Case-Mix Planning Case Study

The Case-Mix Planning Level

At this level, the objective is to generate an optimal case-mix plan of surgery patients with uncertain surgery operations, which includes uncertainty in surgery durations, LOS, surgery demand and the availability of nurses. In order to obtain an optimal case-mix plan, a stochastic optimization model is proposed and the SAA method is applied. The proposed model is used to determine the number of surgery cases to be weekly served in each specialty, the amount of operating rooms' time dedicated to each specialty and the number of ward beds dedicated to each specialty. The optimal case-mix selection criterion is based upon a weighted score taking into account both the waiting list and the historical demand of each patient

As previously mentioned, there are three resources, namely the ORs time, beds and nurses, considered in the model. The constraints are classified into four groups: ORs time capacity constraints (4)-(5), beds capacity constraints (6)-(7), nurses' capacity constraint (8) and demand bounds constraints (9)-(10). Constraint (4) indicates that the total required surgery time for each patient category cannot exceed the assigned hours to this patient category. Constraint (5) guarantees that the total hours dedicated to all patient categories cannot exceed the ORs' total available working hours per week. Constraint (6) denotes that the bed occupancy for each of patient categories cannot exceed its allocated capacity. The maximum total capacity that can be allocated to a patient category is z_p .D. However, this is an over-estimate, because it does not consider the intermediate cleaning and idle time between patients. Therefore, the maximum total capacity is multiplied by BU. The value of BU should be selected carefully in order not to overload beds. Constraint (7) ensures that the total number of beds dedicated to all patient categories cannot exceed the total available beds. Constraint (8) guarantees that the total required nurses' capacity in man-hours per week cannot exceed the available number of nurses in man-hours per week. The maximum

These conditions include the guarantee of: small problem size and the stochastic parameters should be following the normal or uniform distributions. If the problem size gets larger, the closed form model is intractable. Furthermore, it is well known that the distribution of surgery duration is close to a lognormal distribution [73]. While there are computational benefits, due to the limitations of the closed form expression, the SAA approach is employed as a solution method.

SAA [74] is a sampling based approach that can be applied to solve the SCMP (i.e. model (3)-(12)). Since the objective function (∑_(ξ∈Ξ)▒∑_(p∈P)▒〖Φ(ξ) .o_p .x_p^ξ 〗) cannot directly be optimized, the sample average is maximized instead of the original value. The expected value could be written as: E_(ξ∈Ξ) [∑_(p∈P)▒〖o_p .x_p^ξ 〗]. While directly computing the expected value is not possible for most problems, it can be approximated through Monte Carlo sampling in some situations. The expected value, with sample size N, can be approximated by the average of the realizations: E_(ξ∈Ξ) [∑_(p∈P)▒〖o_p .x_p^ξ 〗]≈1/N ∑_(n=1)^N▒∑_(p∈P)▒〖o_p .x_p^n 〗