Analysis of Las Vegas Strip casino hotel capacity--- an inve

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which was completed in 2001,and the other is the 2455-room Le Reve Casino Hotel to be built on the site of the demolished Desert Inn Casino Hotel.Le Reve is scheduled to open in mid-2004.

To maintain healthy growth and decent pro?tability,the gaming industry in Las Vegas needs to carefully plan its capacity based on demand.While overcapacity may cause cutthroat competition and declining pro?ts,undercapacity could lead to substantial opportunity losses.Neither overcapacity nor undercapacity is desir-able.The purpose of this study is to use an inventory model based on probabilistic demand and costs of oversupply and undersupply to estimate the optimal room capacity for the Las Vegas Strip from 2001to 08f6a7a20029bd64783e2c21ing the estimated optimal room supply as a benchmark,the study further predicts the magnitude of possible overcapacity and undercapacity the Strip may face in the near future.

The practical implications of the study are that it may help the gaming industry in Las Vegas to foresee its demand in the next several years and plan its future casino development along the Strip in a scienti?c way.Casino development plans based on sucha model could help the Las Vegas Strip,and other gaming destinations as well,to avoid severe overcapacity or undercapacity in the future.Academically,using an inventory model to identify the optimal room capacity for the Las Vegas Strip,a top tourism destination in NorthAmerica,should contribute to the research in capacity optimiza-tion for tourism development.

2.Inventory model for probabilistic demand

The commonly used economic order quantity (EOQ)model for inventory assumes that the demand for the

inventory items has a constant rate (Anderson,Sweeney,&Williams,2001;Russell &Taylor,2000;Jackson &Frigon,1998),implying that the same amount of items is taken out of inventory for sale or consumption.In other words,in an EOQ model,the demand is pre-determined or deterministic.In hotel operations,the demand for rooms is uncertain rather than deterministic.Therefore,EOQ model is not applicable to room inventory management.

To deal withinventory capacity facing uncertain demand,Anderson et al.(2001)propose a single-period inventory model withprobabilistic demand for optimiz-ing inventory level.The model is applicable to opera-tions withtwo features.First,th e operation involves highly seasonal or perishable items that cannot be stored for future sales,suchas seasonal cloth ing and news-papers.Second,the demand for the inventory item is uncertain but has a probability distribution.The single-period model is derived from an incremental analysis of inventory in relation to the expected loss.The incre-mental analysis shows that the optimal order quantity Q ?occurs when the expected loss (EL)of ordering one incremental unit is equal to the EL of not ordering one incremental unit,or EL(Q *+1)=EL(Q *).Based on the relationship,Anderson et al.(2001)have further developed the single-period optimal inventory model as an equilibrium at which the expected loss associated withover-ordering is equal to th e expected loss associated withunder-ordering.Th e expected loss of an ordering status is de?ned as the probability of the status multiplied by its unit cost.Mathematically,the model is expressed as

Co P edemand p Q ?T?Cu ?1àP edemand p Q ?T :

e1T

In the equation,Co and Cu represent the unit costs of over-and under-ordering,respectively.P (demand p Q *)is the probability of over-ordering.Since the sum of the probabilities of over-and under-ordering must be one,the probability of under-ordering is expressed as [1àP (demand p Q *)].Solving for P (demand p Q *)in Eq.(1),we have

P edemand p Q ?T?Cu =eCu tCo T:

e2T

Eq.(2)provides the general condition for the optimal order quantity Q ?in the single-period inventory model.The model implies that when we have Cu=Co or when the cost ratio of Cu/(Cu+Co)is 0.5,the optimal order Q ?should give equal chance for surplus and shortage.If the cost of under-ordering is higher than the cost of over-ordering or we have Cu/(Cu+Co)>0.5,the optimal order Q ?should give less chance to under-ordering but more chance to over-ordering.Conversely,if the cost of under-ordering is lower than the cost of over-ordering or we have Cu/(Cu+Co)o 0.5,the optimal order Q ?should give more chance to under-ordering and less chance to over-ordering.In essence,

Table 1

Capacity,revenue and pro?ts of casinos hotels on the Las Vegas Strip (1990–2000)Year Room nights available Total revenue Income before taxes 199013,323,771$3,939,331,858$358,135,218199115,727,2074,531,867,842312,929,972199216,454,8484,463,692,494397,130,946199315,583,4894,707,202,656593,755,945199417,931,5865,777,872,257610,199,820199519,737,5706,537,678,305764,539,080199619,897,8606,866,354,281973,685,009199721,394,1897,087,266,194906,397,224199822,529,8997,397,825,633802,773,736199923,760,9978,585,449,542538,372,8202000

26,405,27910,195,669,758185,450,419%Change from 1990to 2000

98.18

158.82

à48.22

Note :Room nights available=rooms available ?365.

Z.Gu /Tourism Management 24(2003)309–314

310

the model holds that greater chance should be given to the ordering status that is associated with lower cost. Analysts typically measure the capacity of a casino hotel using number of rooms(Ader et al.,1999). For casino hotels,rooms unsold cannot be kept for resale in the future and the demand for rooms is likely to be probabilistic rather than deterministic.

A casino hotel’s room operation has both features required for the single-period inventory model, namely perishable item and probabilistic demand,as delineated by Anderson et al.(2001).Therefore,the single-period inventory model is an appropriate ap-proachfor decision-making related to casino h otel capacity.

3.Methodology and data

To develop the capacity model for Las Vegas Strip casino hotels,annual room nights available were used as a measure of the overall capacity of casino hotels on the Las Vegas Strip.Room capacity,in terms of either rooms available or room nights available,is a commonly used capacity measure for casino gaming destinations (Ader et al.,1999).To identify the optimal quantity of room nights available or Q?for the Las Vegas Strip as de?ned in Eq.(2),the demand function for predicting annual room nights sold or demanded from2001to 2004witha probability distribution needs to be?rst established.Furthermore,the cost ratio of Cu/(Cu+Co) must be estimated.Data needed for estimating room nights demanded and the cost ratio for the study were obtained from annual issues of Nevada Gaming Abstract published by Nevada Gaming Control Board (1990–2000).

To estimate the probabilistic room demand for 2001–2004,this study follows the Anderson et al. (2001)suggestion to develop a trend regression line. Future demand was estimated by extrapolating the trend regression line with annual room nights sold as the dependant variable and time as the independent vari-able.Annual room nights sold from1990,when Nevada Gaming Control Board started to report annual room nights sold on the Strip,to2000were utilized to estimate the trend regression model for predicting demand.SPSS regression curve estimation procedure was used to identify the trend regression line that best?ts the data set.One critical assumption of the regression line is that the dependant variable is normally distributed with constant variance(Kleinbaum,Kupper,&Muller, 1988).When predicting future demand Y witha regression model,the model-estimated Y is the mean of future demand and the standard error of the predicted Y is the estimated standard deviation from the mean(Webster,1998).Therefore,a regression model not only predicts the mean of the future demand but also provides the probability distribution around the mean.

Anderson et al.(2001)de?ne the unit cost of over-ordering or Co as the loss of ordering one additional unit and?nding that it cannot be sold.The cost of under-ordering,Cu,is de?ned as the opportunity loss of not ordering one additional unit and?nding that it could have been sold.In this study,the cost of over-ordering was de?ned as?xed cost per room night available because?xed cost occurs whether or not the room is sold.Income before corporate taxes per room night sold,representing the foregone pro?ts or unit opportunity loss,was used as a proxy for the cost of under-ordering.Nevada Gaming Abstract does not report net income after corporate taxes.Therefore, income before taxes was used as the closest proxy for the opportunity loss.Accordingly,the ratio of Cu/ (Cu+Co)in this study is the ratio of?xed cost per room night available to the sum of?xed cost per room night available and income before taxes per room night sold.For calculating the ratio,Strip casino cost and income data of2000published by Nevada Gaming Control Board in2001were used.This study attempts to estimate the optimal room capacity for the Strip from 2001to2004.Therefore,the ratio estimated based on the operating statistics of2000should provide the closest approximation for2001–2004.The signi?cant decline in income before taxes from1999to2000re?ects the deterioration of market conditions for the Las Vegas Strip in recent years.Due to the current US economic recession and the impact of the September11,2001 terrorist attacks on New York,the challenging market environments are not likely to improve 08f6a7a20029bd64783e2c21ing the most current operating statistics of2000,rather than an average of several previous years,would provide conservative yet realistic estimates for the cost ratio of Cu/(Cu+Co)and the optimal capacity.

To derive income before taxes per room night sold, aggregate income before taxes of Strip casino hotels in 2000was pided by total room nights sold during the year.Estimating?xed cost per room night available involved more steps.First,cost items that were obviously?xed charges,namely depreciation and amortization,interests,rents and real estate taxes,were sorted out from the total costs and pided by room nights available to arrive at?xed charge per room night available.Second,the remaining costs were treated as mixed costs and separated for their?xed and variable components.Regression method,as suggested by Schmidgall(1997),was used to separate the two components.Total mixed costs of eachyear were regressed against room nights sold each year from 1990to2000.The slope of the regression line was the estimated variable cost per room night sold.To adjust for in?ation,costs were pided by the relevant year’s consumer price index(CPI)in the estimation of variable

Z.Gu/Tourism Management24(2003)309–314311

cost per room night sold.By subtracting the total variable cost,which was variable cost per room night sold multiplied by number of room nights sold during a year,from the mixed costs of the year,the?xed component of the year’s mixed costs could be identi?ed. Dividing the?xed component by number of room nights available for a year would lead to the?xed component per room night available for the year.By adding the ?xed component per room night available for2000, which was adjusted back for in?ation by the CPI of 2000,to the?xed charge per room night available for 2000,the?xed cost per room night available for2000 was obtained.

Finally,the ratio of Cu/(Cu+Co)was derived based on the?xed cost per room night available and income before taxes per room night sold 08f6a7a20029bd64783e2c21bining the derived cost ratio with the future demand and probability distribution estimated from the regression model,the study was able to determine the optimal capacity Q?for the Las Vegas Strip for each year from 2001to2004.Overcapacity and undercapacity were predicted by comparing Q*withth e expected room capacity based on the LVCVA’s(2001)Hotel/Casino Development—Construction Report for2001–2004.

4.Capacity2001–2004:optimal vers us actual

In2000,the income before taxes per room night sold, or the cost of under-ordering,was calculated at$7.55. On the other hand,the?xed charge per room night available,including depreciation and amortization, interests,rents and real estate taxes,was estimated at $60.54.The?xed component per room night available was found to be$8.43.Therefore,?xed cost per room night available was the sum of the two or$68.97.The cost ratio of Cu/(Cu+Co)for Strip casinos in2000was thus estimated at0.0987.The ratio means that optimal capacity of room nights available or Q?should be at the level where the probability for the demand to be less than Q?(over-ordering)is9.87%and the probability for the demand to exceed Q?(under-ordering)is90.13%.In a standard normal distribution,Q?should be located at the left-hand side of the mean with a Z value ofà1.29. Therefore,if the predicted mean demand Y and standard deviation s of the demand are known,the optimal capacity Q?can be estimated by solving the equation:

à1:29?eQ?àYT=s:e3TTable2shows different regression curve estimates for predicting room demand on the Strip.Among the11 regression models,the linear regression model has the highest adjusted R square,0.972,and the greatest model F value,322.665.Since the linear regression model?ts best the room nights sold data of the Strip,it was selected as the model for predicting room demand of 2001–2004.Table3presents the coef?cients of the linear regression model.The model can be written as Y?10;774;654t1;161;534X:To predict the room demand for2001,the12th year in the data series,X was replaced by12and the predicted mean room nights demanded for 2001were calculated at24,713,063.Accordingly,the model predicts mean room nights demanded for2002–2004at25,874,597;27,036,131;and28,197,664,respec-tively.The standard deviation of the Y estimate,as indicated in the note of Table3,is667,920room nights. For2001,the predicted mean demand is24,713,063 room nights with a standard deviation of667,920room nights.Based on Eq.(3),the optimal capacity for2001 should be23,214,684room nights.Given the predicted mean demand for2002–2004and the standard devia-tion,the optimal capacity for2002–2004was also calculated.Table4compares the optimal capacity with the expected capacity for2001–2004to determine overcapacity or undercapacity.The optimal capacity, Q?;is room nights derived from the model.The expected room nights available from2001to2004were determined based on LVCVA’s Hotel/Casino Develop-ment—Construction Report for2001–2004.The differ-ence between expected room nights available and the model calculated optimal room nights available,or the expected minus the optimal,represents overcapacity or undercapacity.Overcapacity or undercapacity Table2

Regression curve estimation for the demand prediction model Regression method Adjusted R2Model F Stat. Linear0.972332.665 Logarithm0.85359.123 Inverse0.56714.095 Quadratic0.968154.076a Cubic0.968103.106a Compound0.967290.209 Power0.912104.431

S curve0.65920.327 Growth0.967290.209 Exponential0.967290.209 Logistic0.967290.209

a Quadratic and cubic models have two and three independent variables,respectively,resulting in lower mean squares of regression and hence lower F values.Other models have only one independent variable.

Table3

Linear regression forecasting model for room nights

Coef?cient T Stat.P-value Constant10,774,65424.9450.000 X Variable1,161,53418.2390.000 Note:n?11;df=10,standard error of Y?667;920;model F stat.= 332.665,adjusted R2=0.972,model P-value=0.000,Durbin—Watson =1.976.

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difference as a percentage of the optimal capacity,or the difference pided by the optimal capacity,is also presented in the table.The last column of the table shows the difference in terms of number of rooms,which is room nights pided by365.According to the LVCVA’s Hotel/Casino Development—Construction Report,there will be no addition or reduction in rooms on the Strip in2002and2003.The increase in room nights for2004is due to the scheduled opening of the 2455-room Le Reve in mid-2004.

5.Expansion with caution

As Table4indicates,the most severe overcapacity would occur in2001when the Strip’s expected capacity could be14.5%in excess of the optimal level of room nights available.Since there will be no new rooms added to Strip casino hotels in2002and2003,the demand will catchup and overcapacity will abate gradually.In2002 and2003,expected room nights available will be about 6.3%and 1.6%higher than the optimal levels, respectively.

The overcapacity of2001–2003identi?ed in this study con?rms analysts’concern that the Las Vegas market is saturated or fast approaching saturation due to aggres-sive casino expansions along the Las Vegas Strip in the late1990s(Ader et al.,1999).From1998to2000,?ve new casino megaresorts,namely the Bellagio,Mandalay Bay,Venetian,Paris and Aladdin,were launched into operation one after another.The?ve new casino hotels, witha total of about15,000rooms,h ave signi?cantly increased the Strip’s room inventory and contributed to its overcapacity.Facing the severe oversupply,especially the worsening market conditions in the wake of the September11,2001terrorist attacks,some Strip casinos have changed their expansion plans.A most recent example is that the Venetian Casino and Hotel has decided to delay its1000-room Phase I expansion, originally scheduled to complete in late2002,for up to2 years(Strow,2002).

While the analysis of this study con?rms the over-capacity on the Strip,which has forced some casinos to delay their expansions,and measures the magnitude of its current overcapacity,the main purpose of the study is to estimate the demand and optimal capacity for the Strip in the future.Neither overcapacity nor under-capacity is 08f6a7a20029bd64783e2c21s Vegas casino?rms are delaying expansions to soothe the pain caused by the overcapacity at present.The current overcapacity, however,should not prevent building new casino hotels to avoid future undercapacity.According to the model’s prediction,by2004,the overcapacity situation will come to an end and expected room nights available could be about1%below the optimal level even with the addition of2455rooms of Le Reve.Since undercapacity is likely to occur in2004and thereafter,it is advisable that the Las Vegas casino industry should plan on new casino expansions for the year2004and beyond.Typically,it takes about2years to build a mega casino resort in Las Vegas.The Luxor,a30-storey pyramid-shaped casino hotel with2500rooms,and the Treasure Island,a3000-room pirate-themed casino hotel on the Strip,were both completed within2years from1992to1993(Gu&Ku, 1997).Starting an expansion now and completing it in2 years may help a casino?rm capitalize on the future shortage as predicted by the model of the study.

New casino expansions,however,should be planned withgreat caution because some new developments in 2001may affect the predicted optimal capacity Q?: First,the demand forecasted by the regression model was based on information up to2000.The impacts of the2001economic recession and the September11,2001 terrorist attacks were not factored into the model.Both events could have signi?cant and negative impacts on tourism demand for Las Vegas in the near future.In October2001,visitors to Las Vegas fell8%compared with the same month the previous year(Smith,2001).If the impacts of economic and social events last for long, the estimated optimal capacity may need to be adjusted downward for the next several years.

One factor that may push up the optimal capacity is the declining interest rates in the wake of several deep cuts of the prime rate by the Federal Reserve in2001.If Strip casinos could re?nance their debts and substan-tially lower their interest expenses,the?xed cost per room night available or the cost of over-ordering,Co, could be lowered,thus raising the ratio of Cu/(Cu+Co) and increasing the level of optimal capacity.Due to new developments that may affect both future demand and

Table4

Room capacity2001–2004:optimal versus expected

Year Optimal room nightseQ?TExpected room nights available Difference in room nights Percentage difference Diff.in rooms

200123,214,68426,588,1443,373,46014.539242 200225,012,98126,588,1441,575,163 6.304316 200326,174,51526,588,144413,629 1.581133 200427,336,04827,036,182à299,866à1.10à822

Note:Difference in rooms is the difference in room nights pided by365.

Z.Gu/Tourism Management24(2003)309–314313

the cost ratio,the optimal capacity for the Strip needs to be re-estimated when2001operation statistics of Strip casinos become available.Expansion plans for2004and beyond,if any,should be carefully made based on updated information.

6.Summary

Using aggregate operation statistics of Las Vegas Strip casino hotels from1990to2000,this study uses the single-period inventory model proposed by Anderson et al.(2001)to estimate the optimal room capacity for Las Vegas Strip casino hotels for each year from2001to 2004.Based on the model-derived optimal room capacity and expected room nights available for the4 years,the model predicts that the Strip will experience overcapacity from2001to2003.Undercapacity,how-ever,may occur starting from2004.Therefore,new casino expansions should be planned for the year2004 and beyond to avoid possible undercapacity.Since the estimates are based on Strip operation statistics up to 2000and some new developments in2001may have signi?cant impacts on the estimated numbers,the optimal capacity may need to be adjusted when2001 operation statistics are available.Accordingly,expan-sion plans for2004and beyond,if any,would need to be adjusted.

Tourism development,including gaming destination development,involves heavy inputs of capital and human resources and thus needs to be carefully planned. Bothovercapacity and undercapacity are undesirable for tourism destinations.Capacity optimization is a critical issue in tourism strategic planning.The two assumptions of the single-period inventory model, namely perishable products and probabilistic demand, are typical features of many tourism and hospitality operations,including lodging,dining,entertainment and transportation,which involve capacity decision-making.Therefore,the model could?nd wide applications in the tourism and hospitality industries.It certainly deserves more attention in future researchin destination strategic management,capacity planning in particular. References

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