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

In a production process where multiple inputs are applied to produce multiple outputs, some inputs are expected to be solely used in a subprocess to produce a specific output. Some inputs are shared among several subprocesses to produce several outputs. It is interesting to know the percentage of the shared input devoted to the production of each output. The conventional data envelopment analysis (DEA) method usually assigns one to the most productive output and zero to all other outputs, which is unreasonable. This study proposes a compromise solution approach to determine the proportion of a shared input allocated to each output. A case of fifty-one tourist hotels in Taiwan is investigated. There are two types of revenue in running a tourist hotel: accommodations and catering, where the room price, occupancy rate, accommodation employees, and management employees contribute to the generation of the accommodation revenue and food price, catering employees and management employees contribute to the generation of the catering revenue. The two functions share the management of employees. As expected, the conventional DEA method obtains either zero or one as the proportion to the two outputs from the viewpoint of each hotel. The compromise solution method proposed in this study obtains a compromise proportion of 0.45 for accommodation and 0.55 for catering. The proposed model can be generalized to cases of more than one shared input and more than two outputs.