Robustness analysis of BIM production plan via simulations#

This example is a continuation of the BIM chip production problem illustrated here. Recall hat BIM produces logic and memory chips using copper, silicon, germanium, and plastic and that each chip requires the following quantities of raw materials:

chip

copper

silicon

germanium

plastic

logic

0.4

1

-

1

memory

0.2

-

1

1

BIM needs to carefully manage the acquisition and inventory of these raw materials based on the forecasted demand for the chips. Data analysis led to the following prediction of monthly demands:

chip

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

logic

88

125

260

217

238

286

248

238

265

293

259

244

memory

47

62

81

65

95

118

86

89

82

82

84

66

At the beginning of the year, BIM has the following stock:

copper

silicon

germanium

plastic

480

1000

1500

1750

The company would like to have at least the following stock at the end of the year:

copper

silicon

germanium

plastic

200

500

500

1000

Each raw material can be acquired at each month, but the unit prices vary as follows:

product

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

copper

1

1

1

2

2

3

3

2

2

1

1

2

silicon

4

3

3

3

5

5

6

5

4

3

3

5

germanium

5

5

5

3

3

3

3

2

3

4

5

6

plastic

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

The inventory is limited by a capacity of a total of 9000 units per month, regardless of the type of material of products in stock. The holding costs of the inventory are 0.05 per unit per month regardless of the material type. Due to budget constraints, BIM cannot spend more than 5000 per month on acquisition.

BIM aims at minimizing the acquisition and holding costs of the materials while meeting the required quantities for production. The production is made to order, meaning that no inventory of chips is kept.

Let us model the material acquisition planning and solve it optimally based on the forecasted chip demand above.

# install dependencies and select solver
%pip install -q amplpy numpy pandas matplotlib

SOLVER = "cbc"  # highs, scip, cbc, mosek, gurobi, cplex, xpress, knitro

from amplpy import AMPL, ampl_notebook

ampl = ampl_notebook(
    modules=["coin", "highs"],  # modules to install
    license_uuid="default",  # license to use
)  # instantiate AMPL object and register notebook magics

Using default Community Edition License for Colab. Get yours at: https://ampl.com/ce
Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://colab.ampl.com).

from io import StringIO
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

plt.rcParams.update({"font.size": 14})

demand_data = """
chip, Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec
logic, 88, 125, 260, 217, 238, 286, 248, 238, 265, 293, 259, 244
memory, 47, 62, 81, 65, 95, 118, 86, 89, 82, 82, 84, 66
"""

demand_chips = pd.read_csv(StringIO(demand_data), index_col="chip")
display(demand_chips)

price_data = """
product, Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec
copper, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 2
silicon, 4, 3, 3, 3, 5, 5, 6, 5, 4, 3, 3, 5
germanium, 5, 5, 5, 3, 3, 3, 3, 2, 3, 4, 5, 6
plastic, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1
"""

price = pd.read_csv(StringIO(price_data), index_col="product")
display(price)

use = dict()
use["logic"] = {"silicon": 1, "plastic": 1, "copper": 4}
use["memory"] = {"germanium": 1, "plastic": 1, "copper": 2}
use = pd.DataFrame.from_dict(use).fillna(0).astype(int)
material_demand = use.dot(demand_chips)

existing = pd.Series(
    {"silicon": 1000, "germanium": 1500, "plastic": 1750, "copper": 4800}
)
eot_inventory = pd.Series(
    {"silicon": 500, "germanium": 500, "plastic": 1000, "copper": 2000}
)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
chip
logic 88 125 260 217 238 286 248 238 265 293 259 244
memory 47 62 81 65 95 118 86 89 82 82 84 66
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
product
copper 1.0 1.0 1.0 2.0 2.0 3.0 3.0 2.0 2.0 1.0 1.0 2.0
silicon 4.0 3.0 3.0 3.0 5.0 5.0 6.0 5.0 4.0 3.0 3.0 5.0
germanium 5.0 5.0 5.0 3.0 3.0 3.0 3.0 2.0 3.0 4.0 5.0 6.0
plastic 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 
# we store all the problem data in one object to easily perform folding-horizon simulations
def initialize_problem_data():
    problem_data = {
        "price": price.copy(deep=True),
        "inventory_cost": 0.05,
        "material_demand": material_demand.copy(deep=True),
        "demand_chips_ref": demand_chips.copy(deep=True),
        "demand_chips_simulation": demand_chips.copy(deep=True),
        "use": use.copy(deep=True),
        "existing": existing.copy(deep=True),
        "eot_inventory": eot_inventory.copy(deep=True),
        "stock_limit": 9000,
        "month_budget": 2500,
    }
    return problem_data


def ShowTable(X, I, J):
    return pd.DataFrame.from_records(
        [[X[i, j] for j in J] for i in I], index=I, columns=J
    ).round(decimals=2)

%%writefile product_inventory.mod

set PERIODS;
set PRODUCTS;

param first symbolic;
param prev_period{PERIODS} symbolic;
param last symbolic;

param stock_limit;
param month_budget;

param pi{PERIODS, PRODUCTS};        # acquisition price
param h{PERIODS, PRODUCTS};         # holding cost
param delta{PERIODS, PRODUCTS};     # demand

param existing{PRODUCTS};
param desired{PRODUCTS};

var x{PERIODS, PRODUCTS} >= 0;
var s{PERIODS, PRODUCTS} >= 0;

var acquisition_cost
    = sum {t in PERIODS, p in PRODUCTS} pi[t,p] * x[t,p];

var inventory_cost
    = sum {t in PERIODS, p in PRODUCTS} h[t,p] * s[t,p];

minimize TotalCost: acquisition_cost + inventory_cost;

s.t. Balance{t in PERIODS, p in PRODUCTS}:
    (if t==first then existing[p] else s[prev_period[t],p])
        + x[t,p] == delta[t,p] + s[t,p];

s.t. Finish{p in PRODUCTS}:
    s[last,p] >= desired[p];

s.t. Inventory{t in PERIODS}:
    sum {p in PRODUCTS} s[t,p] <= stock_limit;

s.t. Budget{t in PERIODS}:
    sum {p in PRODUCTS} pi[t,p]*x[t,p] <= month_budget;

Overwriting product_inventory.mod

def BIMProductAcquisitionAndInventory(problem_data):
    demand = problem_data["use"].dot(problem_data["demand_chips_ref"])
    acquisition_price = problem_data["price"]
    existing = problem_data["existing"]
    desired = problem_data["eot_inventory"]
    stock_limit = problem_data["stock_limit"]
    month_budget = problem_data["month_budget"]

    ampl = AMPL()
    ampl.read("product_inventory.mod")

    periods = list(demand.columns)
    products = list(demand.index)

    ampl.set["PERIODS"] = periods
    ampl.set["PRODUCTS"] = products
    ampl.param["first"] = periods[0]
    ampl.param["prev_period"] = {j: i for i, j in zip(periods, periods[1:])}
    ampl.param["last"] = periods[-1]

    ampl.param["stock_limit"] = stock_limit
    ampl.param["month_budget"] = month_budget

    ampl.param["pi"] = acquisition_price.T
    ampl.param["h"] = {(t, p): 0.05 for p in products for t in periods}
    ampl.param["delta"] = demand.T

    ampl.param["existing"] = existing
    ampl.param["desired"] = desired

    ampl.option["solver"] = SOLVER
    ampl.solve()

    return ampl, products, periods


problem_data = initialize_problem_data()
m, products, periods = BIMProductAcquisitionAndInventory(problem_data)

print(f"The optimal solution yields a total cost of {m.get_value('TotalCost'):.2f}\n")

x = m.get_variable("x").to_dict()
# x.index = pd.MultiIndex.from_tuples(x.index)
problem_data["purchases"] = ShowTable(x, periods, products).T

s = m.get_variable("s").to_dict()
problem_data["stock"] = ShowTable(s, periods, products).T

display(problem_data["purchases"])
display(problem_data["stock"])

cbc 2.10.10: cbc 2.10.10: optimal solution; objective 23580.34083
0 simplex iterations
 

"option abs_boundtol 1.1368683772161603e-13;"
or "option rel_boundtol 2.2737367544323206e-16;"
will change deduced dual values.

The optimal solution yields a total cost of 23580.34
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
silicon 0.00 833.33 0.0 833.33 0.00 0.0 0.0 0.00 594.33 0.0 0.0 0.0
plastic 0.00 0.00 0.0 0.00 0.00 0.0 266.0 327.00 722.00 0.0 343.0 1310.0
copper 214.67 0.00 2500.0 0.00 536.45 0.0 0.0 1233.65 25.23 2500.0 2465.7 682.3
germanium 0.00 0.00 0.0 0.00 0.00 0.0 0.0 0.00 0.00 0.0 0.0 0.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
silicon 912.00 1620.33 1360.33 1976.67 1738.67 1452.67 1204.67 966.67 1296.0 1003.0 744.0 500.0
plastic 1615.00 1428.00 1087.00 805.00 472.00 68.00 0.00 0.00 375.0 0.0 0.0 1000.0
copper 4568.67 3944.67 5242.67 4244.67 3639.12 2259.12 1095.12 1198.77 0.0 1164.0 2425.7 2000.0
germanium 1453.00 1391.00 1310.00 1245.00 1150.00 1032.00 946.00 857.00 775.0 693.0 609.0 543.0

Actual performance of the robust solution#

We now perform a stochastic simulation to assess the performance of the robust solutions that we found earlier.

%%writefile product_demand_missed_in_period.mod

set PRODUCTS;
set MATERIALS;

param avail{MATERIALS};
param use{MATERIALS, PRODUCTS};
param demand_chips{PRODUCTS};

# Decision variable: nb of chips to produce >= 0
var x{PRODUCTS} >= 0;

# Decision variable: missed demand
var s{PRODUCTS} >= 0;

# Constraint: per resource we cannot use more than there is
s.t. ResourceConstraint{i in MATERIALS}:
    sum {p in PRODUCTS} x[p] * use[i, p] <= avail[i];

# Constraint: production + missed demand = total demand in this period
s.t. ProducedPlusUnmet{p in PRODUCTS}:
    x[p] + s[p] == demand_chips[p];

# Objective - minimize the missed demand
minimize TotalUnmet:
        sum {p in PRODUCTS} s[p];

Overwriting product_demand_missed_in_period.mod

def minimize_missed_demand_in_period(
    inventory, missed_demand, purchases, existing, demand_chips, use, period=None
):
    periods = inventory.columns
    first = periods[0]
    prev = {j: i for i, j in zip(periods, periods[1:])}
    last = periods[-1]

    ampl = AMPL()
    ampl.read("product_demand_missed_in_period.mod")

    products = list(use.columns)
    materials = list(use.index)

    ampl.set["PRODUCTS"] = products
    ampl.set["MATERIALS"] = materials

    ampl.param["avail"] = {
        i: inventory.loc[i, prev[period]] + purchases.loc[i, period] for i in materials
    }
    ampl.param["use"] = {(i, p): use.at[i, p] for i in materials for p in products}
    ampl.param["demand_chips"] = demand_chips.loc[:, period]

    ampl.option["solver"] = SOLVER
    ampl.solve()

    x = ampl.get_variable("x").to_dict()
    s = ampl.get_variable("s").to_dict()

    # update inventory
    for i in materials:
        inventory.loc[i, period] = (
            inventory.loc[i, prev[period]]
            + purchases.loc[i, period]
            - sum([x[p] * use.loc[i, p] for p in products])
        )

    # update missed demand
    for p in products:
        missed_demand.loc[p, period] = s[p]

    return 0


def simulation_per_trajectory(purchases, existing, demand_chips, use):
    # Set up the table to store inventory evolution
    inventory = pd.DataFrame(index=purchases.index, columns=purchases.columns)
    inventory = pd.concat(
        [pd.DataFrame(existing, index=existing.index, columns=["existing"]), inventory],
        axis=1,
    )

    # Set up the DF to store missed demand information
    missed_demand = pd.DataFrame(
        np.zeros((len(demand_chips.index), len(purchases.columns))),
        index=demand_chips.index,
        columns=purchases.columns,
    )

    # Proper simulation
    for period in inventory.columns[1:]:
        minimize_missed_demand_in_period(
            inventory, missed_demand, purchases, existing, demand_chips, use, period
        )

    return inventory.iloc[:, 1:], missed_demand


def simulate_performance(problem_data, n=50, rho=0.05, seed=0):
    rng = np.random.default_rng(seed)

    results = []
    for i in range(n):
        perturbed_demand = problem_data["demand_chips_simulation"].applymap(
            lambda x: x * (1 + rho * (1 - 2 * rng.random()))
        )
        inv, md = simulation_per_trajectory(
            problem_data["purchases"], problem_data["existing"], perturbed_demand, use
        )
        results.append({"inventory": inv, "missing_demand": md})

    MissingDemand = pd.concat(
        [i["missing_demand"] for i in results], keys=[i for i in range(len(results))]
    )
    MissingDemand = MissingDemand.astype("float").swaplevel()

    InventoryEvolution = pd.concat(
        [i["inventory"] for i in results], keys=[i for i in range(len(results))]
    )
    InventoryEvolution = InventoryEvolution.astype("float").swaplevel()

    return {"MissingDemand": MissingDemand, "InventoryEvolution": InventoryEvolution}


def report(MissingDemand, InventoryEvolution, problem_data):
    # list to store DFs with per-group computed quantiles at various levels
    average_missed_demand = MissingDemand.groupby(level=0).mean().transpose()

    # build a plot with as many subplots as there are chip types
    fig, axis = plt.subplots(figsize=(11, 4))
    average_missed_demand.plot(ax=axis, drawstyle="steps-mid", grid=True)
    plt.xticks(
        ticks=np.arange(len(average_missed_demand.index)),
        labels=average_missed_demand.index,
    )
    # axis.set_title("Missed demand of chips under " + str(rho * 100) + "% uncertainty")
    fig.tight_layout(pad=3.0)
    plt.savefig("bim_robust_missed_demand.pdf")

    realized_inv_cost = (
        InventoryEvolution.groupby(level=0).mean().sum(axis=1).sum()
        * problem_data["inventory_cost"]
    )
    print(
        f'Purchasing cost: {(problem_data["price"] * problem_data["purchases"]).sum().sum():.2f}'
    )
    print(
        f'Theoretical inventory cost: {(problem_data["stock"] * problem_data["inventory_cost"]).sum().sum():.2f}\n'
    )
    print(f"Simulated realized inventory cost: {realized_inv_cost:.2f}")
    print(
        f"Simulated average missed demand for logic chips is {MissingDemand.groupby(level = 0).mean().sum(axis = 1)[0]:.3f} and for memory chips is {MissingDemand.groupby(level = 0).mean().sum(axis = 1)[1]:.3f}\n"
    )
    print(
        "Plot of missed chips demand over time under "
        + str(rho * 100)
        + "% uncertainty\n"
    )
    plt.show()

We now simulate 50 trajectories assuming there is a \(\rho=8\%\) uncertainty around the nominal demand.

rho = 0.08
N_sim = 50

problem_data["demand_chips_ref"] = demand_chips
m, products, periods = BIMProductAcquisitionAndInventory(problem_data)

x = m.get_variable("x").to_dict()
problem_data["purchases"] = ShowTable(x, periods, products).T
s = m.get_variable("s").to_dict()
problem_data["stock"] = ShowTable(s, periods, products).T

SimResults = simulate_performance(problem_data, N_sim, rho)

cbc 2.10.10: cbc 2.10.10: optimal solution; objective 23580.34083
0 simplex iterations
 

"option abs_boundtol 1.1368683772161603e-13;"
or "option rel_boundtol 2.2737367544323206e-16;"
will change deduced dual values.

cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 13.82087188
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 2.972689303
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 1.197848606
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 18.83629081
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 1.928102786
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 21.41704284
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 14.39737256
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 19.71720675
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0.2895346977
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 16.82419217
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 3.98996927
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 14.58302638
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 4.601283596
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 16.87890233
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 3.456471017
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 13.15310629
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 8.851052463
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 48.53569211
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 12.34528189
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 9.176017599
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 6.913838808
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 29.24160359
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0.6841452299
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 16.03590389
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 9.597856797
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 21.55840715
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 44.20812945
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 7.220685618
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 2.294975269
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 7.054840807
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 1.171080061
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 9.169182314
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 7.035965405
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 1.270361572
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 10.04285461
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 19.21934309
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 8.883369035
0 simplex iterations
 
cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 36.74701521
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 8.42640034
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 14.47067719
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 28.1304537
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 18.69176404
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 11.49122778
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 17.60432621
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 9.453323895
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 32.62889045
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 23.92289873
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 9.433215566
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 23.64121828
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 30.4397849
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 32.55773796
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0.6895265503
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 13.94010107
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 1.537517002
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 8.049814088
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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cbc 2.10.10: cbc 2.10.10: optimal solution; objective 0
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The simulation results report a sllighly higher inventory cost and a nonzero amount of missed chip demand.

report(SimResults["MissingDemand"], SimResults["InventoryEvolution"], problem_data)

Purchasing cost: 20309.73
Theoretical inventory cost: 3270.58

Simulated realized inventory cost: 3309.54
Simulated average missed demand for logic chips is 4.543 and for memory chips is 13.154

Plot of missed chips demand over time under 8.0% uncertainty
../../_images/86812873764aaf18005221a443e195b3434701c520aab82f999880358dde1900.png