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
