Bechtold–Jacobs generalized model for shift scheduling with extraordinary overlap

In constructing working shifts, the classical Dantzig set covering model uses a great number of variables which makes computation very complicated for some cases that incorporate a high degree of break-placement flexibility. Bechtold and Jacobs proposed an implicit model under the assumption that there is no extraordinary overlap, which considerably reduced the number of variables. In this paper we give a generalization that is valid without this hypothesis by adding a minimal set of constraints. Also, in some cases where there is extraordinary overlap we reduce our constraint set to a subset with the same number or less than that of Bechtold and Jacobs.