Hotel chain performance: a gravity-DEA approach

Abstract

Performance in business management can be measured in terms of competitiveness and efficiency. Generally speaking, competitiveness is a comparative concept of the ability of a firm, sub-sector or country to sell and supply goods and/or services in a given market, as measured by its market share. Particularly in competitive markets, efficiency plays a key role in determining this ability but it is not, by itself, sufficient. Indeed, while competitiveness has more to do with “pursuing the correct strategy” towards the conservation and/or increase of the market share, operational efficiency is mainly a measure of how well the firm, sub-sector or country under study processes inputs to achieve its outputs, as compared to its maximum potential for doing so. Looking at a hotel chain performance, which is what motivates the present study, competitiveness can be expressed as the ability of the hotels belonging to the chain to attract potential customers: the more the hotel chain is competitive in the lodging market, the more customers it will attract. On the efficiency side, instead, the analysis has to be carried out comparing the efficiency scores of the hotels of the chain with the efficient production frontier. The literature dealing with the issue of valuing the efficiency in the hotel sector is rich of examples where Data Envelopment Analysis (DEA) is the preferred methodology (Anderson at al. (1999), Hwang and Chang (2003), Barros (2005), Barros and Mascarenhas (2005)). DEA is a linear programming based technique very useful for measuring the relative efficiency of relatively homogeneous units (authority departments, schools, hospitals, shops, banks, and so on) in the presence of multiple inputs and outputs related to different resources, activities and environmental factors. DEA Window analysis, in particular, works on the principle of moving averages (Charnes et al. (1994)) and allows the researcher to detect performance trends of a unit over time. In fact, DEA Window analysis converts a panel data into an overlapping sequence of windows that are then treated as separate cross-sections. The rationale is that each DMU (Decision Making Unit) in a window is regarded as an entirely different one in the other windows enabling comparison of a DMU efficiency in a particular period with its behaviour in the others. Moreover, by using the DEA Window analysis scores, the Malmquist productivity index (Caves et al. (1982), Fare and Grosskopf (1992), Fare et al. (1994)) can be computed to evaluate changes both in the technical efficiency, called catching-up, and in the frontier of the production possibility, called frontier-shift. Gravitational models have also been largely used in tourism economics to study the level of attractiveness of destinations with respect to economic and service-related factors, the latter focusing mainly on the quality and price of tourism services (Gat (1998)). In this study, we use a gravity model to reproduce the tourism flows towards each unit of a hotel chain and DEA Window analysis to value the efficiency of the chain over a time horizon of 9 years. The gravity model and the DEA Window analysis have three managerially controllable variables in common: the rooms price (single and double room price) and the hedonistic basket (which summarizes quality features of the hotels). Every decision to increase the economic efficiency of the hotel chain by setting the value of the above mentioned variables according to the DEA results will influence the attractiveness of the hotels (as resulting from the gravity analysis) and, as a consequence, the competitiveness of the chain in the lodging industry in the future. A Malmquist productivity index is also computed to decompose the productivity change into the efficiency and the technological change. In this framework, therefore, we can study how, and up to which extent, the opera