Solving surgical cases assignment problem by a branch-and-price approach

In this paper, we study a surgical cases assignment problem (SCAP) of assigning a set of surgical cases to several multifunctional operating rooms with an objective of minimizing total operating cost. Firstly, we formulate this problem as an integer problem and then reformulate the integer program by using Dantzig-Wolf decomposition as a set partitioning problem. Based on this set partitioning formulation, a so-called branch-and-price exact solution algorithm, combining Branch-and-Bound procedure with column generation (CG) method, is designed for the proposed problem where each node is the linear relaxation problem of a set partitioning problem. This linear relaxation problem is solved by a CG approach in which each column represents a plan for one operating room and is generated by solving a sub-problem (SP) of single operating room planning problem. The computational results indicate that the decomposition approach is promising and capable of solving large problems.