台灣國際觀光旅館績效評估－應用方向性距離函數與meta-frontier

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(2) . Institute of Business and Management National University of Kaohsiung, Taiwan.

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(11) . Evaluating Performance of Taiwan’s International Tourist Hotel:. Application of Directional Distance. Function and Meta-Frontier Approach Advisor: Dr. Yang Li Institute of Business and Management National University of Kaohsiung Student: Mei-Yi Jiang Institute of Business and Management National University of Kaohsiung. Abstract As the issue of environmental protection is taken seriously by the world recently, the tourism industry so-called non-chimney industry has been highly respected.. The. production process of tourism industry brings less environment pollution than manufacturing industries. industry.. The government of Taiwan actively promotes the tourism. The international tourist hotel is one of key factors to boost the tourism. industry successfully.. An appropriate way to evaluate the performance of. international tourist hotels can offer a good indicator of the level of the development of tourism in a country. The previous studies used data envelopment analysis (DEA) to measure performance of hotel industry (Tsaur, 2001; Hwang and Chang, 2003; Yand and Lu, 2006).. However, these studies have two disadvantages.. First, they assume that the. different types of hotels share the same production frontier.. We use the. meta-frontier approach to accommodate to sample hotels associated with different production frontiers. . They also neglected the quasi-fixed inputs that can not be .

(12) . adjusted in the short run.. Therefore, this study employ the directional distance. function in the non-convex meta-frontier model by expanding outputs , contracting inputs, and fixed quasi-fixed inputs simultaneously in the short run.. Additionally,. we adopt the directional distance function in the convex meta-frontier model and assume that the quasi-fixed inputs can be adjusted in the long run. The empirical results include: (1) the frontiers of foreign-owned hotels and domestic hotels are significant different; (2) the efficiency and technology gap (TG) of foreign-owned hotels are better than domestic hotels.. Keywords:. International tourist hotel, data envelopment analysis, directional distance function, meta-frontier, quasi-fixed inputs. . .

(13) . TABLE OF CONTENTS. Chapter 1 Introduction ............................................................................................ 1 1.1 Research Background and Motivations ......................................................... 1 1.2 Research purpose.......................................................................................... 5 Chapter 2 Literature review .................................................................................... 5 2.1 Application of DEA approach....................................................................... 6 2.2 Application of SFA approach ....................................................................... 8 2.3 Meta-frontier .............................................................................................. 10 Chapter 3 Methodology ......................................................................................... 12 3.1 Distance function........................................................................................ 12 3.2 Data envelopment analysis ......................................................................... 13 3.3 Directional distance function ...................................................................... 15 3.4 Meta-frontier .............................................................................................. 15 Chapter 4 Empirical results .................................................................................. 22 4.1 Data and Variables ..................................................................................... 22 4.2 Results ....................................................................................................... 24 4.2.1 Short run ................................................................................................. 24 4.2.2 Long run.................................................................................................. 28 Chapter 5 Discussion ............................................................................................. 30 Chapter 6 Conclusions ........................................................................................... 34 References .............................................................................................................. 36. . .

(14) . LIST OF TABLES. Table 1.1 Per visitor per day consumption in Taiwan………………………………..2 Table 1.2 Travel & Tourism Demand and Economy GDP growth……………….....3 Table 4.1 Literature on the Hotel industry………………………………………….26 Table 4.2 Mann Whitney test……………………………………………………….28 Table 4.3 Descriptive statistics for efficiency indicator of groups………………….29 Table 4.4 Mann Whitney test for the efficiency indicators of groups………………29 Table 4.5 Descriptive statistics for efficiency indicator of groups in the long run…30 Table 4.6 Mann Whitney test for the efficiency indicators of groups………………30 Table 5.1 Frequencies of peer references which λ value are more than 0.5………..31 Table 5.2 Frequencies of peer references for β = 0, β m ≠ 0 ………………………32 Table 5.3 Slack analysis…………………………………………………………….33 Table 5.4 Scale of international tourist hotels in Taiwan…………………………..33. . .

(15) . LIST OF FIGURES Figure 3.1 Output distance function………………………………………………….14 Figure 3.2 Illustration of the meta-frontier………………………………………….. 19 Figure 3.3 Illustration of meta-efficiency and technology gap………………………22 Figure 4.1 The testing process for different frontiers………………………………...27. . .

(16) . Chapter 1 Introduction. 1.1 Research Background and Motivations According to the report of World Travel and Tourism (WTTC), the tourism industry has high potential for growth especially in Asia area.. Table 1.1 shows that. the growth of economic activity (total demand) in tourism industry during 2007-2017. It reveals that the benefit of tourism is expected to grow largely in Asia. In Taiwan, it’s estimated that will amount to $2.35 trillion, create $0.24 trillion output value and 57.42 ten thousand job opportunities by 2017. Table 1.2. Travel & Tourism Total Demand during 2007-2017 Travel & Tourism Total Demand (10-year, Real Growth, %). World. 4.4. South Asia. 7.3. Southeast Asia. 6.3. Northeast Asia. 5.8. North Africa. 5.0. Middle East. 4.7. Latin America. 4.5. North America. 4.0. Caribbean. 3.4. Europe. 3.3. Moreover, the government promotes tourism through the direct Cross-Strait flights between Taiwan and Mainland China and allows mainland tourists to visit Taiwan last year. According to Taiwan Tourism Bureau, 91,274 mainland tourists visited Taiwan between July 2008 and February this year.. During that period, daily. arrivals of mainland tourists increased from 274 to 1,000.. They also expect to reach. . .

(17) . the 3,000 person-per-day cap in the future.. As cross-strait interactions become more. frequent, we expect that the demand of mainland tourists visiting Taiwan will increase and bring spectacular benefits. Other policies on tourism industry in Taiwan in 2008 are: to implement the "2015 vision for economic development plan ", the authorities promote "Taiwan travel in 2008-2009" and the “Tourism development and the overall development of the construction of medium-range plan (2008-11)”, which contains (1) the international tourist attraction building; (2) an important domestic scenic spot construction improvement; (3) the National Scenic Area management; (4) industry incentives to set a distinct language (Japanese, Korean) services.. In addition, the. network of tourism services and the inter-connection transfer mechanism will be strength. Encourage business to improve the accommodation, train the employees in service quality and enrich their expertise to attract more foreign tourists. The tourism industry combines a lot of emerging industries, including food and beverage, hotel, airline, transportation, travel and so on.. Therefore, tourism industry boosting is. useful to promote the whole industry connection, increasing consumption and leads to boom the economy.. It’s especially beneficial for creating employment opportunities. and earning foreign exchange.. In conclusion, the tourism boost on the economy of a. country could be expected. In the industry chain of tourism, the role of international tourist hotel is very important because the hotel business can offer various and necessary services to visitors, such as accommodation, catering, entertainment, information and shopping. Table 1.2 shows the average expenditure per visitor a day in Taiwan, a large proportion of the expense of visitor on the hotel (Taiwan Tourism Bureau, TTB). Therefore, the performance of hotel industry can be an indicator of tourism industry development. In view of this, we focus on the operating efficiency of hotels in our . .

(18) . research. Table 1.2. Per visitor per day consumption in Taiwan average expenditure in Taiwan per visitor a day ( dollar). Expenditure on hotel. 2003. 166.08. 42.56%. 2004. 180.52. 47.48%. 2005. 207.50. 44.67%. 2006. 210.87. 44.74%. 2007. 215.21. 43.96%. Due to the important role that International Tourist Hotel plays in the tourism industry. The Government also integrates the Hotel industry into the scope of "important investments" and "important industries".. For this reason, improving the. operating performance of hotels is essential to flourish the tourism industry. There are many literatures which discuss the issue about the assessment of Taiwan International Tourist Hotel performance.. They measure not only Taiwan. International Tourist Hotel overall operational efficiency; some discuss the effect of management style (chain-operated or independent-operated) by two-step method. Wang and Schmidt (2002) verify that the two-step procedure is biased.. Therefore,. this article introduces the Meta-frontier approach to examine the efficiency of Taiwan’s international tourist hotels during 2005 to 2007.. According to different. management style, the observations can be divided into two groups (domestic and international chain hotels). Most of pervious studies discuss the efficiency of these different groups by DEA or SFA approach which using a single frontier to compare the efficiency among different groups.. In other words, these studies imply that the different groups have. the same technology. . However, the hotels in different groups have different .

(19) . available stocks of physical, human and financial capital, resource and characteristics of the physical, social and economic environment, so that they have different technology set (O’Donnell et al., 2008).. Hence, we introduce the Meta-frontier. approach to examine the efficiency of these hotels in different groups. In addition, these past studies employ the input-oriented model to analyze hotels’ operating, but this model is not suitable for hotel industry.. They neglect the. quasi-fixed inputs that may overstate firms’ capability of adjustment, misleading results, and weaken the DEA approach as a decision tool for managers.. Quasi-fixed. inputs prevail in really all sectors of the economy and their optimal value cannot be adjusted even in the long time (Ouellette and Vierstraete, 2004).. In general,. international hotels have various facilities and luxurious decorations, those structures are not easy to reduce and change. Thus, the producers’ behavior should be maximum output instead of minimum input. In view of the problem, we employ the directional distance function and incorporate quasi-fixed inputs in the model.. . .

(20) . 1.2 Research purpose Base on the research background and motivation, we have the twofold research purposes of the study.. First, we use the directional distance function to assess the. operating efficiency of hotels in Taiwan. By this approach, we can consider the output expanding, input reducing and quasi-fixed inputs at the same time.. Second, the. efficiency estimated in hotel industry, the DEA approach and SFA approach are general and largely used in past research, but have no one consider the concept of Meta-frontier.. Hence, we apply the Meta-frontier to compare the efficiency of. different groups, such as domestic hotels and international chain-operated. This paper is organized as follows: the literature review.. Following this introduction, Chapter 2 is. Chapter 3 describes the methodology.. data sources and empirical results. Chapter 5 is discussion. paper.. . . Chapter 4 consists of. Chapter 6 concludes this.

(21) . Chapter 2. Literature review. In this section, we summarize the past researches that assess the efficiency of hotel industry.. These can be divided into three categories: data envelopment analysis. (DEA) studies of the hotel industry, stochastic frontier approach (SFA) studies in hotel industry and incorporating environmental effects into efficiency assessment. However, efficiency is measured the distance of an observation from the efficient boundary.. The boundary or frontier can be constructed by the non-parametric. approach (data envelopment analysis) and the parametric approach (stochastic frontier approach).. In previous studies, these are largely used in the hotel industry.. In the. third subsection is the application of meta-frontier.. 2.1 Application of DEA approach DEA is a linear programming-based technique and a non-parametric model, so it’ not necessary to give the functional form or probability distribution previous analyze. questions.. Moreover, DEA can deal with the multiple input and multiple output It also can be used to compare the relatively efficiency of units by a. common boundary which envelops all observations. Tsaur (2001) uses the DEA to measuring the operating efficiency of 53 international tourist hotels in Taiwan during 1996-1998.. The result reveals a mean. efficiency score of 87.33%, which indicates that managers on average could reduce the input by 12.67% without decreasing the output.. Hwang and Chang (2003). employ DEA to evaluate the managerial performance of 45 hotels of Taiwan in 1998. In addition, they use the Malmquist productivity index to measuring the efficiency change of those hotels over time. . The result shows that the cost on average should .

(22) . be reduced 21% and hotel with different operating environment has different efficiency.. The chain-hotel managerial and leisure hotels are better managed than. independent managerial and urban hotels.. The size of hotels has no significance. relative to operating efficiency. Chiang (2004) utilizes DEA-BCC model to evaluate the overall efficiency, pure technical efficiency and scale efficiency of 25 Taipei Taiwan hotels’ performance in 2000.. The major finding indicates the international chain managerial hotels, not all. perform more efficiently than the independent ones. Yang and Lu (2006) investigate the managerial performance of 56 international tourist hotels in Taiwan by DEA-BCC model.. In this study, they find that the. inefficiency of 56 hotels primarily comes from pure technical inefficiency.. On the. other hand, they examine the operating environment how to influence the performance of hotels.. Those environment variables are including management style,. location, and closeness to Touyan International Airport.. The result is that the. operating characteristics are significance related to managerial efficiency on the statistical. Wang et al. (2006) uses the five different measures, including overall efficiency, allocative efficiency, technical efficiency, scale efficiency and pure technical efficiency to evaluate the operating performance of 49 Taiwan’s hotel sector. Moreover, this study utilizes the Tobit regression model to examine the effect of business or environment characteristics on hotel’s performance.. The finding reveals. that the foreign individual travelers, online transaction function and franchising are related to a better efficiency of Taiwan’s international tourist hotels. But the years of hotel has not significantly related to the efficiency measures. Wang et al. (2006) apply the four-stage DEA to purge away the effect of external operating environments and calculate the pure managerial efficiency of 54 Taiwan’s . .

(23) . international tourist hotels.. The external operating environment variables were. selected: market condition, management style and hotel size.. There are four hotel. size classifies: smallest, next to smallest, next to largest, and largest.. They observe. that the chain-operated and resort hotels are favorable operating environment. Shang et al. (2008) employ the three-stage DEA and find the average efficiency score and the number of efficient hotels increase in the final-stage, implies that the penalty to hotels operating under unfavorable circumstances is greater than the benefit to hotels operating under favorable circumstances.. Besides, they examine the. relationship between ecommerce adoption and managers’ performance after purged the effects of exogenous factors, and reveals that the performance is not affected by increased Internet usage.. One of reasons for the result may be related to the unique. characteristics of hotel industry.. For instance, the “human touch” of service is not. easily substituted by ecommerce.. In other words, from this result we can find that. the staff reduced in hotels is restricted.. 2.2 Application of SFA approach SFA is another way widely used for efficient frontier analysis that is a regression-based model.. One of the advantages of SFA is that it provides statistical. texts of the effect of independent variables on the dependent variable.. Therefore, we. can confirm what kind of external environments will impact the performance of hotels’ operating. Anderson et al. (1999) apply the stochastic frontier model to measure the efficiency of 48 hotels in the United States.. The input and output variables. separately are the number of full-time equivalent employees, the number of rooms, total gaming related expenses, total food and beverage expenses, other expenses, and . .

(24) . total revenue.. The input prices separately are the average wage, the average price of. rooms, the average price of food and beverage operations, the average price of casino operations, the average price of hotel operations, and the average price of other expenses. They found the high efficiency scores in hotel industry.. However, this. work does not describe the resource of the inefficiency. Barros (2004) analyzes the technical efficiency of Portuguese state-owned hotel chain by the stochastic frontier function in order to investigate the chain’s performance.. The Cobb–Douglas cost functional form is comprised with three input. prices (price of labor, price of capital, and price of food) and two outputs (sales and nights occupied).. Chen (2007) also applies the stochastic cost frontier function to. analyze 55 international tourist hotels’ cost efficiency in 2002.. The average. efficiency is 80.3%, implied that the almost 20% costs could be reduced without decreasing output. In addition, this paper uses the one-way ANOVA to examine the relationship between the factors of management type and hotels’ performance. However, this method in Chen’s study has a disadvantage.. Because of the first stage. assumed that the parameter comes from the same distribution, but this assumption is violated in the second stage.. The two-step procedure will give biased results (Wang. and Schmidt, 2002). Although the stochastic frontier approach overcomes some of the statistical limitations of DEA, but the multi-product cost functions must have the information of input price.. In particular, the information of input price is difficult to collect.. These past studies employ the input-oriented model to analyze hotels’ operations, but this model is not suitable for the hotel industry.. These studies neglect the. quasi-fixed inputs, so that they may overstate firms’ capacity to adjust, misleading results, and weaken the DEA approach as a decision tool for managers (Ouellette and Vierstraete, 2004). . The characteristics of the hotel industry are such that the

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(26) . construction of international tourist hotels requires huge capital, various facilities and luxurious décor; these structures are not easy to change.. Hence, the inputs, such as. the number of rooms and the floor space of hotels are not easy to reduce or expand in the short term.. In view of the problem, we employ the directional distance function. and incorporate quasi-fixed inputs in the model to measure the efficiency by expanding outputs, contracting inputs, and fixed quasi-fixed inputs simultaneously. In addition, most of those works estimate a frontier for all hotels from different management types, which implicitly assumes that hotels share a common production technology.. However, because of different operational philosophy, managerial. mode, human resource, financial capital and characteristics of the physical the different groups should have their own production technology.. The meta-frontier. approach allows for efficiency comparisons across groups which have different production frontiers.. However, this problem can be solved by meta-frontier. approach.. 2.3 Meta-frontier Battese and Rao (2002) combine the stochastic frontier approach with meta-frontier function to investigate the technical efficiencies of firms in different groups that may not have the same technology.. There are there are two different. data generation mechanisms in this study: one explains deviations between output of observations and group frontiers, and the other explains deviations between output of observations and meta-frontiers.. This method has a problem that the meta-frontier. may lie below on the group frontiers.. Therefore, Battese et al. (2004) modify the. model by using a single data generation processes and defining the meta-frontier that envelops the group frontiers. . .

(27) . O’Donnell et al. (2008) present the basic analytical framework for the meta-frontier, shows how a meta-frontier can be estimated using non-parametric (DEA) and parametric methods (SFA).. They think that firms in different in regions. face different production opportunities, so that they have different technology sets. For example, firms product in different available stocks of physical, human and financial capital, resource and characteristics of the physical, social and economic environment in reality.. In view of the opinion, the meta-frontier is as the boundary. of an unrestricted technology set and group frontier is as the boundary of a restricted technology set. Portela and Thanassoulis (2008) propose a new Malmquist-type index that is defined in relation to a meta-frontier and can be decomposed into efficiency change and boundary shift.. The frontier is assumed to be convex, which implies true. technology cannot be uninvented.. The true technology is in reality feasible input. output combinations, but which may not have been fully revealed. . .

(28) . Chapter 3. Methodology. In this section, we introduce our research approaches which involve two major concepts: one is directional distance function and the other is meta-frontier. In addition, we incorporate quasi-fixed inputs into the model.. 3.1 Distance function Distance function is a useful way to measure efficiency and productivity.. The. distance between observation and frontier represent that how much the input can be reduced or how much the output can be expanded. The output distance function is defined on the output set, P(x), as:. {. }. Do ( x , y ) = inf δ : ( y / δ ) ∈ P( x ) . To illustrate the concept of an output distance function where two outputs (y1 and y2) are produced using a given input vector ( x ) in the production possibility frontier, PPC-P(x). In the Figure 3.1, the ratio δ =0A/0B means that the production. of all output quantities could be increased while still remaining within the feasible production possibility set for the given input level.. By the output oriented case, we. focus on the output expanded and not to discuss especially for the quasi-fixed inputs. The input distance function, which includes quasi-fixed inputs, is defined on the input set, P(y), as:. Di ( x, k , y ) = sup {ρ : ( x / ρ , k ) ∈ P( y )} This equation means that the quantities of adjustable inputs could be reduced under unchanged output level and quasi-fixed input quantities.. . .

(29) . Y2. B. A PPC Y1. 0. Figure 3.1. Output distance function. 3.2 Data envelopment analysis In the Data envelopment analysis approach, the technical efficiency score could be measured by CCR and BCC model. under constant returns to scale.. CCR model is assumed that firms operate. Actually, not all of firms operate under optimal scale.. Therefore, we consider the BCC model that assumed variable returns to scale.. It is. indicate that the inefficiency can be decomposed into pure technical inefficiency and scale inefficiency. Two aspects of DEA model are an orientation of input and an orientation of output.. Based on the input-orientated case, the objective is seeking the minimum. input usage by giving the output level.. Based on the output-orientated case, the. objective is seeking the maximum possible proportional increase in outputs by holding the input constant.. The output -orientated DEA-BCC model can be written. as following linear programming problem: . .

(30) . ( D 0 ( x , y )) − 1 = m ax β H s .t . ∑ λ h y m h ≥ β ⋅ y m j , m = 1, ..., M h =1. ∑λ. h. ∑λ. h. H. x nh ≤ x nj , n = 1, ..., N. h =1 H. h =1. =1. λ1 , ..., λ h ≥ 0 h = 1, ..., H. Where ymh is the amount of output m from the unit h ,. xnh is the amount of. input n to the unit h , M is the number of outputs, N is the number of inputs, H is the number of units, β is greater than 1, θ is technical efficiency(TE) value equals to 1/ β between 0 and 1. The input-orientated DEA-BCC model, which includes quasi-fixed inputs, can be written as follows: ( D i ( x , k , y ) ) − 1 = M in θ H s .t . ∑ λ h y m h ≥ y m j. m = 1, ... , M. ,. h =1. ∑. λ h x nh ≤ θ ⋅ x nj. ∑. λ h k nh ≤. ∑. λh = 1. H. h =1 H. h =1 H. h =1. k ij. λ 1 , ..., λ h ≥ 0. ,. n = 1, . .., N. , i = 1, .. ., I. h = 1, . .., H. We have a sample of h = 1,..., H producers using a vector of n = 1,..., N inputs ( x ) and i = 1,..., I quasi-fixed inputs (k ) to obtain a vector of m = 1,..., M . outputs ( y ) , θ is technical efficiency value between 0 and 1. . . .

(31) . 3.3 Directional distance function Conventional DEA models can only consider output expansion or input contraction, but not both.. When the technology set is characterized by variable. returns to scale (VRS), both output-oriented and input-oriented technical efficiencies are not equal generally.. If we evaluate efficiency of tourist hotel by the. output-oriented approach, we may not fully characterize operational management of hotels since it cannot distinguish between quasi-fixed inputs and variable inputs. Other the other hand, it may overestimate the ability of adjustment of hotel management if the input-oriented model ignores the existence of quasi-fixed inputs (Ouellette and Vierstraete, 2004).. Furthermore, the objective of tourist hotels is to. expand outputs rather than to contract inputs.. Hence, it is inappropriate to evaluate. hotels’ efficiency ignored output expansion.. The directional distance function,. capable of expanding outputs and contracting inputs simultaneously, can fulfill the request of this study. Färe and Grosskopf (2005) define the directional distance function as follows:. {. D ( x, k , y; − g x , g y ) = sup β : ( x − β g x , k , y + β g y ) ∈ T . Where. }. (1). x = ( x1 ,… , xN ) ∈ N+ , k = (k1 ,… , k I ) ∈ I+ , and y = ( y1 ,… , y P ) ∈ P+ . are. variable input vector, quasi-fixed input vector, and output vector, respectively; T=. {( x , k , y ) : x and k can produce y }. is the technology set. Equation (1) searches. for the largest feasible expansion of output vector y in the g y direction and the largest feasible contraction of input vector x in the − g x direction. treat quasi-fixed input vector k as fixed. . Note that we. This specification can not only. characterize the property of quasi-fixed inputs in the operational management of . .

(32) . hotels, but also satisfy the request of output expansion.. distance function D (⋅) = βˆ .. The value of the directional. The efficient DMU is corresponding to βˆ = 0 .. In. other words, the technology frontier is constructed by those DMU associated with βˆ = 0 .. Hence, the larger the value βˆ , the farer the DMU from the frontier.. 3.4 Meta-frontier Due to different national cultures, operational philosophy, managerial mode, and etc., domestic and foreign-owned hotels apparently belong to different operating systems and thus the assumption of convexity may not be valid. approach allows each group to have its own group-frontier.. The meta-frontier. The meta-frontier is. defined as a common boundary that envelops the group frontiers. set associated with meta-frontier could be convex or non-convex.. The technology We will illustrate. by figure 3.2. Assume that there are two groups, A and B. segment connecting A1, A2, G and A3. of points B1, G, B2 and B3.. The frontier of group A is the line. Similarly, the frontier of groups B consists. If the technology set is non-convex, the relevant. meta-frontier is the line segment connecting A1, A2, G, B2, and B3.. It is apparent. that group-frontiers exhaust the meta-frontier; in other words, each part of meta-frontier belongs to at least one of group-frontiers.. If the technology set is. convex, the relevant meta-frontier is the line segment connecting A1, A2, B2, and B3. The convexity allows that the input-output combinations beyond the boundaries of group-frontiers such as the dot line connecting A2 and B2.. It may imply that. existing technology can upgrade through spillover and/or mutually learning among groups for a considerable period. . In this sense, the non-convex meta-frontier is .

(33) . suitable to analyze efficiency in the short run, while the convex meta-frontier may be appropriate for the analysis of the long run.. Furthermore, we follow the basic. assumption that the quasi-fixed inputs cannot be adjusted in the short run, but they are variable in the long run. Y. B3 B2 frontier of group B. A3. G A2. frontier of group A. B1 A1 X. 0. Figure 3.2. Illustration of the meta-frontier. Before drawing the meta-frontier, we assume that the technology is constant within a given time period.. The meta-technology is regarded as true technology, the. group-technologies are considered as revealed technology.. In the convex case, the. production possibility set (true technology) which constructed by the technology integration of groups is greater then the case of non-convex.. Moreover, the. strategies of firms are usually focused on the adjustment of current operating condition in the short run, but the strategies of firms are focused on the overall planning in the long run. We now describe how to incorporate the directional distance function in the meta-frontier approach.. . Let T m be the meta-technology set that envelopes the G .

(34) . group frontiers such that T m = T 1 ∪ T 2 ∪ ... ∪ T G where T g is the technology set of group g,. g = 1, 2,… , G.. The directional distance function relative to the. meta-technology set can be expressed as:. {. }. m D ( x, k , y; − g x , g y ) = sup β : ( x − β g x , k , y + β g y ) ∈ T m . . (2). The directional distance function relative to the technology set of group g can be defined as:. {. }. D g ( x, k , y; − g x , g y ) = sup β : ( x − β g x , k , y + β g y ) ∈ T g . . (3). This study applies the following approach to calculate the direction distance function for the non-convex meta-technology set:. (1) calculate the direction distance. function of each DMU based on the efficient frontier of group g, say βˆg , g = 1, 2,.., G; (2) the relevant value of the direction distance function βˆ m for each DMU is the maximum of. {βˆ , βˆ ,…, βˆ } ; 1. 2. G. {. }. For G = 2, the linear. ). (4a). i.e. βˆ m = βˆ1 , βˆ2 ,… , βˆG .. programming of DMU j under VRS can be written as:. (. N P D ( x, k , y; − g x , g y ) = Max β j + ε ∑ n = 1 S n− + ∑ p = 1 S +p β j , λ1 ,...,λH s.t. ∑ h∈ A λ h xnh + ∑ h∈ B λ h xnh + S n− = xnj − β j g nx , n = 1,..., N. ∑ ∑. ∑ ∑. h∈ A. λ h y ph + ∑ h∈ B λ. h. y ph − S p+ = y pj + β j g py , p = 1,..., P. (4b) (4c). h∈ A. λ h kih + ∑ h∈ B λ h kih ≤ kij ,. h∈ A. λh = Z A. (4e). h∈B. λh = Z B. (4f ). i = 1,..., I. Z A + ZB = 1. (4d). (4g). Z A , Z B = 0 or 1; λ1 ,..., λH ≥ 0; β. is free. Where H is the total number of DMUs; S +p and S n− are the non-radial p-th output slack and the n-th input slack, respectively; ε is a small non-Archimedean quantity, . .

(35) . usually being 10−6 .. The first constraint labeled (4b) seeks largest contraction of the. n-th variable input in the direction g nx .. The constraints in (4c) search for largest. expansion of p-th output in the direction g py . inputs to fixed in the short run.. Expression (4d) holds the quasi-fixed. Constraints (4e) to (4g) ensure the technology is. VRS. The non-convex meta-technology set is only suitable for the analysis of the short run.. We employ the convex meta-technology set to analyze the efficiency in the. long run.. In addition, we assume that the quasi-fixed inputs can be adjusted in the. long run, so all inputs are variable.. D ( x, k , y; − g x , g y ) = Max β j , λ1 ,...,λH s.t.. The corresponding linear programming is:. βj +ε. ∑ ∑ ∑. H h =1 H h =1 H h =1. (∑. N n =1. S n− + ∑ i =1 Si− + ∑ p =1 S +p I. λ h xnh + S n− = xnj − β j g nx ,. P. ). n = 1,..., N. λ h y ph − S +p = y pj + β j g py ,. p = 1,..., P. λ h kih + Si− = kij − β j g ik ,. i = 1,..., I. λ 1 ,..., λ. H. (5). ≥ 0; β is free. The meta-technology can be viewed as true technology, while the group-technologies regard as revealed technology.. In other words, we measure the. group-efficiency based on the revealed technology, while evaluate the meta-efficiency based on the true technology.. Hence, each DMU can generate two directional. distance functions, one based on the meta-technology βˆm and the other on the group-technology βˆ.. The difference between these two values is technology gap. (TG), measuring the distance between the group-frontier and the meta-frontier; i.e., βˆm = βˆ + TG .. . Figure 3.3 can explain this relation.. .

(36) . Y. ( x − βˆm g x , y + βˆm g y ) A. ∗. Meta-frontier Group-frontier. ˆ ( x − βˆg , y + βˆg ) A x y. (− g x , g y ) . A ( x, y ) . X. 0. Figure 3.3. Illustration of meta-efficiency and technology gap. In this figure, the observation ( x, y ) at A4 is projected in the direction (-g x , g y ) onto the boundary of group technology. . It represented how much the. degree of outputs expanded and inputs reduced from ( x, y ) to the group frontier in the direction (-g x , g y ) . . In the same way, the observation ( x, y ) at A4 is . projected in the direction (-g x , g y ) onto the boundary of meta-technology can be presented as β m .. The value of β m means the maximum degree of outputs. expanded and inputs reduced from point A4 to the meta-frontier in the direction (-g x , g y ) . . The technology gap (TG) represents the difference between group frontier. and meta-frontier. Consider the point A inside the technology set.. The directional distance. g function D (⋅) moves the input-output vector ( x, y ) to the frontier of group g at. . .

(37) . ˆ the point A. ( x − βˆg , y + βˆg ) x. along the direction (− g x , g y ) .. y. Similarly, the. m directional distance function D (⋅) projects the point A to the meta-frontier at the point A* ( x − βˆm g x , y + βˆm (⋅) g y ) along the direction (− g x , g y ) .. We can image. ˆ on the group-frontier to the meta-frontier at the that TG can translate the point A point. ( ( x − βˆg ) − TGg , ( y + βˆg ) + TGg ) x. x. However, both points A* and. direction. (− g x , g y ) .. ( ( x − βˆg ) − TGg , ( y + βˆg ) + TGg ). are coincide.. y. y. x. Hence, we obtain βˆm = βˆ+ TG .. . . along x. the y. y.

(38) . Chapter 4. Empirical results. 4.1 Data and Variables The data set, obtained from the annual report of international tourist hotels published by Taiwan Tourism Bureau (TTB) during 2005~2007, consists of 170 observations.. Because we have three-year data, all nominal variables are. transformed into real variables in 2001 prices by GDP deflators. The choice of input and output variables can be traced to the previous studies in the Table 4.1.. Among input factors, cost of food and beverage represents input. materials, number of employees represents input manpower, and number of rooms and floor space of the catering division represent capital expense. inputs are catering expense and number of employees.. Two variable. However, number of rooms. and floor space of the catering division represent the quasi-fixed inputs in this paper that cannot be adjusted in the short run. According to the annual operating reports, accommodation and meals are the two primary source of revenue for international tourist hotels in Taiwan.. Others include. laundry operations, beauty salons, nightclubs, and service fees, accounted about 20% of total revenue.. . .

(39) . Table 4.1. Literature on the hotel industry. Authors. Title. Inputs. Outputs. Sheng-Hshiung. Evaluating the. *Total operation Expenses. *Total operation revenue. Tsaur ; Chin-I. operating efficiency. *The number of guest rooms. *Occupancy rate of guest room. Chiang ; Te-Yi. of international. *The total floor space of the. *The average production value. Chang (2000). tourist hotels using. catering division. the modified DEA. per employee in the catering division. model Sheng-Hshiung. The operating. *Total operating expenses. *Total operating revenues. Tsaur (2001). efficiency of. *The number of employees. *The number of rooms occupied. international tourist. *The number of guest rooms. *Average daily rate. hotels in Taiwan. *The total floor space of. *The average production value. the catering division *The number of employees in room division *The number of employees in catering division *Catering cost. per employee in the catering division *Total operating revenues of the room division *Total operating revenues of the catering division. Hwang, S.N.. Using data. *Number of full-time employees. *Room revenue. and Chang,. envelopment analysis. *Guest rooms. *Food and beverages revenue. T.Y. (2003). to measure hotel. *Total area of meal department. *Other revenues. managerial efficiency. *Operating expenses. change in Taiwan. Wang, F.C.,. Measuring pure. *Number of full-time employees. * Room revenue. Hung, W.T.,. managerial efficiency. *Guest rooms. * Food and beverages revenue. Shang, J.K.,. of international. *Total area of meal department. * Other revenues. (2006). tourist hotels in. *The average production value. Taiwan Yang, C., Lu.. Performance. *Number of employees. W.M., (2006). benchmarking for. *Number of guest rooms. per employee in the catering. Taiwan’ s. *Total area of catering division. division. international tourist. *Operating expenses. hotels. *Total operating revenues *Average productive value of catering division *Average room rate *Average occupancy rate. . .

(40) . 4.2 Results Based on convex and non-convex properties, the section can be divided into two parts, the short run results and the long run results.. 4.2.1 Short run analysis The software Lingo 10.0 is employed to analyze the operational efficiency of domestic and foreign-owned tourist hotels.. The empirical data show that the average. revenues of catering were higher than those of rooms in the 2005-2007 period.. That. is related to the eating habit of people in Taiwan, they are used to eat out (Tsaur, 2001 and Hu et al., 2008). Table 4.2. Descriptive statistics for variables. (NT$ Million). Variables. Mean. Std. dev.. Min. Max. Number of employees. 318.041. 206.137. 53.000. 982.000. Catering expense. 110.265. 104.368. 3.722. 754.364. Number of guest rooms. 305.406. 152.619. 50.000. 873.000. 1,179.988. 906.517. 48.000. 4,777.000. Room revenue. 270.720. 240.019. 35.643. 1,482.742. Catering revenue. 281.599. 273.427. 8.730. 1,174.773. 95.877. 123.291. 0.360. 595.754. Floor space of catering division. Other revenue. We first investigate whether or not efficient frontiers of both groups, domestic and foreign-owned tourist hotels in Taiwan, are significantly different from each other in order to select an appropriate empirical model.. . . To compare the efficient frontier.

(41) . of two groups, it is naturally to run the DEA model separately in each group and obtain the efficient DMUs of each group. Then we mix all efficient DMUs together to run the DEA model again and perform the nonparametric test.. However, this. procedure excludes a lot of inefficient DMUs which results in the degrees of freedom problem.. Cooper et al. (2000) suggest that each inefficient DMU is replaced by its. corresponding projection point on its respective efficient frontier to avoid the degrees of freedom problem. Figure 4.1 is used to describe this procedure. The efficient frontier of domestic hotels consists of points A, C, and E.. We project the inefficient point B, D, F, and G. onto efficient frontier of domestic hotels to obtain point B*, D*, F*, and G*, respectively.. Hence, the efficient DMUs of domestic hotels will be A, B*, C, D*, E,. F*, and G*.. Similarly, we can get the efficient DMUs of foreign-owned hotels.. All. efficient DMUs are pooled together to run the DEA model.. G*. F* D*. Frontier of domestic . E. C. F. B*. G. D A. (-g x , g y ). B X. 0 Figure 4.1. Projection on the Efficient Frontier. The nonparametric Mann-Whitney U test, based on the ranking of DEA results, is employed to test the hypothesis that both groups, domestic and foreign-owned tourist hotels, have the same efficient frontiers. . . The test statistic indicates that the.

(42) . efficient frontiers of both types of hotels are significantly different with p-value 0.027. Hence, this study uses the meta-frontier approach to evaluate efficiencies of both domestic and foreign-owned tourist hotels. Table 4.3 summarizes the empirical results of the non-convex meta-frontier The average meta-efficiency score βˆm of domestic and foreign-owned. model.. hotel is 0.111 and 0.061, respectively. are more efficient than domestic hotels.. This may suggest that foreign-owned hotels Nevertheless, we need to perform a test to. investigate whether these two meta-efficiency scores are significantly different or not. The nonparametric Mann-Whitney U test statistic indicates that foreign-owned hotels outperform domestic hotels significantly with p-value less than 0.001. Table 4.3. Empirical results of the non-convex meta-frontier model Classification. βˆ. βˆm. TG. Note:. Sample size. Mean. Std. dev.. Domestic. 113. 0.091. Foreign-owned. 51. Domestic. Min. Max. 0.113. 0. 0.467. 0.054. 0.068. 0. 0.382. 113. 0.111. 0.010. 0. 0.467. Foreign-owned. 57. 0.061. 0.015. 0. 0.703. Total. 170. 0.094. 0.009. 0. 0.703. Domestic. 113. 0.023. 0.003. 0. 0.127. Foreign-owned. 57. 0.019. 0.008. 0. 0.321. Total. 170. 0.022. 0.003. 0. 0.321. The p-values of Mann-Whitney U test for TG and βˆm are 0.005 and less than 0.001, respectively.. Table 4.4 lists descriptive statistics for the meta-efficiency indicator and technology gap of each group. better. data set.. It should be noted that a smaller value of beta is. There are 113 domestic hotels, 57 internationally-operated chain hotels in our From this table we can see that the international chain hotels have the better. (i.e., lower) average meta-efficiency score and the average technology gap score than . .

(43) . domestic hotels. In the short run (non-convex), the average meta-efficiency indicator of international chain hotels is 0.061.. This means that they should reduce their. non-fixed inputs and expand their outputs by 6.1% each. technology gap is 0.019.. The mean value of the. This result implies that, for international chain hotels, the. firms should improve their production technologies by 1.9% to the maximum potential available technology.. These two efficiency indicators of international. chain hotels are better than domestic hotels on average.. Table 4.4. Empirical results of the non-convex meta-frontier model Classification. βˆ. βˆm. TG. Note:. Sample size. Mean. Std. dev.. Min. Max. Domestic. 113. 0.091. 0.113. 0. 0.467. Foreign-owned. 51. 0.054. 0.068. 0. 0.382. Domestic. 113. 0.111. 0.010. 0. 0.467. Foreign-owned. 57. 0.061. 0.015. 0. 0.703. Total. 170. 0.094. 0.009. 0. 0.703. Domestic. 113. 0.023. 0.003. 0. 0.127. Foreign-owned. 57. 0.019. 0.008. 0. 0.321. Total. 170. 0.022. 0.003. 0. 0.321. The p-values of Mann-Whitney U test for TG and βˆm are 0.005 and less than 0.001, respectively.. The foreign owned hotels have less proportion of slacks for all outputs. The possible reason might be that the foreign-owned hotels adopt international management systems, training human resource and promoting managerial capacities, share the knowledge assets and benefited by economic of scale.. From an. international network they can cumulate the learning experiences for operating under different country. . They also have a better brand image and reputation, share .

(44) . reservation systems and information so that they can provide better quality of customer service and have more foreign visitors (Mazzeo, 2004; Wang et al., 2006).. 4.2.2 Long run analysis Firms generally operate in the short run and plan in the long run.. A firm has. enough time to adjust its operating scale and/or to adopt different technologies in the long run.. Table 4.5. βˆ. βˆm. TG. Note:. Empirical results of the convex meta-frontier model Classification. Sample size. Mean. Std. dev.. Min. Max. Domestic. 113. 0.088. 0.109. 0. 0.419. Foreign-owned. 57. 0.042. 0.065. 0. 0.382. Domestic. 113. 0.121. 0.010. 0. 0.448. Foreign-owned. 57. 0.065. 0.012. 0.. 0.515. Total. 170. 0.102. 0.008. 0. 0.515. Domestic. 113. 0.032. 0.003. 0. 0.122. Foreign-owned. 57. 0.024. 0.005. 0. 0.212. Total. 170. 0.030. 0.002. 0. 0.212. The p-values of Mann-Whitney U test for TG and βˆm are 0.016 and less than 0.001, respectively.. Hence, we use a convex meta-frontier approach with inputs to be all variable to find appropriately planning strategies. meta-frontier model.. Table 4.5 shows the summary of the convex. The empirical results are basically similar to the non-convex. meta-frontier model. Compare the results of non-convex model and convex model in Table 4.6, we can find that the values of meta-efficiency and technology gap in the short run are both smaller than the values in the long run. . . It means that Taiwan’ s international.

(45) . hotels have greater degree of adjustment and improvement in the long run.. Table 4.6. βˆm TG. . Comparison of short-run results and long-run results Classification. short-run results. long-run results. Domestic. 0.111. 0.121. Foreign-owned. 0.061. 0.065. Domestic. 0.023. 0.032. Foreign-owned. 0.019. 0.024. .

(46) . Chapter 5. Discussion. In accordance with the cases of non-convex and convex, we can develop the short-term and long-term strategies.. Moreover, Duncan (2005) argues that the eight. main issues of hospitality industry are employment, taxation, environment, disability, licensing/gaming, hotel classification, food, and music copyright. However, we don’ t have enough information to analyze the issue of hotel classification.. The grades of international hotels in our data set are more than. four-star, but not clearly to separate which one is four-star or five-star.. In part of the. issue of licensing or gaming, the adoption of game license has passed and the related activities are proceeding in Taiwan.. The value-added tax in Taiwan is lower than. that of the countries in Europe, but higher than that of in the Hong Kong and Macao. With regard to copyright issues, we also have set a clear Act. Base on our empirical results, we can catch some ideas which in these eight main issues.. The issues of employment and food can be discussed by slack analysis.. The human resource of hotel sector is a very important topic, because of the better qualities of labors can provide better service.. Moreover, the food revenue of hotels. are usually higher than room revenue in Taiwan.. The possible reason is that the. increasing ratios of people in Taiwan who eat out as local consumers in Taiwan are used to dining outside (Hu et al., 2008). With regard to the issue of environment can be discussed by the effect of different hotel’ s position.. The international tourist hotels operate under different. environment and the location of these hotels can be classified as urban or country site. The majority passengers of hotels in the urban area are business travelers.. In. contrast, the majority passengers of hotels in the scenic and country areas are leisure visitors. . Leisure visitors are primarily motivated to travel because of they want to .

(47) . explore other cultures, to experience freedom and personal growth.. On the other. hand, the principal motivator of business visitors is the business activity itself rather and need the convenient accommodation and transport facilities in the city.. Table 5.1. The efficiency indicator of urban and leisure hotels Classification Sample size. beta_M. TG. Mean. Std. dev.. Min. Max. Urban. 124. 0.100. 0.008. 0.000. 0.463. Leisure. 46. 0.101. 0.022. 0.000. 0.702. sum. 170. 0.100. 0.008. 0.000. 0.702. Urban. 124. 0.000. 0.000. 0.000. 0.000. Leisure. 46. 0.055. 0.016. 0.000. 0.660. sum. 170. 0.015. 0.004. 0.000. 0.660. In the Table 5.1, the result shows that the performance of urban hotels is better than leisure hotels in Taiwan.. The Mann Whitney test statistic indicates that the. results are significantly with P-value 0.097 and 0.000.. Therefore, we know that the. development of tourism industry in Taiwan is not mature enough.. The government. should do more marketing and promotion for Taiwan tourism which are helpful to enhance the leisure hotels operating efficiencies.. 5.1 Short run strategy The slack analysis can be used to measure outputs expansion and the variable inputs contraction. contraction.. Table 5.2 gives the proportions of output expansion and input. The proportions are the sum of radio and non-radio slacks divided by. the current amount of variables. Both groups have to reduce the similar proportions of catering expense.. However,. the proportion of excess employees of domestic hotels doubles that of forging-owned hotels. . This suggests that domestic hotels have too many unnecessary employees .

(48) . and/or lower labor productivity.. The part of output slacks, domestic hotels also have. to expand the large proportion of room and food revenues, compared with foreign-owned hotels.. In general, the foreign-owned hotels have a better brand. awareness and they can offer a variety of catering service, so that they have less output slacks. The result can provide guidelines to managers of international tourist hotels to set their operational strategies.. In the short run, the domestic hotels can hire the. employees which have experiences about foreign-owned hotel operating. be able to upgrade the productivity of labors.. That may. The domestic hotels can focus on the. marketing and promotion for catering sector to provide the differentiated service.. Table 5.2. Summary of output and variable input slacks Number of employees. Catering expense. Domestic. 0.159. Foreign-owned. 0.078. Note:. Room revenue. Catering revenues. Others revenues. 0.120. 0.239. 0.099. 0.484. 0.121. 0.092. 0.047. 0.272. The values are the sum of radio and non-radio slacks divided by the current amount of variables.. 5.2 Long run strategy The long term strategy can be developed by the scale analysis of hotels. summary the characteristic of returns to scales in Table 5.3.. We. The characteristic of. returns to scales shows that there are about 70% of tourist hotels operating in the stage of increasing returns to scale.. Hence, Taiwan’s tourist hotels should design to. augment the operating scales in order to improve their productivity.. . .

(49) . Table 5.3. Summary of returns to scales DRS. CRS. IRS. Domestic hotels. 0.133. 0.124. 0.713. Foreign-owned hotels. 0.176. 0.105. 0.719. The foreign-owned hotels have best performance on average whether in the long-term or short-term.. The possible reason for this result is that the foreign-owned. hotels adopt international management systems, training human resource and promoting managerial capacities, share the knowledge assets and benefited by economic of scale.. From an international network they can cumulate the learning. experiences for operating under different country.. They also have a better brand. image and reputation, share reservation systems and information so that they can provide better quality of customer service and have more foreign visitors (Mazzeo, 2004; Wang et al., 2006). Thus, the managers of the domestic hotels can participate in international exhibitions, such as the International Travel Expo Hong Kong (ITE), to promote their own hotels and link to the international network.. They also can join in the. international hotel association (i.e., The Leading Hotels of the World).. Their service. quality will be monitored and share the information, so that the operating efficiency may be better than others. Moreover, according to the result of environment analysis, Taiwan’ s government should continue to improve the development of the tourist attractions and promote the Taiwan’ s tourism to the world.. . .

(50) . Chapter 6 Conclusions Leisure visitors are primarily motivated to travel because of they want to explore other cultures, to experience freedom and personal growth.. On the other hand, the. principal motivator of business visitors is the business activity itself rather and need the convenient accommodation and transport facilities in the city. DEA is widely used to measure performance of hotel industry.. Previous studies. assume that all hotels share the same production frontier, i.e., they have the same technology set.. However, different types of tourist hotels may have distinct. production frontiers because of different national cultures, operational philosophy, managerial mode, and etc.. This study uses the meta-frontier approach to. accommodate to sample hotels associated with different production frontiers.. In. addition, previous studies of hotel performance neglected the quasi-fixed inputs that may overstate firms’ capability of adjustment. This article proposes a more complete framework for the assessment of hotels performance.. This analysis combines the directional distance function and. meta-frontier to consider the expanding outputs and contracting inputs simultaneously and different production technologies of groups. The meta-frontier can be assumed to be convexity or non-convexity.. Based on. the convex case, the firm’ s input-output combination may over their own frontier through the mutual integration. and all of inputs can be adjusted.. In general, this situation may occur in the long run Another case is non-convex meta-frontier that the. group frontiers are exhaustive envelop all the input-output combinations. Therefore, we apply the non-convex meta-frontier in the short run and assume that the quasi-fixed inputs cannot be changed.. The data set, obtained from the annual report of international tourist hotels, . .

(51) . consists of 170 observations.. Empirical results show: the meta-efficiency and. technology gap (TG) of foreign owned hotels are better than those of domestic hotels; employees of foreign-owned hotels are more productive than those of domestic hotels; Taiwan’ s tourist hotels should plan to augment the operating scales.. . .

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