production.py

To meet the demands of its customers, a company manufactures its products in its own factories (inside production) or buys them from other companies (outside production). The inside production is subject to some resource constraints: each product consumes a certain amount of each resource. In contrast, outside production is theoretically unlimited. The problem is to determine how much of each product should be produced inside and outside the company while minimizing the overall production cost, meeting the demand, and satisfying the resource constraints.

The model aims at minimizing the production cost for a number of products while satisfying customer demand. Each product can be produced either inside the company or outside, at a higher cost. The inside production is constrained by the company’s resources, while outside production is considered unlimited. The model first declares the products and the resources. The data consists of the description of the products (the demand, the inside and outside costs, and the resource consumption) and the capacity of the various resources.

The variables for this problem are the inside and outside production for each product.

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# --------------------------------------------------------------------------
# Source file provided under Apache License, Version 2.0, January 2004,
# http://www.apache.org/licenses/
# (c) Copyright IBM Corp. 2015, 2018
# --------------------------------------------------------------------------

"""The model aims at minimizing the production cost for a number of products
while satisfying customer demand. Each product can be produced either inside
the company or outside, at a higher cost.

The inside production is constrained by the company's resources, while outside
production is considered unlimited.

The model first declares the products and the resources.
The data consists of the description of the products (the demand, the inside
and outside costs, and the resource consumption) and the capacity of the
various resources.

The variables for this problem are the inside and outside production for each
product.
"""

from docplex.mp.model import Model
from docplex.util.environment import get_environment


# ----------------------------------------------------------------------------
# Initialize the problem data
# ----------------------------------------------------------------------------
PRODUCTS = [("kluski", 100, 0.6, 0.8),
            ("capellini", 200, 0.8, 0.9),
            ("fettucine", 300, 0.3, 0.4)]

# resources are a list of simple tuples (name, capacity)
RESOURCES = [("flour", 20),
             ("eggs", 40)]

CONSUMPTIONS = {("kluski", "flour"): 0.5,
                ("kluski", "eggs"): 0.2,
                ("capellini", "flour"): 0.4,
                ("capellini", "eggs"): 0.4,
                ("fettucine", "flour"): 0.3,
                ("fettucine", "eggs"): 0.6}


# ----------------------------------------------------------------------------
# Build the model
# ----------------------------------------------------------------------------
def build_production_problem(mdl, products, resources, consumptions, **kwargs):
    """ Takes as input:
        - a list of product tuples (name, demand, inside, outside)
        - a list of resource tuples (name, capacity)
        - a list of consumption tuples (product_name, resource_named, consumed)
    """
      # --- decision variables ---
    mdl.inside_vars  = mdl.continuous_var_dict(products, name=lambda p: 'inside_%s' % p[0])
    mdl.outside_vars = mdl.continuous_var_dict(products, name=lambda p: 'outside_%s' % p[0])

    # --- constraints ---
    # demand satisfaction
    mdl.add_constraints((mdl.inside_vars[prod] + mdl.outside_vars[prod] >= prod[1], 'ct_demand_%s' % prod[0]) for prod in products)

    # --- resource capacity ---
    mdl.add_constraints((mdl.sum(mdl.inside_vars[p] * consumptions[p[0], res[0]] for p in products) <= res[1],
                         'ct_res_%s' % res[0]) for res in resources)

    # --- objective ---
    mdl.total_inside_cost = mdl.sum(mdl.inside_vars[p] * p[2] for p in products)
    mdl.add_kpi(mdl.total_inside_cost, "inside cost")
    mdl.total_outside_cost = mdl.sum(mdl.outside_vars[p] * p[3] for p in products)
    mdl.add_kpi(mdl.total_outside_cost, "outside cost")
    mdl.minimize(mdl.total_inside_cost + mdl.total_outside_cost)
    return mdl


def print_production_solution(mdl, products):
    obj = mdl.objective_value
    print("* Production model solved with objective: {:g}".format(obj))
    print("* Total inside cost=%g" % mdl.total_inside_cost.solution_value)
    for p in products:
        print("Inside production of {product}: {ins_var}".format
              (product=p[0], ins_var=mdl.inside_vars[p].solution_value))
    print("* Total outside cost=%g" % mdl.total_outside_cost.solution_value)
    for p in products:
        print("Outside production of {product}: {out_var}".format
              (product=p[0], out_var=mdl.outside_vars[p].solution_value))

def build_default_production_problem(**kwargs):
    mdl = Model( **kwargs)
    return build_production_problem(mdl, PRODUCTS, RESOURCES, CONSUMPTIONS)
# ----------------------------------------------------------------------------
# Solve the model and display the result
# ----------------------------------------------------------------------------
if __name__ == '__main__':
    # Build the model
    with Model(name='production') as model:
        model = build_production_problem(model, PRODUCTS, RESOURCES, CONSUMPTIONS)
        model.print_information()
        # Solve the model.
        if model.solve():
            print_production_solution(model, PRODUCTS)
            # Save the CPLEX solution as "solution.json" program output
            with get_environment().get_output_stream("solution.json") as fp:
                model.solution.export(fp, "json")
        else:
            print("Problem has no solution")