A compromise solution approach for efficiency measurement with shared input: The case of tourist hotels in Taiwan

Shared input occurs often when a production system performs two or more functions and some of the functions share the same input. To determine the proportion of the shared input devoted to each function, the conventional data envelopment analysis (DEA) models that allow each decision making unit (DMU) to select the most favorable value to attain the highest efficiency score is usually used. The result is that many DMUs assign proportions of different bound values to the same function, which is not reasonable. This paper proposes a compromise solution approach that aggregates the viewpoints of all DMUs to obtain a consensus regarding the proportion of the shared input used by each function. The approach is actually a parametric DEA approach for constructing the production function. To increase the explanation power, transcendental functions are considered. The tourist hotel, where the accommodation and catering functions share the input of management employees is used for illustration. The results show that a transcendental function has stronger explanation power, and reasonable compromised values for the proportions of the effort of the management employees devoted to the two functions are obtained.