The first thing to think about is how you might identify a likely swapper without a computer, and what characteristics might identify that swapper, e.g. what role they have, how many times they swapped in the last year, 6 months, 6 weeks etc, how many times they've taken each shift, how long they've been around, do they have a family, etc. In this initial step you don't need to figure out HOW those characteristics identify the swapper, just that they might help to identify them.
Once those "features" have been identified, you are ready to build a model of how you might identify a likely swapper. You would take a few examples of instances where two individuals swapped shifts, and map out the characteristics of each individual. This will identify a number of instances of your positive class. Flesh our your dataset with all other combinations of individuals and shifts which are, of course, instances where no switch occurred. These are your negative class.
Before doing any modeling, check to see if any of your features are highly correlated with your target variable. If there are a couple of features that are highly correlated, you may not even need to use machine learning. Remember, machine learning is just using an algorithm to learn a pattern. If you can learn the pattern without an algorithm, you're done.
If you're still looking at several features that may be involved in a complex model to identify who might swap shifts, then you can start trying various model algorithms. To start with you could try logistic regression, random forest, naïve bayes, and SVM. Split your data and try and overfit on your training set. If you manage to overfit, you've got a chance. Start scaling back the features and try and find something that generalizes.