This study aims to construct a mathematical model to determine the dimensions of an economic, social, and environmental project with the goal of sustainable management. By identifying the optimal weights, the synergy values for sustainable management can be maximized. Taking aesthetic medicine companies as examples, this study attempts to construct the index projects of the economic, social, and environmental dimensions of sustainable management in an uncertain environment. Linear relationships (a combination of fixed synergistic values and varying synergistic values) are used to calculate the import optimal weight under optimistic, normal, and pessimistic circumstances. This study helped companies to introduce triple bottom line (TBL) indices to plan their issues under sustainable management and development, thus, enabling the parent company to achieve the optimal weight for the project costs to put in its subsidiaries. Additionally, this study prioritizes the weight of the influence on the management of the aesthetic medicine industry according to the risk probabilities, to minimize the uncertainties of risk management in corporate management and reduce the possibility of direct and indirect cost losses caused by financial distress, functional fluctuations, and negative impact on the medical equipment market, thereby maximizing the estimated total project value under sustainable management. This study constructs an aesthetic medicine-specific mathematical model concept using the triple bottom line model as the basis for sustainable corporate management and proposes an approach to obtain sustainable weight in uncertain conditions. By doing so, companies can add various managerial methods for the same industry, and new ideas are provided to the academic community to discuss the development of decision-making assessment criteria for risk assessments in sustainable management.

Medical disputes that result in medical compensation and losses affect the financial management and sustainable operational risks of enterprises. Employee training plays an important role in the sustainable growth of human resource management and also can help avoid any potential risks to enterprises’ operating revenue. Based on data of a company, this study’s model aims to establish a mathematical model to find the most suitable decision variables in order to provide decision-making analysis and judgment of a company’s individual economic behaviors. From the second-order differential modeling method, where the functional training time of the aesthetic medicine industry (including medical errors/dispute incidences, functional training costs, and medical benefits) links to a specific functional relationship, the optimal decision-making model and evaluation criteria for the proportion of this training time under the concept of sustainable management can be constructed. The method proposed herein reduces medical errors or disputes, strengthens risk and financial management, provides customers with the best service quality, and serves as the basis for decision-making evaluation of the maximum benefits of sustainable operations.

Considering advertising efficiency capital investment and overall revenue efficiency, this study explores how to construct the most appropriate advertising distribution of medical cosmetology, which is viewed as the overall research focus. (1) This study explores how the aesthetic medicine industry determines its optimal resource allocation ratio of advertising investment that can create maximum output value under the condition that the advertising budget for subsidiaries is limited and that advertising efficiency is uncertain. (2) The model of this study is based on the concept of dynamic programming, which is used to solve problems in multistage decision-making. Under limited advertising investment by subsidiaries in new media and traditional media advertisements, we aim to increase the number of visitors and high-consumption customers. (3) The contribution of this research is to construct a practical model for the optimal allocation of advertising investment in the aesthetic medicine industry. The research results, including a mathematical model and practical application, can be used as a reference for the aesthetics medicine industry or general companies to determine the best allocation of advertisement cost inputs.