Activity and value orientated decision support
for the development planning of a theme park
Ren-Jye Dzeng
*, Hsin-Yun Lee
Department of Civil Engineering, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsinchu 30050, Taiwan, ROC
Abstract
The development of a large theme park usually includes multiple phases. The combination and development ordering of facilities in these phases have a great impact on the attractiveness of the theme park. Examples of such facilities are attractions, food service, accom-modation, and supporting facilities. Some of these facilities although highly profitable, cannot attract visitors on their own, while others may boost the visitor count, yet by themselves do not make a profit. This research considers the values that each development activity brings to the project, and prioritizes feasible alternatives based on their net present values. Based on the integration of simulation and the genetic algorithm, a decision support system has been developed to determine the combination and ordering of facilities, and the resources needed for each development step. This development plan will provide investors with systematic and quantitative information that will help them to determine the development portfolio of each facility under the constraint of the funding program.
2006 Elsevier Ltd. All rights reserved.
Keywords: Theme park; Development plan; Genetic algorithms; Simulation
1. Introduction
Developing a theme park may often span decades, requiring a high level of capital investment, and a large par-cel of land to build a large number of facilities on. Conse-quently, the project scheduling is usually contracted out to a consulting firm, and includes: (1) a project feasibility study and an estimate of the development scale; (2) the ini-tial design concept of the facilities; (3) a stage-based devel-opment progress and a financial model; and (4) a list of the detailed designs of facilities that need to be developed.
Inappropriate strategy as well as incorrect scheduling may cause the failure of any development project, and especially that of a theme park. Disneyland Resort Paris is a case in point. Within eighteen months after its opening, it had lost 10 billion US dollars. Up to December 1993, less than two years after the opening, not only was the initial capital consumed, but they had to raise an additional loan
of 1.75 billion US dollars to maintain the operation (
Spen-cer, 1995). Three months later, a new crisis threatened its
survival. Two major oversights attributed to the failure of this development project. First, Paris is located at about 48 latitude, and relatively close to the North Atlantic Ocean, resulting in cold and wet winters. This fact alone will drastically decrease the enthusiasm of people to partic-ipation in the outdoor activities offered by the theme park. However, this fact was simply neglected. Second, even though the visitor count was expected to decrease in the cold wintry months, excessive shows and activities kept being launched, resulting in an even further waste of capital. An additional issue that was not considered or investigated was the fact that there is a fair amount of ‘‘anti-Americanism’’ in France, and Disney is seen as the epiphany of US commercialism by many French as well as many Europeans.
The case of Disneyland Resort Paris shows the vital importance of having the right strategy and a correct sche-dule prior to even executing such large a project. During the extensive period of project development, continuously changing risks become embedded in the construction cost 0957-4174/$ - see front matter 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2006.08.002
*
Corresponding author. Tel.: +886 3564 7525; fax: +886 3571 6257. E-mail address:rjdzeng@mail.nctu.edu.tw(R.-J. Dzeng).
www.elsevier.com/locate/eswa Expert Systems with Applications 33 (2007) 923–935
affecting the operation of each facility, as well as the rela-tionship between facilities, especially those involving the supply of resources. The fact that the planner will have to consider multiple variable factors simultaneously is inev-itable. This will make it very difficult to settle on an optimal development strategy among the multitude of combina-tions of potential facilities and scheduling plans. Therefore, support in the decision making process of the development schedule will aid the planner to better understand the influ-ence of each variant on the project outcome, as well as the effectiveness of each schedule combinations, allowing him to determine the optimal development strategy.
Various researches have focused on the issue of model-ing the project decision-makmodel-ing and plan optimization,
such as the Multi-Criteria Decision Model (e.g., Hsieh &
Liu, 1997), Resource-Constrained Scheduling (e.g.,Leu &
Hwang, 2002), and the Ranking and Combination of the
Project Investment Model (e.g., Ghasemzadeh & Archer,
2000). These models are unsuitable for theme park
devel-opment projects because they cannot simultaneously deal with selection, ordering, and scheduling of feasible invest-ment items.
For example, Hsieh and Liu’s Time-series Combinato-rial Planning Model in Infrastructure Plan (Hsieh & Liu,
1997) has two assumptions: (1) sub-projects are
indepen-dent to each other, and (2) activities cannot be separated or partially completed. These two assumptions are unsatis-factory for a theme park development. Example 2, Most Resource-Constrained Scheduling models fail to consider the selection of activities (i.e., not every activity must be executed) but can only provide solutions with specified activities and resources. Example 3, Ghasemzadeh and Archer’s supporting system for decision making of a
port-folio with multiple items (Ghasemzadeh & Archer, 2000)
fails to consider potential situations when the start and fin-ish dates of items are movable.
This study is aimed at constructing a decision support system for the decision-making process when laying out the order of a development plan. The project planner inputs the activities, their start and finish dates, estimated costs and revenues, and resource relationships. All these data are simulated and analyzed in order to predict the overall effectiveness of the project. Various schedule combi-nations will be calculated to determine the best develop-ment strategy so as to provide the planner with a point of reference. This will help overcome the complexities of the decision-making in the development of a theme park facility. This study attempts to achieve its goal through the following approaches:
(1) Investigate the characteristics of a theme park devel-opment project, the different types of facilities and their features, characteristics of different types of strategies and scheduling systems, and the demand, supply, and the effect of different facilities.
(2) Construct a simulation network model of a theme park development project, that includes all the
features and correlations of the activities involved in the planning, construction, and operation. (3) Integrate the polyploidy genetic algorithm (GA) and
the simulation analysis to design a decision support system for determining the project strategy and sche-dule plan with the maximum net present value (NPV) for the reference of project investors and planners. 2. Characteristics of a theme park
2.1. Type of project
A theme park development project is a subcategory of land development. While other development projects are intended to be rented, sold or used as an operating facility, a theme park facility is constructed and has a cost efficiency model that are aimed at recreation and entertainment. It has 3 main characteristics:
(1) It requires a large investment of resources: A compar-atively large parcel of land is required for a theme park, such as 105 hectares for the Six Flags Magic Mountain, Los Angeles, USA. In addition, very large capital investments are needed for the construction of facilities; for example, ‘‘Floorless Coaster’’ in Janfu-sun Fancyworld of Taiwan costs $ US 13 million, which is similar to other roller coasters in other theme parks. Also, the need for human labor to operate the facilities once they are built is enormous, such as Dis-neyland Resort Paris with as many as 12 000 employ-ees (Wylson & Wylson, 1994).
(2) Simultaneous progress of construction and opera-tion: Due to the huge scale of theme parks, the devel-opment project is often decomposed into several segments to be executed in different periods or loca-tions, resulting in the construction of one set of facil-ities while operating another set. The revenue gained from operating the facilities already built becomes an essential source of capital for financing the construc-tion of the other facilities. A properly staged develop-ment project can drastically reduce the initial capital requirements, as well as restrain the cash flow within a secure condition.
(3) Multiple variable factors and risks: As a result of the extended length of time and the large number of facil-ities involved in the development of theme parks, many of the factors that may impact upon the overall performance of the project tend to vary with time, such as the preferences of the customers (old facilities tend to gradually lose favor) and risks from the nat-ural environment (such as, seasonal climatic varia-tions or acts of God like earthquake). Some factors may influence only specific facilities, such as water slide, boating, and other outdoor water activities which are subject to the impact of the weather. Also, construction costs and the costs to operate a facility vary with the fluctuation of the price index.
A theme park development project differs from a con-struction or portfolio project, as shown inTable 1. A theme park development project has unique features, such as fre-quent non-continuity and a close resources sharing/support relationship between activities, making it more complicated than the other two project types.
2.2. Facilities
Previous research into theme park operations revealed that theme park facilities must expand continuously in
order to maintain their attraction to the visitors (Wylson
& Wylson, 1994). This characteristic demands constant
investment of resources in new facilities to maintain and
increase revenue.Table 2shows some of the common
facil-ities in theme parks.
Attractions play a crucial role in drawing ticket-buyers to a theme park. Each attraction has its own product life cycle for its ability to attract visitors, with a profit that fluc-tuates over time. In general, an attraction that has a higher initial cost may remain attractive for a longer period. In addition, whether or not neighboring resorts provide simi-lar attractions also has a considerable influence on the level
of revenue. The gross income of certain attractions is sub-ject to seasonal peaks. For example, in Northern Europe where the weather is often too cool for water activities even during the summer months, most water parks are designed indoors, and provide year-round entertainment. On the other hand in Southern Europe and Southern USA, many water parks are built outdoors and are open for only a few
months each year (Wylson & Wylson, 1994). The
develop-ment and construction of large-scale facilities usually takes a long time, and some may even require 2–3 years from the initial design phase, through the ordering from the vendor, construction, and installation, to operation.
As shown inTable 2, attractions can be categorized into
five types; mechanics, scenes, shows, electrical instruments, and sports. With the advances in both electrical and mechanical technologies, the attractions are becoming more versatile. A complete theme park is composed of var-ious types of attractions to satisfy visitors of all ages and preferences.
In addition to attractions, providing food services, com-modities, and accommodations are an additional source of considerable profits. For example, in the Six Flags theme parks, 55% of the total revenue comes from theme park Table 1
Comparison of different projects
Characteristics Theme park development projects Construction projects Portfolio projects Project planning tasks h Selection of development
items
h Scheduling h Selection of
investment items
h Scheduling h Allocation of capitals
Strategic objective h Maximum project benefits
h Shortest duration h maximum project benefits h Lowest cost
Activity continuity h Usually assumed as non-continuous
h Usually assumed as continuous
h Usually assumed as continuous
Activity relationship h Sequential relationship h Sequential relationship h No sequential relationship h Sharing and support of
resources among activities Resource utilization/
production
h Utilization h Utilization h Utilization
h Production h Production
Resource allocation h Consideration of both utilization and production
h Leveling of only resource utilization
h Consideration of both utilization and production
Table 2
Common facilities in theme parks
Type Common facilities
1. Attractions Mechanics Roller coaster, Ferris wheel, Merry-go-round
Scenes Garden, maze, ghost house, zoo
Shows Outdoor theater, 3D theatre, animal show or acrobatics, fireworks Electrical instruments Electrical game park, space trip simulator, remote control car racing Sports Horseback riding, boating, golf course
2. Food service Restaurant, snack bar, vendor machine
3. Commodity selling Souvenir shop, shopping alley
4. Accommodation Hotel, camping ground, villa
5. Service facilities Roads, parking lot, ticket box, phone booth, toilets, visitor center, tour bus service 6. Supporting facilities Administration office, water treatment plant, cremator, common duct
admissions, and 45% comes from food, merchandise,
accommodations and others (Six Flags Co., 2005).
Accom-modation facilities include hotels, villas, and camping grounds, all of which may yield significant profits when there are sufficient attractions to entertain the visitors for more than one day. In Disneyland Resort Paris, Walter Disney Co. built 5 hotels and 1 large camping ground in the first stage of the whole project, to create profits by sat-isfying the visitors’ demand for accommodation (Wylson &
Wylson, 1994).
However, the income gained from the food services, commodity sales, and accommodation strictly depends on the amount of visitors and their average length of stay, all of which is greatly influenced by the ability of the attrac-tions to draw in visitors. Therefore, the construction and operation schedule of these facilities must correspond with the development and the scale of the attractions in order to avoid the wasting of resources caused by hasty devel-opment.
The other two facilities in Table 2are service facilities and supporting facilities. Service facilities refer to equip-ment that can be used by visitors but doesnot provide enter-tainment, while supporting facilities maintain the operation of the whole theme park. Except for the parking lot, most of the supporting facilities do not yield income, but they are crucial to the sound operation of the attractions, the food services, commodity sales, as well as the accommodations. Usually, service and supporting facilities are necessary for the operation of theme parks, yet many of them can be con-structed stage by stage and in accordance with the develop-ment of the theme park’s scale, such as roads.
The above characteristics indicate that timely develop-ment of facilities for the allocation of limited resources is important for generating optimal revenue. A cycle of ‘‘develop–operate–create income–invest income in further development’’ is created in the project scheduling to achieve optimal profits of the whole project.
2.3. Supply, demand, and effect of facilities
The allocation of the type of facilities, the quantity, and the scale must all be based on the potential to draw visitors and the potential profits that can be obtained thereof, as
estimated by a detailed market survey (Wylson & Wylson,
1994). Target subjects are usually divided by the distance
they live away from the theme park. The majority of the visitors, 70–80% of the total, spend 2–3 h on getting to the theme park. Research methods for determining market scale and for sales forecasting of products and/or services are not discussed in this paper.
The construction and operation of any facility in a theme park development project must be carefully consid-ered in conjunction with external and internal effects. External effects refer to, for example, when the launching of a merry-go-round may have to compete with a similar attraction in a neighboring resort and therefore may bring in profits less than estimated. Internal effects include a
situation where for example a shortage of food services may shorten the length of stay, as well as reducing the level of satisfaction originally anticipated by the attractions provided.
3. Simulation networks
The ordering of the stages of development in theme parks can be arrived at through analysis in simulation net-works, in which the relationship between activities can be described by, and the project efficiency can be estimated from, the results of the simulation.
Each facility involved in the development of a theme park must undergo a certain amount of planning, construc-tion, operaconstruc-tion, closing, dismantling, and divesting. In pro-ject scheduling, each stage can be viewed as an individual activity that includes lead time, cost, and revenue. The cost and revenue of an activity may be viewed as the input and output of capital resource. In addition to capital funds, resources may be generated or utilized by other activities. For example, the operation of a horse-riding field may be utilizing the parking spaces that were created for operating parking lots. This study constructed simulation networks to explain the relationships between the generation and utiliza-tion of resources in all activities. These simulautiliza-tion networks
are based on the CYCLONE (Halpin, 1974) modeling
because it has a clear and simple symbolic structure com-pared to other simulation techniques. STROBOSCOPE
(Martinez, 1996) is incorporated in this simulation analysis
program with setting options for priority values, making it appropriate for system architecture in this study.
3.1. Activities and resources
The simulation network inFig. 1is designed for project
activities involving a roller coaster. The duration of each Combi (Units arriving at Combi will be processed if units are available in each preceding Queue node.) in this figure occurs in the same time unit, which can be set as one month, one quarter, or one year. Both Combi and Queue (Queue provides a position that allows units to be delayed pending Combi activities) can be divided into two catego-ries, actual and virtual.
3.1.1. Actual activity and resource
Combi and Queue denote the actual activity and resource in project scheduling. InFig. 1, there are seven actual activ-ities, Design_RollerCoaster, Construct_RollerCoaster, Oper-ate_RollerCoaster, Operate_Hotel, Operate_SouvenirShop, Operate_ParkingLot, and Operate_SupportFacilities, as well as five actual resources: Cash, Parking_Capacity, Sup-port_Capacity, SouvenirShop_Demand, and Lodging_De-mand. They have a utilization relationship with each other. For example, Parking_Capacity, which is as a result from the execution of Operate_ParkingLot, is consumed by visitors who are drawn by Operate_RollerCoaster. On the other hand, SouvenirShop_Demand and
Lodging_De-mand are as a result from Operate_RollerCoaster, and these demands may influence the revenues (which later become Cash) generated by Operate_SouvenirShop and Operate_ Hotel.
Actual resources can be divided into accumulative and non-accumulative ones. Since the duration of each Combi is fixed as one time unit, the surplus of some resources may be accumulated to be used in the following time unit (such as Cash). However, some resources cannot be accu-mulated, such as Parking_Capacity.
An actual activity, expressed as a Combi, is executed (or not) according to the sufficiency of the resources required. In reality, the execution of a project shows differ-ent degrees of priority in the utilization of the same single resource among different activities. For example, parking lots with limited capacity should be used for facilities that can generate a higher return. In STROBOSCOPE, each activity possesses a priority value, either fixed or variable. At a certain point in time, an activity with a higher priority value implies a higher execution moment. The execution value of an activity depends on current or future ‘‘direct revenues derived as such’’ and ‘‘their contribution to facil-itate the operation of other facilities’’. For instance, a roller coaster has an execution value because it provides direct income from ticket sales; while service facilities, such as roads, also have their own execution value even though they may not yield direct revenue they facilitate the smooth operation of the roller coaster that brings income. In other words, the revenue of the roller coaster shows the execution value of both the roller coaster and the service facilities.
In our research, the priority value of each activity to resource utilization is applied to determine the execution
value. Set between 0 and 1, the relative measures of the pri-ority values are used to control the dynamic balance between the supply and the demand of the resources. For
example, when both Construct_RollerCoaster and
Design_FerrisWheel needed Cash at the same time, the activity with the higher priority value should be given preference.
3.1.2. Virtual activity and resource
Virtual activity does not exist in actual project schedul-ing; rather, its purpose is to determine whether the activity or project should be carried out or not. Postponing the exe-cution of activities when enough resources are available should be controlled by virtual activity. Even when pro-vided with sufficient resources, sometimes activities in a theme park development project may be postponed for a few reasons. One example is the case of Operate_Parkin-gLot, which is expected to be sufficient, and is supposed to have been supported by the income it produced during the year. There is no capital money to be invested in the expansion of the parking lot, because an overcapacity in parking would cause unnecessary cost for maintenance and management. Each virtual activity has a corresponding actual resource (such as Cash_Activation_Threshold, in
Fig. 1, corresponding to the actual resource Cash). A
com-parison of priority values between virtual activity and actual activity that intend to use the resource in question is conducted to determine the priorities of resource utiliza-tion and allocautiliza-tion. The priority value of each virtual activ-ity is 0 while those of the actual activities that could be executed fell between 0 and 1. On the other hand, the vir-tual activities hinder the execution of the acvir-tual activities Fig. 1. Simulation network of roller coaster.
with a priority value of 1 by capturing all the correspond-ing resources, even when sufficient resources are available. The virtual resources are used to control the activity sequence. Activities associated with one facility may fea-ture a sequential order. In the case of the roller coaster, activities should abide by the order of ‘‘design–construct– operate’’, in which the execution of the next step shall not be prior to the completion of the previous one.
Fig. 1shows that the three virtual resources
(Design_Roll-erCoaster_Queue, Construct_RollerCoaster_Queue, and
Operate_RollerCoaster_Queue) correspond to the three actual activities. For example, the virtual resource Design_RollerCoaster_Queue corresponds to the actual activity Design_RollerCoaster. In the beginning, the quan-tity of the stand-by resources is set as 1, and the execution of Design_RollerCoaster for a unit of time may consume 1/6th of Design_RollerCoaster_Queue. After 6 units of time, all the Design_RollerCoaster_Queues are consumed, indicat-ing that Design_RollerCoaster is completed with a quantity of Construct_RollerCoaster_Queue as 1, which further trig-gers the execution of the activity Construct_RollerCoaster. 3.2. Execution value of activities
In the above simulation network, the priority value of the activity decides whether the activity may be executed, indicating the execution value of that activity at that point in time. Combining all the priority values of the activities for all units of time is the project development strategy, and the start and finish date of each activity estimated in the simulation with priority value combinations will be the project schedule.
Since various factors must be considered in the evalua-tion of the execuevalua-tion value of an activity, project planners may find it difficult to determine the optimal plan with only individual judgments and experiences. Therefore, this study is facilitated by a computer in order to construct an application system. The GA was applied in the search of a near-optimal solution from combinations of priority values of activities. In addition, viewpoints of activity exe-cution value are included to achieve optimal project scheduling.
4. Architecture of AVO-PLAN
This study attempts to construct an AVO-PLAN (Activ-ity-Value- Oriented PLANning) decision support system, in order to facilitate the decision-making process of devel-opment ordering of facilities in theme parks. Since the problem-solving of this issue has features of multiple peri-ods and situations, employing a polyploidy GA structure is an ideal approach to combine development strategies of each period into a plurality of chromosomes. At the same time, a large number of development strategy combina-tions can rapidly reach convergence and solution. An esti-mate on the project NPV of each development strategy can be obtained from the simulation.
4.1. Application of a polyploidy GA
Since the introduction by John Holland in 1975
(Holland, 1975), the GA has been gradually applied to a
wide range of fields. However, the traditional GA usually applies the genetic structure of haploid, in which single-dimensional genetic encoding is severely limited to express potential solutions. In the real world, many problems feature multi-periods, multi-steps, or multi-situations. Therefore, a polyploidy genetic structure may express and reveal more practical solutions.
The genetic structure of polyploidy can be seen in a gene composed of multiple chromosomes. Human genes, for example, are diploid type with 23 sets. In fact, the poly-ploidy structure is very common among creature in nature,
including diploid, triploid, and teraploid. Fig. 2 shows a
diagram for haploid, triploid, and complex chromosomes
(Wu, 2002). Haploid genes are usually utilized to express
a biological appearance (such as skin color), while a poly-ploidy structure may be viewed as a combination of several haploid genes.
Polyploidy structure provides various phenotypes or applicable behaviors, so that individuals may perform dif-ferent strategies for survival during changes in the environ-ment. On the other hand, the polyploidy structure still follows the model of genetic dominance proposed by Men-del in the 19th century, in which only one chromosome among all others in the polyploidy gene would become the phenotype for the organism at a single period of time (Wu & Sun, 2002).
The polyploidy may be applied to solve complex issues with multiple situations or parameters. Collingwood observed the process of searching for the optimal solution for the analytical comparison between the effects of a polyploidy and a haploid GA. It was found that, since the polyploidy structure conserves more information, more opportunities to achieve better solutions may be obtained from it rather than from the haploid structure for the same issue (Collingwood, Corne, & Ross, 1996).
Many studies have been proposed applying the poly-ploidy GA to construct problem-solving models. For example, Wu and Sun constructed the fuzzy dominances of several typical fuzzy models in a study that applied
haploid
triploid
complex chromosomes
polyploidy structure to the structure of membership func-tions (Wu, 2002) (Wu & Sun, 2002). Their experimental results revealed that the proposed model could not only effectively solve problems of multiple situations but also evolved into adequate polyploidy structure, featuring
advantages in performance and efficiency (Wu, 2002).
The multi-period and multi-situational issue in this study may be solved under the structure of polyploidy genes, in order to record and modify the strategies of the project activities in each time unit.
4.2. Integration of simulation and GA
The integration of simulation and GA has been applied to many different fields, because it may yield a satisfactory result in the search for an optimal solution. In construction
projects, for example, Cheng and Feng integrated
CYCLONE and the GA to develop a GACOST system.
Their study presented a mechanism that integrates simula-tion with the GA to find the best resource combinasimula-tion for a construction operation (Cheng & Feng, 2003). In addi-tion, Marzouk and Moselhi integrated simulation and the GA to estimate the time and cost of earthmoving opera-tions (Marzouk & Moselhi, 2002).
A similarity between theme park development projects and other studies that applied simulation lies in the huge number of uncertainties and the probability distribution of the data (such as the ticket income). On the other hand, the difference is that the development ordering is based on the execution value of the operations. Instead of incorpo-rating the start and the finish date of each activity into the genetic coding, this approach calculates the priority value of each activity in each time unit. In addition, the pri-ority value of each time unit is regarded as an independent chromosome, and all the chromosomes are combined together to form a polyploidy. Thus, the structure can be
better expressed than in other studies with only one chro-mosome (haploid).
4.3. Constructing the system
As shown in Fig. 3, AVO-PLAN is comprised of two
sub mechanisms: simulation and the polyploidy GA. After inputting data by the user, AVO-PLAN automatically constructs a simulation network and then conducts the polyploidy GA with NPVs calculated from the results of the simulation. Conditions for convergence toward near-maximum NPV are then determined after constant selections via generations, in order to end up with the near-optimal priority value strategy combination and pro-ject schedule.
First, the user is required to input the total duration of the project for calculating the NPV. Also, the user has to input activity information of each facility to be developed
(including name, duration, and resources) and the demand-and-supply relationship of the resources between each activity. In addition, the parameters of the polyploidy GA are indispensable, including the initial number for pop-ulation size, generation size, crossover rate, and mutation rate.
Second, AVO-PLAN constructs a simulation network in accordance with the data input by the user. Each activity in this network has a priority value, to which the resource application sequence is referred. All the priority values of each activity are incorporated into a set of priority values, which then undergoes simulation analysis. Estimations on cash flow of the project are then obtained from the simula-tion results, followed by the calculasimula-tion of the NPV.
Third, the NPV derived through the calculation in the simulation analysis is taken as the fitness value for the GA. The near-optimal solution is then determined by the judgment of whether this fitness value satisfies the conditions for convergence in the GA. In order to incor-porate the priority values set into the polyploidy GA, AVO-PLAN randomly generates a priority value set of the first generation as the genetic code.
In each time unit T, each activity possesses a priority value. As T = i, activity A1 has a priority value of P1,i,
and the priority value set of n activities (A1, A2, . . . , An) at
T = i can be stated as P1,i, P2,i, P3,i, . . . , Pn,i., the genetic
encoding of a chromosome is therefore constructed. If a project spans a period of m time units (such as 120 months, 40 quarters, or 10 years) in total, then the genetic encoding of the priority value sets at each time unit combines into a Table 3
Genetic code of priority value sets as T = 0 m
A1 A2 A3 A4 A5 . . . An T = 0 P1,0 P2,0 P3,0 P4,0 P5,0 . . . Pn,0 T = 1 P1,1 P2,1 P3,1 P4,1 P5,1 . . . Pn,1 T = 2 P1,2 P2,2 P3,2 P4,2 P5,2 . . . Pn,2 T = 3 P1,3 P2,3 P3,3 P4,3 P5,3 . . . Pn,3 T = 4 P1,4 P2,4 P3,4 P4,4 P5,4 . . . Pn,4 T = 5 P1,5 P2,5 P3,5 P4,5 P5,5 . . . Pn,5 . . . . T = m P1,m P2,m P3,m P4,m P5,m . . . Pn,m uniform-point crossover A1 A2 A3 A4 A5 … An T=0 0.21 -1 0.15 0.85 0.05 … 0.33 T=1 0.77 0.34 0.73 -1 0.41 … 0.81 T=2 -1 0.61 0.34 0.98 0.18 … -1 T=3 0.03 0.88 0.27 0.46 0.62 … 0.59 T=4 0.16 0.25 0.92 0.78 0.55 … 0.11 T=5 0.82 0.02 0.68 -1 0.29 … 0.09 … … … … … T=m0.52 -1 0.09 0.57 0.38 … 0.07 A1 A2 A3 A4 A5 … An T=0 0.15 0.42 0.72 0.57 0.55 … 0.37 T=1 0.53 0.78 0.35 0.90 0.11 … 0.66 T=2 0.81 0.91 0.24 0.54 0.24 … -1 T=3 0.68 0.10 0.81 0.85 0.48 … 0.04 T=4 0.31 0.69 -1 0.72 0.71 … 0.47 T=5 0.02 0.45 0.95 0.36 0.75 … 0.19 … … … … … T=m0.28 0.73 0.08 -1 0.66 … 0.83 A1 A2 A3 A4 A5 … An T=0 0.21 0.42 0.15 0.85 0.55 … 0.33 T=1 0.53 0.34 0.73 -1 0.11 … 0.66 T=2 -1 0.91 0.24 0.98 0.18 … -1 T=3 0.03 0.88 0.27 0.85 0.62 … 0.59 T=4 0.31 0.25 -1 0.78 0.71 … 0.11 T=5 0.82 0.02 0.95 0.36 0.29 … 0.19 … … … … … T=m0.28 0.73 0.08 0.57 0.38 … 0.83 A1 A2 A3 A4 A5 … An T=0 0.15 -1 0.72 0.57 0.05 … 0.37 T=1 0.77 0.78 0.35 0.90 0.41 … 0.81 T=2 0.81 0.61 0.34 0.54 0.24 … -1 T=3 0.68 0.10 0.81 0.46 0.48 … 0.04 T=4 0.16 0.69 0.92 0.72 0.55 … 0.47 T=5 0.02 0.45 0.68 -1 0.75 … 0.09 … … … … … T=m0.52 -1 0.09 -1 0.66 … 0.07 Fig. 4. Uniform-point crossover of polyploidy genes.
polyploidy with multiple chromosomes, which can be used to describe the priority value of the resource utilization of
each activity at each time unit, as shown inTable 3.
Fourth, the ‘‘Roulette wheel’’ method was applied to select the priority value set with an equal number to the population size. The probability of selection is propor-tional to the area in the circle graph; a greater area brings more chances to be selected, which is correlated to the
fit-ness of the individual (Falkenauer, 1999). To avoid
excel-lent individuals from being dropped during the selection process, AVO-PLAN preserves individuals with NPV ranked among the top 5 percentile.
Fifth, the priority value sets selected can undergo cross-over and mutation, so as to produce priority value sets of the next generation. In most case, crossover in haploid may be performed in one-point crossover, two-point
cross-over or uniform-point crosscross-over.Fig. 4plots the process of
uniform-point crossover performed in every gene of the individual, in which the exchange between each gene is independent from each other.
In addition to the crossovers in the haploid GA, the time unit crossover can be executed in the polyploidy GA in this paper, as shown inFig. 5. The time unit crossover is a kind of crossover performed by all chromosomes at the same time unit. The priority values of the same time unit became a chromosome of polyploidy, and their comparative size determines the demand-and-supply of resources in this par-ticular time unit. After several generations, some of the pri-ority value sets in a certain time unit of the generation individual may have been excellent. A time unit crossover can maintain these superior chromosomes and prevent the
chromosome from being broken during crossover. There-fore, timely adoption of a time unit crossover in the selec-tion through generaselec-tions may very possibly figure out more ideal priority value sets. Further investigation on this hypothesis is discussed in the case study of this paper.
Sixth, the next-generation priority value sets generated via crossover and mutation then undergo another simula-tion analysis, and the NPV is then decided based on the simulation results. This procedure to generate next-genera-tion priority value sets is continuously repeated till the maximum NPV reaches stability, i.e., satisfies the conver-gence conditions of the GA. The priority value with maximum NPV becomes the guideline of the project devel-opment strategy, by which AVO-PLAN conducts a simu-lation analysis and uses the results to estimate the near-optimal project schedule, as a reference for the user in project planning.
5. Case study
To understand the advantages brought by AVO-PLAN proposed to the scheduling of a theme park development project, we will compare our system with experts and other methodologies. A case adopted and simplified from ‘‘BADA Forest Theme Park in Taiwan’’ is applied for the analysis and the verification of our system.
5.1. Case introduction
Usually, dozens of facilities are involved in a theme park development project. To facilitate analysis, it is supposed in
time unit crossover
A1 A2 A3 A4 A5 … An T=0 0.21 -1 0.15 0.85 0.05 … 0.33 T=1 0.77 0.34 0.73 -1 0.41 … 0.81 T=2 -1 0.61 0.34 0.98 0.18 … -1 T=3 0.03 0.88 0.27 0.46 0.62 … 0.59 T=4 0.16 0.25 0.92 0.78 0.55 … 0.11 T=5 0.82 0.02 0.68 -1 0.29 … 0.09 … … … … … T=m0.52 -1 0.09 0.57 0.38 … 0.07 A1 A2 A3 A4 A5 … An T=0 0.15 0.42 0.72 0.57 0.55 … 0.37 T=1 0.53 0.78 0.35 0.90 0.11 … 0.66 T=2 0.81 0.91 0.24 0.54 0.24 … -1 T=3 0.68 0.10 0.81 0.85 0.48 … 0.04 T=4 0.31 0.69 -1 0.72 0.71 … 0.47 T=5 0.02 0.45 0.95 0.36 0.75 … 0.19 … … … … … T=m 0.28 0.73 0.08 -1 0.66 … 0.83 A1 A2 A3 A4 A5 … An T=0 0.21 -1 0.15 0.85 0.05 … 0.33 T=1 0.53 0.78 0.35 0.90 0.11 … 0.66 T=2 -1 0.61 0.34 0.98 0.18 … -1 T=3 0.68 0.10 0.81 0.85 0.48 … 0.04 T=4 0.31 0.69 -1 0.72 0.71 … 0.47 T=5 0.82 0.02 0.68 -1 0.29 … 0.09 … … … … … T=m 0.28 0.73 0.08 -1 0.66 … 0.83 A1 A2 A3 A4 A5 … An T=0 0.15 0.42 0.72 0.57 0.55 … 0.37 T=1 0.77 0.34 0.73 -1 0.41 … 0.81 T=2 0.81 0.91 0.24 0.54 0.24 … -1 T=3 0.03 0.88 0.27 0.46 0.62 … 0.59 T=4 0.16 0.25 0.92 0.78 0.55 … 0.11 T=5 0.02 0.45 0.95 0.36 0.75 … 0.19 … … … … … T=m0.52 -1 0.09 0.57 0.38 … 0.07 Fig. 5. Time unit crossover of polyploidy genes.
this case study that only five main facilities are included: (1) attractions (comprising all attractions); (2) parking lot; (3) souvenir shop; (4) hotel and (5) supporting facilities (including water treatment plant, garbage dump, a main sanitary sewer line, and so on). Each facility involves three activities: (1) planning and designing, (2) construction and (3) operation. So, the development project compasses 15 activities in total. Duration is calculated in units of a
month (as shown in Table 4), and the operation activity
of each facility is performed till the end of the project. From the beginning of the construction of the infra-structure to the staged expansion after operation has com-menced, a theme park development project may span a few decades. With the reduced quantity of facilities and activi-ties in the case study, the total duration of the project is set as 120 months (10 years), so as to facilitate calculation of the NPV. Other factors are considered that may influence the NPV; the annual compounded interest rate is set as 5%, and the linear depreciation to 0 of each facility is set at 20 years.
The Activities and Resources in the case are shown in
Table 5. Given that five resources are involved in this case:
1. Capital: Available capital in the beginning of the project is NT$ 710 000 000 and no capital increase occurs during the project. Any capitals involved during the operation of the facilities are denoted in units of NT$ /month.
2. Capacity of parking lot: This is provided by ‘‘operation of parking lot’’ to satisfy the demands of both visitors and employees during the operation of other facilities. The calculation is based on the time unit of ‘‘month’’ and the capacity is denoted by the unit of ‘‘cars/ month’’, which is 0 at the beginning of the project.
3. Capacity of supporting facilities: The calculation unit is ‘‘visitor count/ month’’, which is 0 at the beginning of the project and is provided by the ‘‘operation of sup-porting facilities’’ to meet the demands from ‘‘operation of attractions’’, ‘‘operation of souvenir shop’’, and ‘‘operation of hotel’’.
4. Demand for consumption in souvenir shop: The calcula-tion unit is ‘‘NT$/ month’’ and the value is 0 in the beginning of the project. It is produced by ‘‘operation of attractions’’ and ‘‘operation of accommodation’’ (vis-itors and hotel customers purchasing souvenirs). The total demand is equal to the capital output from ‘‘oper-ation of souvenir shop’’.
5. Demand for accommodation: The calculation unit is ‘‘vis-itor count/ month’’ and the value is 0 at the beginning of the project. It is produced by ‘‘operation of attractions’’. The total demand x NT$ 650/visitor count equals the capital output from ‘‘operation of hotel’’.
Various types of resources are required in the develop-ment of a theme park, but in our case study all the resources except the fifth are omitted. For example, the land required in the project is supposed to have been suffi-ciently acquired.
5.2. Performance and comparison
Based on AVO-PLAN proposed in this research, an application system was constructed with Visual Basic 6.0, and Stroboscope 2.0.1.7 was applied in the compiling of the project scheduling planning and simulation. Inputting relevant data of the case study into the system constructs the simulation network automatically. Through the natural selection of generations in GA, AVO-PLAN figured out near-optimal solutions of the NPV.
In the case study, the number of solutions with 15 activ-ities is (15!)120, which are not likely to be solved individu-ally with the method of exhaustion. Therefore the GA should be applied to enhance the speed in the search of near-optimal solutions. Generally, direct scheduling by GA combines the start and the finish date of each activity as the first generation. An example is ‘‘Time-series Combi-natorial Planning Model in Infrastructure Plan’’ proposed
by Hsieh and Liu (1997). However, AVO-PLAN in this
study applies the priority value of each activity in each time unit for genetic coding. The convergence curves of AVO-PLAN and the direct scheduling by GA are shown in
Fig. 6., where the former obviously surpasses the latter.
AVO-PLAN is oriented to abide by the activity execution value, making it easier to derive the scheduling for optimi-zation of resource utilioptimi-zation.
Generally the haploid genes structure applies a uniform crossover in which each gene encounters exchange with independent probability. The polyploidy GA constructed in this study may also perform crossovers in terms of time units. In other words, the whole chromosomes of each time unit may be paired for crossover. The application of the Table 4
Facilities in the case
Facility Activity Duration
(Month) F1 Attractions A1 planning and design of attractions 6
A2 construction of attractions 16 A3 operation of attractions – F2 Parking lot A4 planning and design of parking lot 1
A5 construction of parking lot 3 A6 operation of parking lot – F3 Souvenir
shop
A7 planning and design of souvenir shop
2 A8 construction of souvenir shop 5 A9 operation of souvenir shop – F4 Hotel A10 planning and design of hotel 6
A11 construction of hotel 18
A12 operation of hotel –
F5 Supporting facilities
A13 planning and design of supporting facilities
2 A14 construction of supporting facilities 4 A15 operation of supporting facilities –
polyploidy GA in this system is the ‘‘time unit crossover’’. The following approaches were adopted in the attempt to understand the effectiveness of ‘‘time unit crossover’’: (1) Change even generations after the first generation into ‘‘time unit crossover’’; (2) Change even generations after the fifth generation into ‘‘time unit crossover’’; (3) Change
each generation into ‘‘time unit crossover’’. Fig. 7 is the
comparison between the convergence curves of the above three modified crossover methods and that with the ‘‘uniform-point crossover in each generation’’. With ‘‘uni-form-point crossover in each generation’’, convergence is completed in the 85th generation at an optimal value of 5415. The most effective modified crossover method is with ‘‘time unit crossover for the even generations after the 15th generation’’. It accelerates the convergence in the 69th generation and increases the optimal value to 5718. It can be found that ‘‘time unit crossover’’ in appro-priate generations may yield better efficiency in the search
of better near-optimal solutions than setting each gen-eration as ‘‘uniform-point crossover’’ or as ‘‘time unit crossover’’.
To understand the difference in effectiveness between AVO-PLAN and a human-being, we invited five experts to complete the scheduling for the case. These experts included 2 managers in real estate development companies, 2 project management consultants, 1 manager of a theme park. They were all familiar with bar charts, the concept of project investment and NPV, and they had practical
experiences of over 3 years. Table 6 lists the result of the
comparison. Scheduling with AVO-PLAN took 1.3 h (including the user’s operation time), which is far less than the average time spent by experts of 5.7 h. Also, the opti-mal NPV obtained by AVO-PLAN is also higher.
Experts also share a similar opinion that in the past the demand-and-supply relationship of resources between activities were only roughly calculated or even neglected Table 5
The activities and resources in the case
Activity Resource input Resource output
A1 R1 Capital: NT$ 30 000 000 –
A2 R1 Capital: NT$ 350 000 000 –
A3 R1 Capital: NT$ 1 050 000/month R1 Capital: NT$ 3 250 000/month
R2 Capacity of parking lot: 300 cars R4 Demand of consumption in souvenir shop: NT$ 152 000/month R3 Capacity of supporting facilities: 15 600 visitor count/month R5 Demand for accommodation: 3600 visitor counts/month
A4 R1 Capital: NT$ 600 000 –
A5 R1 Capital: NT$ 6 800 000 –
A6 R1 Capital: NT$ 200 000/month R1 Capital: NT$ 525 000/month
R2 Capacity of parking lot: 600 cars
A7 R1 Capital: NT$ 350 000 –
A8 R1 Capital: NT$ 6 800 000 –
A9 R1 Capital: NT$ 120 000/month R1 Capital: A3 (operation of attractions), Total R4 (Demand of consumption in souvenir shop) produced from A12 (operation of hotel)
R2 Capacity of parking lot: 60 cars
R3 Capacity of supporting facilities: 3 120 visitor count/month R4 Demand of consumption in souvenir shop: A3
(operation of attractions), Total R4 (Demand of consumption in souvenir shop) produced from A12 (operation of hotel)
A10 R1 Capital: NT$ 3 200 000 –
A11 R1 Capital: NT$ 270 000 000 –
A12 R1 Capital: NT$ 1 500 000/month R1 Capital: R5 (Demand for accommodation)· NT$650/ visitor counts produced from A3 (operation of attractions) R2 Capacity of parking lot: 100 cars R4 Demand of consumption in souvenir shop: R5
(Demand for accommodation)· NT$15/visitor counts produced from A3 (operation of attractions) R3 Capacity of supporting facilities: 5200 visitor count/month
R5 Demand for accommodation: R5 (Demand for accommodation) produced from A3 (operation of attractions)
A13 R1 Capital: NT$ 1 650 000 –
A14 R1 Capital: NT$ 17 000 000 –
A15 R1 Capital: NT$ 650 000/month R3 Capacity of supporting facilities: 25 000 visitor counts/month R2 Capacity of parking lot: 50 cars
in scheduling. Including this aspect into the calculation in the case study may better reflect the actual situation, but it also dramatically increases the level of complexity for the scheduling. Repeated calculations have to be carried out to evaluate the influence of different start and finish dates of activities on the cash flow, as well as to confirm
whether other activities will be interfered with or must be postponed. After the demonstration in AVO-PLAN, experts also reached the consensus that the integration of the simulation analysis and the GA can indeed enhance project scheduling as well as the efficiency of the search for the near-optimal NPV.
-8000 -6000 -4000 -2000 0 2000 4000 6000 0 25 50 75 100 125 150 175 200 225Generation
Direct GA with activity scheduling
AVO-PLAN model
NPV (NT$)
Fig. 6. Convergence curves with AVO-PLAN and direct scheduling by the GA.
0 1000 2000 3000 4000 5000 6000 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 NPV (NT$) 5718 85 69 5415
Uniform-point crossover in each generation
Uniform-point crossover in odd generations and time unit crossover in even generations since the first generation
Uniform-point crossover in 1~15 generations and time unit crossover in even generations since the fifteenth generation
Time unit crossover in each generation
Generation Fig. 7. Influence of ‘‘Time unit crossover’’ on convergence curve.
6. Conclusions
Much research has been devoted to project scheduling of construction projects and optimization of financial portfo-lio. However, very few studies have been dedicated to the problem of theme park development, which requires con-sideration of both scheduling and portfolio optimization. This study analyzed the features of theme park develop-ment projects and divided the associated facilities into five categories.
To facilitate the scheduler to develop the optimal project schedule, the proposed AVO-PLAN system integrates sim-ulation and the GA to predict the NPV of each combina-tion and determine the priorities of each facility with the GA. The priority values of each facility in each time unit are expressed with genetic coding, and the optimal develop-ment strategy and scheduling are determined after genera-tions of evolugenera-tions.
Since the focus of a theme park development project is the value of the investment items, and since there is a com-plicated demand-and-supply relationship between activi-ties, the genetic coding with start and finish date of each activity may not reflect the importance of execution for each item. Unlike other studies of scheduling with the aid of the GA, AVO-PLAN incorporates the priority values of each development item in each time unit into genetic coding, so as to facilitate a quicker search of near-optimal solution via simulation. In addition, this study also com-bined the priority values of each time unit into a polyploidy genetic structure, which provides a better reflection of the Time-series than ordinary applications with haploid.
The testing in our case study revealed that AVO-PLAN surpassed the experts by a faster search and a better NPV. With regards to the demand-and-supply relationship of the resources between activities; the experts couldnot provide a thorough consideration in their scheduling, while AVO-PLAN integrates it completely into the project scheduling
via simulation. Scheduling of theme park requires a consid-erable versatility of combination. In the past, its comple-tion relied on the experience of experts. On the other hand, AVO-PLAN applies the GA to effectively figure out the near-optimal project scheduling for schedulers. Our proposed system can not only be applied to theme park development projects but also to the decision-making and scheduling portions of other projects that require staged or segmented execution, such as staged urban renewal projects.
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Table 6
Comparison of effectiveness between AVO-PLAN and experts
Result AVO-PLAN Scheduling by experts
Time (h) 1.3 Average: 5.7
Optimal NPV (NT$) 5718.4 Average: 4588.7 Max.: 5445.6 Min.: 4084.4
