Determining a better global solution

How can we address both objectives and find a global solution? A mathematical treatment of creating a QUBO that represents both objectives and includes the appropriate constraint with a set cover formulation is outside the scope of this book. Please check out the Further reading section for examples and more details regarding this area. However, we can use a simple method with the techniques we have developed to find an answer.

Here are the high-level steps we will go over:

1. Create a combined BQM matrix, Mf, with both the Ms and Mi matrices and find an appropriate way to "connect" the items to the suppliers using Ma. We are looking for a way where, if an item is picked in the solution, there is a large negative coupling value that will also cause the optimization to pick the appropriate supplier of that item (and vice versa). We will use a multiplier, A, that is large enough to ensure this condition is enforced:

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