Multiobjective Optimization for Healthcare Revenue and Costs

(1) Objective Related to a Health-Care Institution's Revenue. Health-care institutions are nonprofit organizations; however, they must generate sufficient revenue to operate sustainably. Some health-care institutions have also started commercializing their services. They must earn revenue that at least equals the operating cost and the capitalized cost related to the new investments. In addition, under the influences of an unlimited insurance policy and private patient fees, achieving maximum revenue has become a major objective of most health-care institutions. This objective can be considered the first objective in this study and can be expressed as follows: $\begin{array}{c}{f}_1=E_1+E_2+E_3+E_4\text{,}\\ E_1=G_1\left(1+x_1\right)+G_2\left(1+x_1\right)+G_3\left(1+x_1\right)\text{,}\\ E_2=G_1\left(1+x_2\right)+G_2\left(1+x_2\right)+G_3\left(1+x_2\right)\text{,}\\ E_3=G_1\left(1+x_3\right)+G_2\left(1+x_3\right)+G_3\left(1+x_3\right)\text{,}\\ E_4=G_1\left(1+x_4\right)+G_2\left(1+x_4\right)+G_3\left(1+x_4\right)\text{.}\end{array}$
(2) Objective Related to the Insurance System. Unlimited growth in the global insurance budget is impossible, and this budget influences the economy and civil atmosphere of a nation. Rapid aging in a society engenders increased health-care demand, and a gap between health-care demand and supply is a developmental bottleneck for health-care institutions. Therefore, reducing insurance fees is a major objective of the National Health Insurance Administration (NHIA) of Taiwan, which can be considered the second objective in this study. This objective can be expressed as follows: $\begin{array}{c}{f}_2=C_1+C_2+C_3+C_4-C_5\text{,}\\ C_1=G_1\left(1+x_1\right)a_{11}+G_2\left(1+x_2\right)a_{12}+G_3\left(1+x_3\right)a_{13}\text{,}\\ C_2=G_1\left(1+x_1\right)a_{21}+G_2\left(1+x_2\right)a_{22}+G_3\left(1+x_3\right)a_{23}\text{,}\\ C_3=G_1\left(1+x_1\right)a_{31}+G_2\left(1+x_2\right)a_{32}+G_3\left(1+x_3\right)a_{33}\text{,}\\ C_4=G_1\left(1+x_1\right)a_{41}+G_2\left(1+x_2\right)a_{42}+G_3\left(1+x_3\right)a_{43}\text{,}\\ C_5=x_4{\alpha }_1\text{,}\end{array}$ where C₁, C₂, C₃, and C₄ represent the global budgets of western medicine consumption, western primary medicine consumption, Chinese medicine consumption, and dental medicine consumption, respectively, at the three hospital levels (medical centers, metropolitan hospitals, and district hospital). Moreover, C₅ denotes the insurance amount saved through any budget control policy.
(3) Objective Related to the HR Cost. The expansion of a hospital is limited by the total population in its region and the global budget of insurance fee point calculation systems, which can result in a crowding-out effect. Thus, hospital expenses should be decreased to raise hospital profits; the HR cost accounts for the highest proportion of the total expenses of a health-care institution. However, according to the causal loop diagram, expense reductions might increase the risks associated with patient care. Therefore, the HR cost must be minimized such that patient safety is not compromised. This can be considered the third objective in this study and can be expressed as follows: $\begin{array}{c}{f}_3=s_1{c}_1+s_2{c}_2+s_3{c}_3-x_5{\alpha }_2\text{.}\end{array}$
The final item in equation (3) is the NHI claim reduction resulting from the health-care institution's internal adjustment policy.