Operating Rooms Planning Using Lagrangian Relaxation Technique

This paper addresses the elective surgery planning problem when the operating rooms\´ capacity is shared between elective and emergency patients. The planning problem consists in determining the set of elective patients that would be operated in each period over a planning horizon in order to minimize patients related costs and overtime costs of operating rooms. A stochastic integer programming model is proposed. Lagrangian relaxation is used to decompose the planning problem into period-level sub-problems that are solved by a dynamic programming method. The dual problem is solved iteratively using a sub-gradient algorithm. Feasible plans are derived from relaxed solutions using a heuristic and improved with a "local search heuristic". This approach results in both near-optimal solution and a lower bound to assess the degree of optimality. Numerical experimentations show that solutions within 1% of the optimum are obtained in a short computation time for problems of practical sizes