The Pasta Production Problem

This tutorial includes everything you need to set up IBM Decision Optimization CPLEX Modeling for Python (DOcplex), build a Mathematical Programming model, and get its solution by solving the model on the cloud with IBM ILOG CPLEX Optimizer.

When you finish this tutorial, you'll have a foundational knowledge of Prescriptive Analytics.

This notebook is part of Prescriptive Analytics for Python

It requires either an installation of CPLEX Optimizers or it can be run on IBM Watson Studio Cloud (Sign up for a free IBM Cloud account and you can start using Watson Studio Cloud right away).

Table of contents:

Describe the business problem
How decision optimization (prescriptive analytics) can help
Use decision optimization
Summary

Describe the business problem

This notebook describes how to use CPLEX Modeling for Python to manage the production of pasta to meet demand with your resources.

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.

How decision optimization can help

Prescriptive analytics (decision optimization) technology recommends actions that are based on desired outcomes. It takes into account specific scenarios, resources, and knowledge of past and current events. With this insight, your organization can make better decisions and have greater control of business outcomes.
Prescriptive analytics is the next step on the path to insight-based actions. It creates value through synergy with predictive analytics, which analyzes data to predict future outcomes.
Prescriptive analytics takes that insight to the next level by suggesting the optimal way to handle that future situation. Organizations that can act fast in dynamic conditions and make superior decisions in uncertain environments gain a strong competitive advantage.

With prescriptive analytics, you can:

Automate the complex decisions and trade-offs to better manage your limited resources.
Take advantage of a future opportunity or mitigate a future risk.
Proactively update recommendations based on changing events.
Meet operational goals, increase customer loyalty, prevent threats and fraud, and optimize business processes.

Use decision optimization

Step 1: Import the library

Run the following code to import the Decision Optimization CPLEX Modeling library. The DOcplex library contains the two modeling packages, Mathematical Programming (docplex.mp) and Constraint Programming (docplex.cp).



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import sys
try:
    import docplex.mp
except:
    raise Exception('Please install docplex. See https://pypi.org/project/docplex/')

Step 2: Model the data

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.



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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}

Step 3: Prepare the data

Data is very simple and is ready to use without any cleasning, massage, refactoring.

Step 4: Set up the prescriptive model



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from docplex.mp.environment import Environment
env = Environment()
env.print_information()

Create the DOcplex model

The model contains all the business constraints and defines the objective.

We now use CPLEX Modeling for Python to build a Mixed Integer Programming (MIP) model for this problem.



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from docplex.mp.model import Model
mdl = Model(name="pasta")

Define the decision variables



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inside_vars = mdl.continuous_var_dict(products, name='inside')
outside_vars = mdl.continuous_var_dict(products, name='outside')

Express the business constraints

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.



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

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

mdl.print_information()

Express the objective

Minimizing the production cost for a number of products while satisfying customer demand



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total_inside_cost = mdl.sum(inside_vars[p] * p[2] for p in products)
total_outside_cost = mdl.sum(outside_vars[p] * p[3] for p in products)

mdl.minimize(total_inside_cost + total_outside_cost)

Solve with Decision Optimization

Now we have everything we need to solve the model, using Model.solve(). The following cell solves using your local CPLEX (if any, and provided you have added it to your PYTHONPATH variable).



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mdl.solve()

Step 5: Investigate the solution and then run an example analysis



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obj = mdl.objective_value

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

In the above figure, all nurses but one are assigned the average of 7 shifts, which is what we expected.

Summary

You learned how to set up and use IBM Decision Optimization CPLEX Modeling for Python to formulate a Mathematical Programming model and solve it with IBM Decision Optimization on Cloud.

References

CPLEX Modeling for Python documentation
Decision Optimization on Cloud
Need help with DOcplex or to report a bug? Please go here.
Contact us at dofeedback@wwpdl.vnet.ibm.com.



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