Implicit shift scheduling with multiple breaks and work stretch duration restrictions

This paper considers a shift scheduling problem that includes different forms of flexibility in terms of shift starting times, break lengths and break placement. Two particular forms are studied: fractionable breaks and work stretch duration restrictions. Unlike standard breaks, fractionable breaks are not required to be attributed as a whole. They can be divided into fractions of breaks under some conditions. The distribution of breaks within a shift is done with respect to work stretch duration restrictions to ensure a correct mix of periods of work and rest. Two implicit models are proposed. They extend previous work on implicit modeling of break placement to incorporate the concepts of fractionable breaks and work stretch duration restrictions. In this context, we show the merits of using the so-called forward and backward constraints to model work stretch duration restrictions. We also introduce a new formulation of the forward and backward constraints and demonstrate that it considerably reduces the density of the constraint matrix of the two proposed models. Finally, we study the impact of fractionable breaks and work stretch duration restrictions and show that, for some instances, the use of these concepts considerably reduces the workforce size when compared to other traditional approaches.