The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article the authors demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1). They postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. The authors have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, they prove that the earlier postulate was accurate. Additionally, the authors discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate.