Food Manufacture 1¶
Reference¶
SAS/OR example: http://go.documentation.sas.com/?docsetId=ormpex&docsetTarget=ormpex_ex1_toc.htm&docsetVersion=15.1&locale=en
SAS/OR code for example: http://support.sas.com/documentation/onlinedoc/or/ex_code/151/mpex01.html
Model¶
import sasoptpy as so
import pandas as pd
def test(cas_conn):
# Problem data
OILS = ['veg1', 'veg2', 'oil1', 'oil2', 'oil3']
PERIODS = range(1, 7)
cost_data = [
[110, 120, 130, 110, 115],
[130, 130, 110, 90, 115],
[110, 140, 130, 100, 95],
[120, 110, 120, 120, 125],
[100, 120, 150, 110, 105],
[90, 100, 140, 80, 135]]
cost = pd.DataFrame(cost_data, columns=OILS, index=PERIODS).transpose()
hardness_data = [8.8, 6.1, 2.0, 4.2, 5.0]
hardness = {OILS[i]: hardness_data[i] for i in range(len(OILS))}
revenue_per_ton = 150
veg_ub = 200
nonveg_ub = 250
store_ub = 1000
storage_cost_per_ton = 5
hardness_lb = 3
hardness_ub = 6
init_storage = 500
# Problem initialization
m = so.Model(name='food_manufacture_1', session=cas_conn)
# Problem definition
buy = m.add_variables(OILS, PERIODS, lb=0, name='buy')
use = m.add_variables(OILS, PERIODS, lb=0, name='use')
manufacture = m.add_implicit_variable((use.sum('*', p) for p in PERIODS),
name='manufacture')
last_period = len(PERIODS)
store = m.add_variables(OILS, [0] + list(PERIODS), lb=0, ub=store_ub,
name='store')
for oil in OILS:
store[oil, 0].set_bounds(lb=init_storage, ub=init_storage)
store[oil, last_period].set_bounds(lb=init_storage, ub=init_storage)
VEG = [i for i in OILS if 'veg' in i]
NONVEG = [i for i in OILS if i not in VEG]
revenue = so.expr_sum(revenue_per_ton * manufacture[p] for p in PERIODS)
rawcost = so.expr_sum(cost.at[o, p] * buy[o, p]
for o in OILS for p in PERIODS)
storagecost = so.expr_sum(storage_cost_per_ton * store[o, p]
for o in OILS for p in PERIODS)
m.set_objective(revenue - rawcost - storagecost, sense=so.MAX,
name='profit')
# Constraints
m.add_constraints((use.sum(VEG, p) <= veg_ub for p in PERIODS),
name='veg_ub')
m.add_constraints((use.sum(NONVEG, p) <= nonveg_ub for p in PERIODS),
name='nonveg_ub')
m.add_constraints((store[o, p-1] + buy[o, p] == use[o, p] + store[o, p]
for o in OILS for p in PERIODS),
name='flow_balance')
m.add_constraints((so.expr_sum(hardness[o]*use[o, p] for o in OILS) >=
hardness_lb * manufacture[p] for p in PERIODS),
name='hardness_ub')
m.add_constraints((so.expr_sum(hardness[o]*use[o, p] for o in OILS) <=
hardness_ub * manufacture[p] for p in PERIODS),
name='hardness_lb')
# Solver call
res = m.solve()
# With other solve options
m.solve(options={'with': 'lp', 'algorithm': 'PS'})
m.solve(options={'with': 'lp', 'algorithm': 'IP'})
m.solve(options={'with': 'lp', 'algorithm': 'NS'})
if res is not None:
print(so.get_solution_table(buy, use, store))
return m.get_objective_value()
Output¶
In [1]: import os
In [2]: hostname = os.getenv('CASHOST')
In [3]: port = os.getenv('CASPORT')
In [4]: from swat import CAS
In [5]: cas_conn = CAS(hostname, port)
In [6]: import sasoptpy
In [7]: from examples.client_side.food_manufacture_1 import test
In [8]: test(cas_conn)
NOTE: Initialized model food_manufacture_1.
NOTE: Added action set 'optimization'.
NOTE: Converting model food_manufacture_1 to OPTMODEL.
NOTE: Submitting OPTMODEL code to CAS server.
NOTE: Problem generation will use 8 threads.
NOTE: The problem has 95 variables (0 free, 10 fixed).
NOTE: The problem has 54 linear constraints (18 LE, 30 EQ, 6 GE, 0 range).
NOTE: The problem has 210 linear constraint coefficients.
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).
NOTE: The OPTMODEL presolver is disabled for linear problems.
NOTE: The LP presolver value AUTOMATIC is applied.
NOTE: The LP presolver time is 0.00 seconds.
NOTE: The LP presolver removed 44 variables and 4 constraints.
NOTE: The LP presolver removed 48 constraint coefficients.
NOTE: The presolved problem has 51 variables, 50 constraints, and 162 constraint coefficients.
NOTE: The LP solver is called.
NOTE: The Dual Simplex algorithm is used.
Objective
Phase Iteration Value Time
D 2 1 4.755480E+05 0
P 2 49 1.078426E+05 0
NOTE: Optimal.
NOTE: Objective = 107842.59259.
NOTE: The Dual Simplex solve time is 0.01 seconds.
NOTE: The output table 'SOLUTION' in caslib 'CASUSER(casuser)' has 95 rows and 6 columns.
NOTE: The output table 'DUAL' in caslib 'CASUSER(casuser)' has 54 rows and 4 columns.
NOTE: The CAS table 'solutionSummary' in caslib 'CASUSER(casuser)' has 13 rows and 4 columns.
NOTE: The CAS table 'problemSummary' in caslib 'CASUSER(casuser)' has 18 rows and 4 columns.
NOTE: Added action set 'optimization'.
NOTE: Converting model food_manufacture_1 to OPTMODEL.
NOTE: Submitting OPTMODEL code to CAS server.
NOTE: Problem generation will use 8 threads.
NOTE: The problem has 95 variables (0 free, 10 fixed).
NOTE: The problem has 54 linear constraints (18 LE, 30 EQ, 6 GE, 0 range).
NOTE: The problem has 210 linear constraint coefficients.
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).
NOTE: The LP presolver value AUTOMATIC is applied.
NOTE: The LP presolver time is 0.00 seconds.
NOTE: The LP presolver removed 44 variables and 4 constraints.
NOTE: The LP presolver removed 48 constraint coefficients.
NOTE: The presolved problem has 51 variables, 50 constraints, and 162 constraint coefficients.
NOTE: The LP solver is called.
NOTE: The Primal Simplex algorithm is used.
Objective
Phase Iteration Value Time
P 1 1 1.749040E+03 0
P 2 32 3.638889E+04 0
D 2 51 1.078426E+05 0
NOTE: Optimal.
NOTE: Objective = 107842.59259.
NOTE: The Primal Simplex solve time is 0.01 seconds.
NOTE: The output table 'SOLUTION' in caslib 'CASUSER(casuser)' has 95 rows and 6 columns.
NOTE: The output table 'DUAL' in caslib 'CASUSER(casuser)' has 54 rows and 4 columns.
NOTE: The CAS table 'solutionSummary' in caslib 'CASUSER(casuser)' has 13 rows and 4 columns.
NOTE: The CAS table 'problemSummary' in caslib 'CASUSER(casuser)' has 18 rows and 4 columns.
NOTE: Added action set 'optimization'.
NOTE: Converting model food_manufacture_1 to OPTMODEL.
NOTE: Submitting OPTMODEL code to CAS server.
NOTE: Problem generation will use 8 threads.
NOTE: The problem has 95 variables (0 free, 10 fixed).
NOTE: The problem has 54 linear constraints (18 LE, 30 EQ, 6 GE, 0 range).
NOTE: The problem has 210 linear constraint coefficients.
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).
NOTE: The LP presolver value AUTOMATIC is applied.
NOTE: The LP presolver time is 0.00 seconds.
NOTE: The LP presolver removed 44 variables and 4 constraints.
NOTE: The LP presolver removed 48 constraint coefficients.
NOTE: The LP presolver modified 0 constraint coefficients.
NOTE: The presolved problem has 51 variables, 50 constraints, and 162 constraint coefficients.
NOTE: The LP solver is called.
NOTE: The Interior Point algorithm is used.
NOTE: The deterministic parallel mode is enabled.
NOTE: The Interior Point algorithm is using up to 8 threads.
Primal Bound Dual
Iter Complement Duality Gap Infeas Infeas Infeas Time
0 1.1003E+04 1.3994E+01 2.0602E-02 1.1145E-02 1.2444E+00 0
1 1.0498E+04 4.1015E+01 1.7385E-02 9.4051E-03 1.0928E+00 0
2 7.2084E+03 7.4551E+00 5.6703E-03 3.0675E-03 6.8365E-01 0
3 1.7518E+03 1.1221E+00 1.5798E-03 8.5465E-04 1.1852E-01 0
4 4.1038E+02 2.5544E-01 5.6092E-04 3.0344E-04 1.1852E-03 0
5 3.9774E+01 2.2775E-02 7.2994E-05 3.9488E-05 1.9281E-05 0
6 9.9400E-01 5.6526E-04 7.9112E-07 4.2798E-07 7.7185E-07 0
7 9.9572E-03 5.6615E-06 7.9420E-09 4.2964E-09 7.7239E-09 0
8 0.0000E+00 1.8686E-08 1.6613E-07 1.1864E-10 6.2833E-07 0
NOTE: The Interior Point solve time is 0.02 seconds.
NOTE: The CROSSOVER option is enabled.
NOTE: The crossover basis contains 11 primal and 3 dual superbasic variables.
Objective
Phase Iteration Value Time
P C 1 1.014226E+03 0
D C 13 9.697429E+00 0
D 2 16 1.078426E+05 0
P 2 17 1.078426E+05 0
D 2 18 1.078426E+05 0
NOTE: The Crossover time is 0.01 seconds.
NOTE: Optimal.
NOTE: Objective = 107842.59259.
NOTE: The output table 'SOLUTION' in caslib 'CASUSER(casuser)' has 95 rows and 6 columns.
NOTE: The output table 'DUAL' in caslib 'CASUSER(casuser)' has 54 rows and 4 columns.
NOTE: The CAS table 'solutionSummary' in caslib 'CASUSER(casuser)' has 16 rows and 4 columns.
NOTE: The CAS table 'problemSummary' in caslib 'CASUSER(casuser)' has 18 rows and 4 columns.
NOTE: Added action set 'optimization'.
NOTE: Converting model food_manufacture_1 to OPTMODEL.
NOTE: Submitting OPTMODEL code to CAS server.
NOTE: Problem generation will use 8 threads.
NOTE: The problem has 95 variables (0 free, 10 fixed).
NOTE: The problem has 54 linear constraints (18 LE, 30 EQ, 6 GE, 0 range).
NOTE: The problem has 210 linear constraint coefficients.
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).
NOTE: The LP presolver value AUTOMATIC is applied.
NOTE: The LP presolver time is 0.00 seconds.
NOTE: The LP presolver removed 44 variables and 4 constraints.
NOTE: The LP presolver removed 48 constraint coefficients.
NOTE: The presolved problem has 51 variables, 50 constraints, and 162 constraint coefficients.
NOTE: The LP solver is called.
NOTE: The Network Simplex algorithm is used.
NOTE: The network has 20 rows (40.00%), 29 columns (56.86%), and 1 component.
NOTE: The network extraction and setup time is 0.03 seconds.
Primal Primal Dual
Iteration Objective Infeasibility Infeasibility Time
1 3.750000E+03 5.000000E+02 1.551000E+03 0.03
24 7.125000E+04 0.000000E+00 0.000000E+00 0.03
NOTE: The Network Simplex solve time is 0.00 seconds.
NOTE: The total Network Simplex solve time is 0.03 seconds.
NOTE: The Dual Simplex algorithm is used.
Objective
Phase Iteration Value Time
D 2 1 2.240180E+05 0
P 2 43 1.078426E+05 0
NOTE: Optimal.
NOTE: Objective = 107842.59259.
NOTE: The Simplex solve time is 0.04 seconds.
NOTE: The output table 'SOLUTION' in caslib 'CASUSER(casuser)' has 95 rows and 6 columns.
NOTE: The output table 'DUAL' in caslib 'CASUSER(casuser)' has 54 rows and 4 columns.
NOTE: The CAS table 'solutionSummary' in caslib 'CASUSER(casuser)' has 14 rows and 4 columns.
NOTE: The CAS table 'problemSummary' in caslib 'CASUSER(casuser)' has 18 rows and 4 columns.
buy use store
veg1 1 0.000000e+00 8.518519e+01 4.148148e+02
veg1 2 0.000000e+00 1.592593e+02 2.555556e+02
veg1 3 2.842171e-14 0.000000e+00 2.555556e+02
veg1 4 -1.421085e-14 1.592593e+02 9.629630e+01
veg1 5 7.105427e-14 9.629630e+01 0.000000e+00
veg1 6 6.592593e+02 1.592593e+02 5.000000e+02
veg2 1 -5.684342e-14 1.148148e+02 3.851852e+02
veg2 2 0.000000e+00 4.074074e+01 3.444444e+02
veg2 3 2.842171e-14 2.000000e+02 1.444444e+02
veg2 4 -2.842171e-14 4.074074e+01 1.037037e+02
veg2 5 0.000000e+00 1.037037e+02 0.000000e+00
veg2 6 5.407407e+02 4.074074e+01 5.000000e+02
oil1 1 0.000000e+00 0.000000e+00 5.000000e+02
oil1 2 0.000000e+00 0.000000e+00 5.000000e+02
oil1 3 0.000000e+00 0.000000e+00 5.000000e+02
oil1 4 0.000000e+00 -1.744059e-14 5.000000e+02
oil1 5 0.000000e+00 0.000000e+00 5.000000e+02
oil1 6 0.000000e+00 0.000000e+00 5.000000e+02
oil2 1 0.000000e+00 0.000000e+00 5.000000e+02
oil2 2 2.500000e+02 2.500000e+02 5.000000e+02
oil2 3 0.000000e+00 2.273737e-13 5.000000e+02
oil2 4 2.842171e-14 2.500000e+02 2.500000e+02
oil2 5 0.000000e+00 2.500000e+02 0.000000e+00
oil2 6 7.500000e+02 2.500000e+02 5.000000e+02
oil3 1 0.000000e+00 2.500000e+02 2.500000e+02
oil3 2 0.000000e+00 0.000000e+00 2.500000e+02
oil3 3 -5.048710e-29 2.500000e+02 -2.842171e-13
oil3 4 2.842171e-13 0.000000e+00 0.000000e+00
oil3 5 5.000000e+02 0.000000e+00 5.000000e+02
oil3 6 0.000000e+00 0.000000e+00 5.000000e+02
veg1 0 NaN NaN 5.000000e+02
veg2 0 NaN NaN 5.000000e+02
oil1 0 NaN NaN 5.000000e+02
oil2 0 NaN NaN 5.000000e+02
oil3 0 NaN NaN 5.000000e+02
Out[8]: 107842.59259259264