7 October 2021 (144 words)

Vamshi Jandhyala has an interesting series of blog posts about Optimization using linear models.

Each article includes a description of the topic, along with several examples written in Python and solved using the Gurobi commercial solver:

• Modeling using Linear Programming. Illustrates some concepts of linear programming via the formulation and solution of a resource allocation problem.
• Modeling using Integer Programming. Describes several applications of integer programming, including an assignment problem, graph coloring, the 0-1 knapsack problem, a set covering problem, and a class scheduling example.
• Graphs and Integer Programming. Explores some graph theory applications of integer programming, including finding a maximal independent set and finding the maximal clique of a set.

The examples include Python source code, though they are sufficiently small that they could be translated to use your preferred modelling tool and solver.

3 October 2021 (2,419 words)

OpenSolver uses the free, open-source CBC solver. For most linear models, CBC is good enough. But sometimes CBC struggles to solve a model in a reasonable time. That usually happens when the model has a large number of variables or constraints, though some small models can also be difficult to solve.

When CBC doesn't get the job done, we can try using a more powerful solver. One way to apply more power is to use the NEOS Server, which is an online service that provides access to many different solvers, including commercial solvers, for free.

This article describes an example of how we can solve a model using the CPLEX solver via the NEOS Server.