Theme Park

APPLICATION OF OPERATIONSRESEARCH IN AMUSEMENT PARKINDUSTRY

UTKU YILDIRIMProrize, LLC, Atlanta,

Georgia

The amusement park is a well-knownconcept that describes a highly capitalizedrecreational environment consisting of rides,attractions, and facilities aimed towardfamily-oriented entertainment. Although theconcept of amusement park is regarded asan American invention, the world’s oldestoperating amusement park, Bakken, datesback to 1583 and is located in Klampenborg,Denmark [1]. The first amusement parkbuilt in the United States, which is still inoperation, is Lake Compounce in Bristol,Connecticut, which was opened in 1846 [2].In 1955, Disneyland was introduced as a newamusement park concept that puts emphasison several themes by combining architec-tural elements with costumed personnel,restaurants, and retail shops.

In the latter part of the twentieth century,theme parks have turned into one of mostvisited tourist destinations. Currently, thereare more than 400 amusement and themeparks in the United States. According toInternational Association of AmusementParks and Attractions (IAAPA), 341 millionpeople visited amusement and theme parksin the United States in 2007 and enjoyedmore than 1.5 billion rides [2]. Number ofvisitors and revenue increased 14% and 42%,respectively, from 1997 to 2007. In the sametime frame, amusement parks and themeparks in the United States generated $12billion in revenues [2].

Amusement parks face increasing com-petition as the number of amusement parksincreases and new entertainment technolog-ies emerge. In order to attract new customersand increase repeat visits of loyal customers,theme park management needs to under-stand and manage customer expectations.

Wiley Encyclopedia of Operations Research and Management Science, edited by James J. CochranCopyright © 2010 John Wiley & Sons, Inc.

To that end, theme parks are collecting moreinformation about their customers, includ-ing but not limited to ride selection, foodand beverage choice, and shopping habitsthrough the use of cutting edge technology.

Operations research is uniquely posi-tioned to take advantage of this explosionof data. Customer behavior inside the parkcan be tracked and modeled with the goal ofimproving customer experience by reducingthe wait time at attractions or supportingfacilities (such as food and beverage loca-tions). Optimizing the throughput of eachfacility based on the level of demand canalso serve to improve operational efficiency.Lastly, pricing and revenue managementtechniques can be used to match customerdemand segments with revenue-maximizingticket prices.

The main purpose of this article is toprovide a review of operations research mod-els applied to the amusement park industry.Although there is a long history of researchon the marketing and strategic managementof theme parks, literature on applications ofoperations research to the amusement parkindustry is limited. The remainder of thearticle is organized as follows: First, we givean overview of simulation techniques usedin the design of rides and management ofthe wait time associated with rides. Then weconcern ourselves with the intelligent man-agement of park resources to increase visitorsatisfaction via utilization of optimizationtechniques. The next two sections providean overview of revenue management tac-tics that can be applied to pricing ticketseffectively to prevent revenue leakage andto ancillary revenue sources. Since themepark and amusement park possess similarcharacteristics except the concept of themingused in theme parks, these terms are usedinterchangeably in the article.

RIDE DESIGN AND MANAGEMENT

In a survey completed by IAAPA, rides arelisted as the number one factor that attracts

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2 APPLICATION OF OPERATIONS RESEARCH IN AMUSEMENT PARK INDUSTRY

visitors to theme parks, and 46% of people putthe roller coasters as their favorite ride [1].Visitors frequently attempt to take as manyrides as possible to get the most enjoymentout of their park visits. Unpleasant conse-quences of high participation, such as longlines and high wait time, can be avoided byincreasing the park capacity.

On the other hand, construction of newrides and renovation of existing rides makeup the biggest portion of the theme park’scapital investment. O’Brien reported thatinvestment required for a new roller coasteris between $3 and $26 million dollar per ride[3]. Signature attractions such as Walt Dis-ney World’s ‘‘Mission: Space’’ can cost up to$150 million [4]. The cost of increasing anexisting ride’s capacity can also cost millions.For example, the renovation of the ‘‘FindingNemo’’ ride cost Disney nearly $100 million[4]. Hence, a ride designed to handle maxi-mum expected demand and avoid long linesrequires a massive initial investment thatmay lead to wasted/idle capacity.

Theme park management can utilizeOperations research models to address thisproblem. The first step in this process isto estimate the number of customers whowill attend the park each day of the year.Since these numbers are highly variable andseasonal, a ‘‘design day’’ concept is utilized tosummarize this information. A design day isa hypothetical day that possesses a specificcharacteristic defined by the targets of atheme park: i.e., forecasted demand for thedesign day has to be greater than forecasteddemand for 95% of days across year. Finally,design day is employed to identify theoptimal capacity of rides, facilities, and othersupporting elements that balance the initialcost and customer experience.

Estimation of the capacity of a ride dueto complex safety regulations, theme-specificrequirements, and customer mix arrival pat-tern is challenging. The realized ride capacityis a combination of theoretical ride capac-ity and throughput rate of the ride. Ahmadireports high variability of the throughputrate due to individual visitors and familieswho wish to ride together [5,6]. For instance,take a ride that consists of operating units,such as cars or trains, with four seats. When a

family of three is seated in an operating unitand there are no individuals in the queue tofill the last spot, throughput is 75% of the the-oretical ride capacity. Ahmadi used a neuralnetwork approach to reveal the relationshipbetween group size mixture, queue length,and throughput of the ride [7].

Desai and Hunsucker [8] proposed a simu-lation-based tool to estimate the capacity of aride when one or more operational variablesis altered during the design or renovation ofa ride. Three existing rides are selected todevelop this tool. Common operational char-acteristics for these rides consist of fixedride time and capacity, loading/unloadingmethod, and restraint checking process.

Common activities, and hence operationalvariables, are defined and calculated on thebasis of collected data and common opera-tional characteristics of these rides. Real-lifedata is organized in three groups: (i) opera-tional variables such as loading time (timerequired to load customers), storage time(time required for customers to store theirpersonal items), restraint checking time, sig-nal ok time (time required to complete safetychecks), and unloading time(time requiredto unload customers); (ii) ride configuration-related variables such as number of cars,number of seats per car, and ride time; (iii)customer-related variables such as arrivalpattern and group sizes. In order to gener-alize the model, ride speed is adjusted whiletrack length is fixed to accommodate differ-ent ride times, and triangular distribution isused to fit all random variables.

Desai and Hunsucker compared thethroughput of the final model to empiricalobservations to validate their model. Theyreported that the difference between thetheoretical model and the empirical resultsis not statistically significant. Furthermore,they designed an experiment in which theychanged the parameters of each randomand fixed variable to see the changes in thehourly and daily ride capacity. The resultsof the experiment illustrated that reductionin time spent during storage, restraintchecking, and signal ok activities appearedto generate the greatest improvement incapacity. Other variables such as unloadingtime and number of parallel queues showed

APPLICATION OF OPERATIONS RESEARCH IN AMUSEMENT PARK INDUSTRY 3

no significant impact on capacity. Althoughthe experiment does not consider whetherthe parameters are achievable in real life,it demonstrates how a decision maker canutilize this tool: (i) to estimate the increasein throughput if number of employees isincreased, restraining time is reduced orextra cars are added, and (ii) to identifythe optimal operating environment whendemand is less than maximum capacity.

This tool can also be used in the designand analysis of new rides by using designparameters for the new ride (when avail-able) along with operational data associatedwith existing rides that are similar in charac-teristics. Also see Tibben-Lembke [6] whereclosed queueing models are used rather thansimulation under similar settings.

Despite all the efforts, waiting lines areunavoidable. One way to boost the customersatisfaction is to improve the quality of thetime spent in the line. Theme parks oftenattempt to ensure that their visitors are occu-pied with theming, shows, or TV monitorswhile they are waiting. Parks also managecustomers’ expectation by posting estimatedwait times. However, Dickson et al. reportthat wait time is still a major contributor tocustomer dissatisfaction [9].

Disney introduced the concept of a vir-tual queue, called Fastpass, at Walt DisneyWorld. The main promise behind the conceptis that visitors are assigned to a virtual loca-tion in the line and their physical attendanceis not required until it is their turn in theline. As a consequence, average time spentwaiting is reduced while average spendingper person is increased [9].

Currently, several paid and unpaid ver-sions of Disney’s Fastpass are used in themarket. The success of such an implementa-tion depends on the number and timing of theFastpass distribution during the day. Opera-tions research models can be used to identifythe optimal distribution that minimizes theoverall wait time of visitors while consideringthe decision-making process of visitors (i.e.,when the waiting time at the physical lineis 30 min, would a visitor immediately jointhe line or return in an hour later?). Simula-tion, Kalman filtering, and queueing theorybased models are proposed solve the problem

[7,10,11]. Note that virtual queues and theirimplementation should also be incorporatedin the simulation models described earlier inthis section.

PARK CAPACITY MANAGEMENT

As mentioned in the previous section, cus-tomers generally strive to maximize the num-ber of rides they take during their visit to atheme park. One of the main factors thatimpacts customer flows in the park is thewait time for these rides. As the wait time fora ride increases, the customers are temptedto try other rides with shorter wait times tobenefit from their limited time in the park;else they leave the park early and unsatis-fied. Hence, it is crucial to understand anddirect the flow of visitors in the park inorder to improve service quality and customersatisfaction.

Ahmadi [5] used real data provided by amajor theme park and analyzed how visitors’flow can be managed. The real data usedin the analysis consists of survey data thattracks visitors’ transition from one ride toanother, operational data such as park open-ing and closing hours, ride capacities, andhistorical daily demand. Conceptualizationof a visitor flow model consists of the des-tination of the visitors and the time thatthey spent at each destination. Once thetransition probabilities are estimated via thesurvey answers, the remaining issue to beaddressed is determining how much time thevisitors are spending on rides. Intending toproduce the desired result, one of the modelsdescribed in the previous section can be uti-lized to estimate the throughput of each ride.

Ahmadi provides two different opti-mization models that maximize minimum-weighted number of rides given any periodof time during the day [5]. The author usesa weighted average rather than the averagenumber of rides per person per day (which isa standard metric in the industry due to factthat all rides are not equally desired). Thefirst optimization model utilizes the actualtransition probabilities and determinesoptimal ride capacities but ignores the flowmanagement problem. Second optimization


model imposes actual transition probabilitieswhen they are zero and determines theminimum ride capacity as well as guidelinesfor transition probabilities. The author rep-orts substantial gains when visitor transitionprobabilities are influenced by the themepark management along with the ridecapacity optimization.

An emerging trend in the research is theutilization of multiagent systems to modelcomplex social structures. Kawamura et al.[12] implemented this concept to the themepark industry. The main requirement behindthe model is utilization of some type of com-munication device that provides informationon rides to visitors. The model is designedto control the flow of the visitors via thecommunication device in order to reduce con-gestion and increase visitor satisfaction usingtheir preferences. Although it seems straight-forward to conceptualize the problem, it isvery difficult to find the optimal solution.Hence, authors developed several approxi-mations that maximize the social welfare ofthe all visitors.

At this point the question is: What isrequired to implement a successful parkcapacity management solution? One keyaspect is the workforce scheduling. Work-force has to be managed carefully to achieveoptimal ride capacity while reducing the costas well as considering demand variabilityand business requirements such as minimumcustomer satisfaction level. Work force of atheme park consists of part-time, seasonal,and full-time employees. To better utilizethe flexibility provided by the part-timeemployees, number of visitors arriving everyhour and how those visitors flow in the parkhave to be tracked. Operations researchtechniques, such as resource allocationmodels, can then be utilized to determinethe number and mix of employees as well astheir schedule during the day.

TICKET PRICING

As mentioned in Formica and Olsen [13],the theme park industry requires substan-tial capital investment not only to facilitatethe design and development of the initial

establishment but also to update existingattractions and build new attractions. Com-pared to the upfront high fixed cost, theimpact of additional customers on the vari-able operating cost is minimal [14]. On theother hand, the unused capacity (or unsoldtickets) at the end of each day representswasted opportunity cost. Characteristics ofthe theme park business, such as high fixedcost, low variable cost, seasonal demand, andthe perishability of the inventory, are similarto those faced by other resemble industries(e.g., airline) in which revenue managementtactics are implemented effectively. Similarto those industries, the theme park industryalso seeks high utilization via price differen-tiation and increased repeat customers.

Differential pricing and promotionalstrategies are used to increase the numberof visitors during the low season and tocontrol the surplus demand during the peakseason. To that end, several ticket typesand bundles are introduced to accommodatedifferent customer segments such as locals,frequent visitors, corporate affiliates, andfree travelers. Introduction of annual passesis one example of how demand is stimulatedduring the low season by providing visitorsfull year access at a deeply discounted price.As one would expect, this deep discountcomes with restrictions. Restrictions such asnumber and timing of block-out days thatan annual pass holder cannot access thepark determines the price tag and purchaselikelihood of each annual pass.

Several annual pass packages are intro-duced on the basis of add-on features suchas free parking and restrictions in order tosegment locals and domestic visitors. On localbases, short-term marketing campaigns suchas three day resident packages are frequentlyused to stimulate local demand during peri-ods when demand is expected to be lower thanusual. Additionally, several discount levelsare made available to corporate affiliates andmultiday visitors.

Although the main portion of a themepark’s revenue comes from admission fees,a number of theme parks generate addi-tional revenue through hotel reservations,merchandise, and food and beverage sales.Additional services provide an advantage and


flexibility in pricing by allowing park ticketsto be bundled with hotel rooms and/or foodand beverage credit to attract families.

The key problem that the decision makerfaces is determining the mix of the cus-tomer segments in order to maximize theadmission revenue of the theme park. Heoand Lee [14] reviewed the current ticketpricing practice in the theme park indus-try. Based on their findings, they proposedimplementing the traditional revenue man-agement tactics used in hospitality and travelindustry such as pricing based on season, dayof week, demand level, and ticket purchasetime. Next, an example is provided to illus-trate how pricing based on purchase timeis used in the hospitality industry to sepa-rate customer segments. Airlines as well ashotels provide discounted fares if customersmake reservations 14 days ahead of theiractual travel dates. Unlike most businesstrips, leisure trips can be planned in advance;hence leisure customers readily take advan-tage of the low fares by reserving hotel roomsand/or plane tickets early.

Heo and Lee tested the perceived fairnessof the proposed strategies and comparedthese with the hospitality industry where thecustomers are well aware of the implemen-tation of revenue management tactics. As aresult of their survey, they concluded thatcustomers’ perceived pricing based on seasonand day of week in the theme park industry tobe fairer than a similar strategy implementedin the hospitality industry. Although mostof the US theme parks currently implementflat-rate admission fees and try to achievethese authors’ suggestions through seasonalpromotions and discounting programs, theauthors propose a more dynamic pricingstrategy based on the season and the day ofweek. One should also note that implemen-tation of such a strategy in the theme parkindustry is costly and not straightforward.The name of the customer has to be printedon the tickets and validated while accessingthe parks to prevent revenue leakages thatcan occur due to secondary markets.

While Heo and Lee do not provide detailson how the suggested strategies might beoperationalized, one might surmise that asuccessful implementation of a disciplined

pricing strategy requires understanding andanticipation; in other words, forecasts of dailydemand for each customer segment and esti-mates of seasonal demand–price relation-ship. The forecasts then have to be fed intosome type of optimization or heuristic algo-rithm to develop ticket prices while consider-ing business constraints.

In a manner similar to travel and hos-pitality industries, one solution may be torely on an algorithm that generates a min-imum ticket price (bid price) for each dayand then blocks all discount levels below theminimum ticket price. At first, this solutionmight appear easily implementable, but theproblem with implementation of this strategyis twofold: First, it is very difficult to asso-ciate a daily ticket value with an annual pass.Second, annual pass demand blocked duringthe peak season will impact the demand forthe low season. As the number of dates thatare blocked during peak season increases, thevolume of the annual pass sales decreases aswell as the business that annual pass holdersbring during the low season.

An alternative to this approach is buil-ding a simulation model that gives thedecision maker flexibility to test differentparameters and strategies easily. Advan-tages and disadvantages of each approachcan then be determined before making thefinal decision.

OTHER REVENUE SOURCES

Although the main portion of a themepark’s revenue comes from admission fees,other sources, such as hotel reservations,merchandise, and food and beverage sales,contribute up to 70% of the revenue. SixFlags and Disney generated, respectively,47.6% and 68% [15,16] in the same order oftheir revenue from admissions in 2007.

Price Waterhouse Coopers completed aresearch on the on-site accommodations at29 top European theme parks [17]. Of these29 theme parks, 14 posses on-site accom-modations and 5 planned to develop on-siteaccommodations by the end of 2010. A formergroup of theme parks reported that on-siteaccommodations contributed to the satisfac-tion of customers by providing a complete


experience, and contributed to the themepark’s revenue by tapping into the corporatemarket.

Although the degree of the theming variesacross hotels, it is reported as the mainelement that contributed to the overall expe-rience of the leisure visitors. Consequently,this led to an increased mean length of stayof 2.8 days for theme parks with hotels com-pared to 1.7 days without hotels. Themeparks also command higher room rates withthe introduction of the themed rooms. Onthe other hand, facilities such as confer-ence rooms and spas allowed theme parks toreach different markets and increase utiliza-tion during the low season. In addition, parktickets that are bundled with hotel roomsincreased the marketing power and revenueof the theme parks.

During the high season, the real challengeis to match excess demand with the limitedsupply on hand. Hence, theme parks have tobe clever about how to price the hotel roomsin order to maximize revenue. Rooms pricedtoo high keep the customers away and theunused capacity will perish; rooms pricedtoo low cause a theme park to miss revenueopportunity. This problem is a specific caseof the capacity control problem that is wellknown in operations research. The solutionof the problem is inventory assigned to eachprice level: in other words, price for eachremaining room in the inventory. While it isknown that the capacity control problem canbe formulated as a dynamic programmingmodel, this formulation is intractable in prac-tice due to its size and complexity. As a result,various approximation methods are proposedin the literature. Decomposition and deter-ministic linear programming approximationsare formulated and have been successfullyused in practice. Lately, several stochasticprogramming approaches that considerdemand uncertainty have been published.For further discussion see Buke et al. [18].

Food and beverage facilities in a themepark consist of quick-service and sit-downrestaurants. Sit-down restaurants share sev-eral characteristics with the hotels, such asreservation lead time, fixed capacity, perish-able inventory, and seasonal demand. Hence,the associated revenue optimization problem

can be conceptualized in a similar manner.In the case of a restaurant business, inven-tory is defined as the time that is required tocomplete a meal and output is the number oftables available for reservation in addition toprice differentiation. For further discussionof this topic, see Kimes [19].

In addition to hotels and restaurants,Rajaram and Ahmadi [20] estimated thatmerchandise sales contribute up to 40%of theme park profits. Unlike the hoteland restaurant businesses, merchandiseinventory is not perishable and location ofinventory in the store is adjustable. Hence,a different revenue optimization approachmust be taken. Pricing with the considerationof inventory is a well-studied topic not justin general but also specifically in the field ofrevenue management. Please see the liter-ature for a general review of this topic [21].For such problems, the kernel of the solutionis in the estimation of the price–demandrelation. In real-world applications, it isdifficult to find a case for which demand foran item is related only to its price. Ke [22]took a more holistic approach and consideredshelf space and location of each productas well. Assortment changes in a store areincorporated in to the price–demand modelalong with seasonality. The model aimed toidentify the assortment changes (i.e., shelfspace and/or location of one or more productsare changed) that made positive impact onthe store revenue. He utilized data from amajor resort destination and reported 5%revenue improvement over historical assort-ment changes. Other factors that cannot becontrolled by the store management such asnumber of visitors, weather, and competingproducts that contribute to the variability indemand must be identified and incorporatedinto the formulation in order to isolate theirimpact on demand.

Rajaram and Ahmadi [20] developed a sur-vey to assess the relationship between visitorflow and store sales. In the survey, visitorswere expected to enter the rides in whichthey participated, time that they enteredthe queue, time that they left the ride, andamount of money they spent after each ride.A regression in which the dependent vari-able is store revenue and the independent


variable is the number of visitors is devel-oped, and the adjusted R2 is for the resultingmodel is 0.96. Contrary to the aforemen-tioned approach, authors developed a modelthat utilizes this relationship to maximizerevenue rather than price. They built an opti-mization model in which revenue is modeledas weighted visitor flow where weights arecalculated for each location using per-personspending at that location. As a result of theanalysis, they estimated an average profitlift of 9%.

CONCLUSION

Although marketing and strategic manage-ment issues in the theme park industry havebeen studied extensively, documented appli-cations of operations research in the themepark industry are limited. Simulation tech-niques have been used to design rides andmanage the wait time associated with ridesas well as controlling the flow of the vis-itors via multiagent systems. Optimizationtechniques have been used to manage parkresources intelligently and increase visitorsatisfaction. Finally, revenue managementtactics have been applied to pricing ticketseffectively to prevent revenue leakage.

Because theme parks share several char-acteristics with other service industries, theresearch on the latter one can be a good start-ing point to augment the literature. Althoughthere is detailed research in the field of rev-enue management on hotels, merchandise,and food and beverage, it is still an open ques-tion how existing models can be improved byincorporating the characteristics of the themepark industry. Also, there is no publishedresearch completed on theme park work forcescheduling problem.

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