivityTwo': 5} #Also called ProfitRate
Resources = ['ResourceOne', 'ResourceTwo']
ResourcesAvailable = {'ResourceOne': 10, 'ResourceTwo': 12}
ResourcesPerUnit = {
('ActivityOne', 'ResourceOne'): 1,
('ActivityTwo', 'ResourceOne'): 2,
('ActivityOne', 'ResourceTwo'): 1,
('ActivityTwo', 'ResourceTwo'): 3
}
#Concrete Model
model = ConcreteModel()
#Decision Variables
model.Prod = Var(Activities, within=NonNegativeReals)
#Objective
model.obj = Objective(expr=sum(UnitProfit[i] * model.Prod[i]
for i in Activities),
sense=maximize)
def ActivityRule(model, r):
return sum(ResourcesPerUnit[i, r] * model.Prod[i]
for i in Activities) <= ResourcesAvailable[r]
model.Utilization = Constraint(Resources, rule=ActivityRule)