Solving the strategic case mix problem optimally by using branch-and-price algorithms

This paper describes a methodology for the case mix problem at the strategic level in the health care sector. Aiming to maximize hospital profits under the given resource capacity, a mathematical model is developed to produce an optimal case mix pattern and a corresponding resource allocation scheme. Two exact methods, integer linear programming and branch-and-price, are deployed to solve the constructed model. For the branch-and-price approach, new formulations based on various decomposition units, namely wards and surgeon groups, are proposed and can be solved efficiently with branch-and-price algorithms. Numerical results are compared and illustrate that the branch-and-price algorithm outperforms the integer program approach and that a large decomposition unit improves the solution both on solution quality and on computational speed.