Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming

In this paper, we present a mathematical model for cyclic and non-cyclic scheduling of 12 h shift nurses. The model exploits the fact that a nurse's schedule is made up of an alternating sequence of work-stretch and ‘off-stretch’ patterns. We introduce a concept called a stint, which is a pattern characterized by a start date, a length, a ‘cost’ and the shifts worked. Using the stints as nodes in a network, we construct an acyclic graph on which the nurse's schedules can be defined. The resulting model is essentially a shortest-path problem with side constraints. The model is quite flexible and can accommodate a variety of constraints. With a minor modification, the network is used to define both the cyclic and non-cyclic scheduling problems. The models are illustrated on sample data from a local hospital and solved using CPLEX optimization software on an IBM RISC6000/340 workstation.