Keywords:Health care Case mix and capacity planning Master surgery schedule Multilevel Resource efficiency Service level a b s t r a c t Hospital case mix and capacity planning involves the decision making both on patient volumes that can be taken care of at a hospital and on resource requirements and capacity management. In this research, to advance both the hospital resource efficiency and the health care service level, a multilevel integrative approach to the planning problem is proposed on the basis of mathematical programming modeling and simulation analysis. It consists of three stages, namely the case mix planning phase, the master surgery scheduling phase and the operational performance evaluation phase. At the case mix planning phase, a hospital is assumed to choose the optimal patient mix and volume that can bring the maximum overall financial contribution under the given resource capacity. Then, in order to improve the patient service level potentially, the total expected bed shortage due to the variable length of stay of patients is minimized through reallocating the bed capacity and building balanced master surgery schedules at the master surgery scheduling phase. After that, the performance evaluation is carried out at the operational stage through simulation analysis, and a few effective operational policies are suggested and analyzed to enhance the tradeoffs between resource efficiency and service level. The three stages are interacting and are combined in an iterative way to make sound decisions both on the patient case mix and on the resource allocation.

This paper describes a methodology for the case mix problem in the health care sector. Aiming at maximizing the overall financial contribution of the given resource capacity within a hospital, the case mix problem is formulated as an integer linear programming model to produce the optimal patient mix pattern together with its associated resource allocation scheme. In order to solve the huge integer program optimally, an efficient solution approach, branch-and-price, is proposed, developed and implemented in this research. When studied from the column generation perspective, the integer linear programming model can be formulated differently. According to different decomposition units, namely wards, surgeon groups and patient groups, three decomposition based reformulations are built respectively. Among them, the first two reformulations are suitable to be solved within the framework of branch-and-price, while this is not the case for the last one. Numerical experiments are carried out, and the computational results are presented and compared, which demonstrate that the branch-and-price approach outperforms the integer linear programming method significantly and that decomposition on wards performs much better than decomposition on surgeon groups both with respect to the solution quality and the computation speed.

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