An On-Call Shift for Anaesthetist Rostering Problem (ARP): A Mathematical Model

This work dealt with a real-world Anaesthetist Rostering Problem (ARP) for an on-call shift. An on-call shift for an anaesthetist had already been resolved under the physician's rostering problem. However, in their work, each individual can be assigned to only one place throughout the daily on-call shift. In addition, no consecutive days are rostered for the on-call shift, and each level of preference for the on-call shift is excluded from the study. This scenario is irrelevant to the real-world ARP of an on-call shift at Hospital Canselor Tuanku Muhriz (HCTM) in Malaysia, as an anaesthetist is rostered for multiple places of the on-call shifts daily. Also, they can be rostered on consecutive days for on-call shifts, and each anaesthetist will be rostered depending on their preference level for the on-call shift. Therefore, this work proposes a new mathematical formulation with constraints, parameters, and an evaluation function. We utilise Mixed-integer programming to formulate and solve the model with IBM ILOG CPLEX Optimization Studio. The quality of the solution generated by our model is measured using our proposed evaluation function to minimise the violation of constraints. A case study of real-world data from the HCTM was run and tested to validate the model. The result shows that a new model can produce a better optimal solution, whilst the current solution methodology at HCTM is unable to do.