Operating theatre scheduling using Lagrangian relaxation

This paper addresses the surgery operation scheduling problem. Three types of resources are considered: transporters, operating rooms and recovery beds. The patient is first transported from the ward to the operating theatre, is operated on in an operating room and then transferred immediately to a recovery bed before being transported back to the ward. The operating room needs to be cleaned after the surgery before starting another operation. The problem consists in assigning patients to transporters, operating rooms and recovery beds in order to minimise a criterion function of their completion times. The problem is NP-hard. A Lagrangian relaxation approach is proposed to determine a near-optimal schedule and a tight lower bound. Numerical results will be presented to show the efficiency of the method. [Received 31 January 2007; Revised 01 August 2007; Accepted 14 October 2007]