At the heart of any optimization model lies a set of decision variables. Finding a convenient way to store and access these variables can often represent the main challenge in implementing the model. While the variables in some models map naturally to simple programming language constructs (e.g., x[i] for contiguous integer values i), other models can present a much greater challenge. For example, consider a model that optimizes the flow of multiple different commodities through a supply network. You might have a variable x['Pens', 'Denver', 'New York'] that captures the flow of a manufactured item (pens in this example) from Denver to New York. At the same time, you might not want to have a variable x['Pencils', 'Denver', 'Seattle'], since not all combinations of commodities, source cities, and destination cities represent valid paths through the network. Representing a sparse set of decision variables in a typical programming language can be cumbersome.

To compound the challenge, you typically need to build constraints that involve subsets of these decision variables. For example, in our network flow model you might want to put an upper bound on the total flow that enters a particular city. You could certainly collect the relevant decision variables by iterating over all possible cities and selecting only those variables that capture possible flow from that source city into the desired destination city. However, this is clearly wasteful if not all origin-destination pairs are valid. In a large network problem, the inefficiency of this approach could lead to major performance issues. Handling this efficiently can require complex data structures.

The Gurobi Python interface has been designed to make the issues we've just described quite easy to manage. We'll present a specific example of how this is done shortly. Before we do, though, we'll need to describe a few important Python constructs: lists, tuples, dictionaries, list comprehension, and generator expressions. These are standard Python concepts that are particularly important in our interface. We'll also introduce the tuplelist and tupledict classes, which are custom classes that we've added to the Gurobi Python interface.

A quick reminder: you can consult the online Python documentation for additional information on any of the Python data structures mentioned here.

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