Logistical routing of park tours with waiting times: case of Beijing Zoo

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Logistical routing of park tours withwaiting times: case of Beijing ZooHaiying Xua, Qiang Lia, Xiang Chenb, Jin Chenc, Jingting Guoc & YuWangd

a College of Resources Science and Technology, Beijing NormalUniversity, Beijing, Chinab Department of Emergency Management, Arkansas TechUniversity Russellville AR, USAc Academy of Disaster Reduction and Emergency Management,Beijing Normal University, Beijing, Chinad Beijing Research Center of Urban System Engineering, Beijing,ChinaPublished online: 30 Jan 2015.

To cite this article: Haiying Xu, Qiang Li, Xiang Chen, Jin Chen, Jingting Guo & Yu Wang (2015)Logistical routing of park tours with waiting times: case of Beijing Zoo, Tourism Geographies:An International Journal of Tourism Space, Place and Environment, 17:2, 208-222, DOI:10.1080/14616688.2014.997281

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Logistical routing of park tours with waiting times: case of Beijing Zoo

Haiying Xua, Qiang Lia*, Xiang Chenb, Jin Chenc, Jingting Guoc and Yu Wangd

aCollege of Resources Science and Technology, Beijing Normal University, Beijing, China;bDepartment of Emergency Management, Arkansas Tech University Russellville AR, USA;cAcademy of Disaster Reduction and Emergency Management, Beijing Normal University, Beijing,China;dBeijing Research Center of Urban System Engineering, Beijing, China

(Received 10 June 2014; accepted 10 November 2014)

Site planning for parks consists of synthetic strategies to improve visitors’ experienceand appreciation of park features. An important aspect in site planning is to coordinatevisitor flows in order to avoid excessive congestion that may depreciate visitingexperience. An emerging need in the coordination strategies is to personalize visitingroutes and enhance the enjoyment of the tour for individual visitors. On the individuallevel, visitors have diverse preferences for park attractions. Scheduling a tour to visitattractions is restricted by not only the layout of park facilities but also the uncertaintyof waiting induced by different lengths of lines at attractions. This paper proposes atentative solution to optimize the logistics of individual tours by considering thedynamic nature of waiting time at park attractions derived from empirical data. Theoptimal solution is achieved using the branch-and-bound algorithm and is implementedin a real-world case of Beijing Zoo, a metropolitan zoology park in Beijing, China. Thecase study provides corroborating evidence for studying the logistical routing of parktours that: (1) visitors arriving at the park earlier can avoid crowds and excessive lineswhereas visiting at midday would encounter excessive waiting and (2) the shortest tourroute may not necessarily be the most efficient; strategically scheduling the visit topopular exhibits in their off-peak hours could effectively shorten overall tour time. Thisproblem, called the Traveling Salesman Problem with Waiting Times (TSPWT)increases the realism of the routing problem while shedding new light on personalizedrouting strategies for improving individual touring experience.

Keywords: traveling salesman problem; logistics; waiting times; time-dependent;route planning; optimization

1. Introduction

Metropolitan parks are symbolic landmarks serving recreational needs for urban residents

and tourists. Not only do parks contribute to the aesthetic design of city landscape but

they also make a significant contribution to local economy. Site planning for parks must

ensure both the safety and accessibility for visitors through optimized road planning and

efficient park management. This is of particular importance during weekends and national

holidays when parks are likely to experience overcrowding. The congestion of visitors

involves much uncertainty that may develop into rare yet tragic events such as injuries

and deaths from mass stampede. Crowd control by facility administrators is one way to

promote the overall efficiency and security for visitors and to provide them with the

satisfaction expected from tours (Rodriguez, Molina, P�erez, & Caballero, 2012).

*Corresponding author. Email: [email protected]

� 2015 Taylor & Francis

Tourism Geographies, 2015

Vol. 17, No. 2, 208�222, http://dx.doi.org/10.1080/14616688.2014.997281

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An emerging need in the coordination strategies is to personalize visiting experi-

ence and enhance the enjoyment of the tour for individual visitors. On the individual

level, visitors have diverse preferences for park attractions in terms of the priority

and timing to experience rides, visit exhibits, and patronize service outlets. The

availability and flexibility of visiting these attractions is restricted by not only the

spatial placement of park infrastructure but also the uncertainty of congestion in

terms of queuing and waiting (Ahmadi, 1997). The waiting time at attractions is dic-

tated by three major factors: (1) the attendance level that fluctuates by time of day

as evidenced by tracking visitors’ activity pattern that exhibited diurnal and intra-

diurnal rhythms in a park (Birenboim, Anton-Clav�e, Paolo Russo, & Shoval, 2013);

(2) the popularity of attractions as visitors tend to wait longer for attractions that

take more time to experience (Kemperman, Borgers, Timmermans, & Oppewal,

2003); and (3) the duration of the activity. Exploring the empirical pattern of waiting

time and utilizing this information for customizing routes for individual visitors is an

important aspect in personalizing location-based tour services (Yu & Chang, 2009).

Designing the optimal routing of activities for individuals and delivering the service

to visitors through web-enabled mobile devices have significant implications for

avoiding contingent waiting time. For example, amusement parks employ customized

iPhone apps to inform visitors of the updated waiting time for rides, using apps such

as ‘Lines’ by Walt Disney World (Wang, Park, & Fesenmaier, 2012). However,

knowing the waiting time is merely sufficient for deriving the most efficient routing

strategy, as the efficiency is dictated by both the locations of rides and waiting time.

As waiting time changes dynamically by time of day and it takes time to walk to

the ride, waiting would be longer than expected at the time when the visitor arrives

at the ride.

In this respect, planning the visiting route that achieves the maximum efficiency is

significant to fulfill tourists’ satisfaction. However, it is relatively difficult to illumi-

nate the underlying methodology of logistical routing. The routing of tours can be

traced back to the classic Traveling Salesman Problem (TSP) that was frequently

employed for route optimization in a variety of planning scenarios. Theoretically,

solving TSP is computational challenging. Approximate solutions could be derived by

less costly yet more effective methods such as heuristic algorithms (Lin & Kernigha,

1973). When TSP is implemented in the case of routing for a park tour, it would be

more realistic to consider the waiting time expected from each activity. In this paper,

we developed an extended TSP model by incorporating a flexible waiting time as a

time-dependent variable. We then have devised a branch-and-bound algorithm for

identifying the optimal route given the variety of times spent at each attraction. The

model was further employed in a route planning scenario for Beijing Zoo, an urban

zoological park in Beijing, China with the actual placement of exhibits. The results

gained from the case study could serve to optimize routes that improve the overall

accessibility of a tour and eventually to shed light on the logistical coordination strat-

egies of visiting similar parks.

The paper is organized as follows. Followed by the introduction, Section 2 reviews

the TSP and its extensions in solving park routing problem. Section 3 develops the

mathematical formulation of the routing model. Section 4 implements the model in

the Beijing Zoo that incorporates the different variables of route planning scenarios

and different waiting times at selected animal exhibits. By taking stock of the pros

and cons of the method, Section 5 concludes the study with possible avenues for

extending this method in the future.

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2. Literature review: Routing with traveling salesman problem

One goal of tour route planning is to maximize the expected efficiency in terms of mini-

mal time or travel distance. This goal is achieved by taking into consideration different

tourist objectives under various conditions (Godart, 2003; Hagen, Modsching, & Krarner,

2005; Hyde & Lawson, 2003; Kramer, Modsching, & Hagen, 2007; Rodriguez et al.,

2012). The Traveling Salesman Problem (TSP), which requires finding the shortest path

to visit each location only once and returning to the starting location, is frequently

employed for tour route planning.

The classic TSP is mathematically produced in the form of a linear programming

problem, given G D (V, E) a complete and directed weighted graph, V D {1,2, . . ., n} theset of vertices, and E the set of edges:

Min Z ¼X

i 6¼jdijxij (1)

s.t.

Xj6¼i

xij ¼ 1; i2V (2)

Xi6¼j

xij ¼ 1; j2V (3)

Xi;j2 S

xij�s¡ 1; for all subsets S of V (4)

xij 2 f0; 1g; i; j2V (5)

where

xij ¼�1 edgeði; jÞ is on the optimal route

0 otherwise

dij: distance between vertex i and j (dij> 0, dii D C1, i, j2V)s: number of vertices contained in the set S

Equations (2) and (3) ensure that there is only one inflow and one outflow for each

vertex in the optimal route. Equation (4) ensures that any subset of graph G has no inde-

pendent cycles. The solution derived is a path in the shape of a Hamilton cycle (Garey &

Johnson, 1979).

Recent decades have witnessed a myriad of extensions of the TSP to handle con-

straints of multiple scenarios. Examples of these extensions include: the asymmetric TSP

where the travel is restricted by road direction, and travel costs are different in opposite

directions (Carpaneto & Toth, 1980); the bottleneck TSP where the maximum travel cost

of two neighboring locations is minimized (Parker & Rardin, 1984); the multi-objective

TSP where multiple factors like travel costs and collected tolls need to be simultaneously

optimized (Samanlioglu, Ferrell, & Kurz, 2008); the time-dependent TSP where the start-

ing time of a route is taken into consideration (Picard & Queyranne, 1978; Vander Wiel

& Sahinidis, 1996); TSP with time windows where each location must be visited within a

specific time period (Focacci, Milano, & Lodi, 1999).

TSP can be described as an NP-hard problem in that with the increase of candidate

locations the running time for solving the problem will increase exponentially. It is a com-

binatorial optimization problem solved for a limited problem size by simple enumeration

(also known as a brute force search), and some global optimization algorithms, such as the

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linear programming method (Dantzig, Fulkerson, & Johnson, 1954), the branch-and-bound

algorithm (Lawler & Wood, 1966; Padberg & Hong, 1980), and the dynamic programming

method (Bellman, 1962; Bellmore & Nemhauser, 1968; Held & Karp, 1971).

The traditional TSP was designed to simplify the delivery of goods to a series of loca-

tions. The scenario that the salesman waits at each location is not considered, as waiting

time is a fixed cost that does not affect the result. This assumption is merely sufficient for

applying the theory for the route planning problem in parks where a series of individual

attractions exist. In reality, taking rides in an amusement park, touring a zoo, or visiting a

museum undoubtedly involves some waiting in line and stopping to enjoy the activities.

The problem is very manageable if the time budget for each activity is fixed, in which

case the total time cost for activities becomes a constant under the premise that the patron

will visit each location only once. In more common cases, the waiting time at each venue

is a time-dependent variable influenced by visitor’s preferences and the length of queues

at venues. For example, at an amusement park, the line for a ride would usually be much

shorter when closer to park opening than at its peak hours (Birenboim et al., 2013). In

this respect, when a flexible waiting time is imposed upon touring activities, route plan-

ning will be dependent on the time of arrival at each location and therefore the optimal

route cannot be easily recognized. The component of the flexible waiting time needs to

be incorporated into the TSP to accommodate this very situation.

3. Methodology: park routing with variable waiting times

The time budget for a park activity is the duration of time for undertaking a scheduled

activity. This time budget can be separated into two components: (1) a fixed time budget

for conducting the activity, such as taking a ride or watching an exhibit, and (2) a flexible

time budget, which comprises the element of uncertainty involved in the activity, such as

waiting in a line. In most cases, this uncertainty cannot be precisely defined due to the

many contingencies arising from the touring environment. However, in some specific

cases, a pattern characterizing the flexible time budget can be identified through observ-

ing visitors’ waiting times on a regular basis. For example, the time spent waiting in line

for a ride in an amusement park always demonstrates a strong temporal pattern over the

period of a day (Birenboim et al., 2013).

To date, little has been done regarding park tour planning by taking into account the

flexible time budget in terms of variable waiting times. We then would like to propose the

formalism of this problem within the methodological framework of TSP. we have consid-

ered that the time budget is composed of a fixed time cost Ti at location i and a flexible

time cost T(i, t�i ). This flexible cost is dependent on the location i and the time of day t�i(in this paper, a small t indicates a point in time and a capital T indicates a duration of

time.). The objective is to find a tour path that visits each location only once and returns to

the starting location of the tour. This path minimizes the total time spent on expected activi-

ties. We call this problem the Traveling Salesman Problem with Waiting Times (TSPWT).

The following formulation is defined for conceptualizing this scenario:

Given G D (V, E) a weighted graph, V D {1,2, . . ., n} the set of vertices (locations),

and E the set of edges, the TSPWT is a non-linear programming problem as described

below.

Min Z ¼Xi 6¼j

dij

yxij þ

Xi2V

Ti þXi2V

Tði; t�i Þ (6)

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s.t.

Xj6¼i

xij ¼ 1; i2V (7)

Xi6¼j

xij ¼ 1; j2V (8)

Xi;j2 S

xij � s¡ 1; for all subsets S of V (9)

xij 2 f0; 1g; i; j2V (10)

where

xij ¼�1 edgeði; jÞ is on the optimal route

0 otherwise

t�i ¼ tv0 CXj2Vi

Tj CXj2Vi

Xk 2Vi

djk

yxjk C

Xj2Vi

dij

yxij C

Xj2Vi

Tðj; t�j Þi; j; k 2V

dij: distance between location i and j (dij > 0, dii D C1, i, j2V)s: number of locations contained in set S

tv0 : starting time of the travel at initial location v0Ti: expected fixed time budget at location i

Tði; t�i Þ: flexible time budget(waiting time) at location i starting at the time of t�iv: travel speed

Vi: subset of V containing all locations before visiting location i

In this formulation, the objective function (6) is to minimize the expected total time

cost for the tour. This total time cost is composed of three parts: time spent on travel

between locations, expected total fixed time budget for participating in activities at all

locations, and total waiting times at all locations. The time budget Tði; t�i Þ is consideredto be a time-dependent variable at the specific location i at a specific arrival time t�i . Spe-cifically, Tði; t�i Þ is calculated based on a trip with a particular starting time of t0, the duration

of all fixed time budgets for all visited locations ðPj2ViTjÞ, travel time between visited loca-

tions ðPj2Vi

Pk 2Vi

djkyxjkÞ, the travel time from the last location j to the current location

i ðPj2Vi

dijyxijÞ, and the total waiting time for all previous activities ðPj2Vi

Tðj; t�j ÞÞ.Equations (7) through (10) are constraints that a typical TSP must satisfy. These equations

ensure the solution is a closed path with each location being visited only once.

4. Case study: Optimal routing through the Beijing Zoo

The case study of the TSPWT was conducted in the real-world scenario of the Beijing

Zoo. Beijing Zoo is an urban zoological park located in downtown Beijing, the capital of

China. The zoo possesses one of the largest animal collections in China, hosting approxi-

mately 15,000 animals. Because of the complex layout of exhibits, we have made neces-

sary abstraction to a map by extracting a total of 26 venues in one visit. Figure 1 depicts a

bird’s eye view of the zoo, including these 26 venues (1�26), four entrances (E1�E4),

and main pathways and trails connecting these locations.

212 H. Xu et al.

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4.1. Estimation of time variables

We acquired the visitor statistics for each exhibit from the zoo administration office and

used this information to estimate the fixed time budget spent on each exhibit. A major

exhibit (venue 19) was used as a reference location. The average time of shows at venue

19 is approximately 90 minutes. We made an assumption that the attractiveness of an

exhibit in terms of visiting time is linearly dependent on the size of the exhibit. The aver-

age visiting time for venue i (Ti) is given in Equation (11) taking the fixed time budget of

venue 19 as a control variable

Ti ¼ Si

S19� T19 (11)

where Si is the area around exhibit i, T19 is 90 minutes and S19 is 8250 m2. Based on Equa-

tion (11), the estimates of average fixed time for visiting other exhibits of the zoo are pre-

sented in Table 1.

The flexible time budget Tði; t�i Þ involves much uncertainty and is difficult to accu-

rately reproduce. In order to investigate which exhibits would have excessively long wait-

ing periods, we employed the surveillance videos at exhibits that were collected from the

zoo administration office for all the weekends of 2012. We investigated these videos and

found visitors experienced relatively long wait at six major indoor exhibits (3, 11, 15, 19,

20, and 23). Further analysis of these videos also identified that the waiting times at these

exhibits displayed temporal regularity throughout the day. We then selected four weekend

days of October and estimated the waiting time outside each exhibit by every 15 minutes.

We found that the phenomenon of queuing only occurred during certain hours of the day,

the peak of which was similar to a quadratic function, as shown in Figure 2. Moreover,

waiting time peaks for various exhibits occurred at different times (Figure 2), depending

on the proximity to the zoo entrances. According to the averaged temporal variation

Figure 1. A bird’s eye view of the Beijing Zoo with main exhibits and connecting pathways.

Tourism Geographies 213

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patterns for different exhibits, the waiting times were regressed by a quadratic function as

follows:

Tð3; t�Þ ¼� ¡ 2:5ðt� ¡ 11:5Þ2 þ 10 9:5�t��13:5

0 t� < 9:5; t� > 13:5(12)

Tð11; t�Þ ¼� ¡ 5ðt� ¡ 11Þ2 þ 20 9�t��13

0 t� < 9; t� > 13(13)

Tð15; t�Þ ¼� ¡ 10ðt� ¡ 10:5Þ2 þ 40 8:5�t��12:5

0 t� < 8:5; t� > 12:5(14)

Tð19; t�Þ ¼� ¡ 7:5ðt� ¡ 12:7Þ2 þ 30 10:7�t��14:7

0 t� < 10:7; t� > 14:7(15)

Table 1. The expected time budget including fixed time budget (activity time) and flexible timebudget (waiting time) at each exhibit of the zoo.

Exhibit ID (i) Area (m2, Si)Fixed time

budget (minutes, Ti)Flexible time

budget (minutes, T(i,t�))

1 1460 15.93 0

2 1696 18.50 0

3 440 4.80 Equation (12)

4 522 5.69 0

5 2405 26.24 0

6 792 8.64 0

7 2476 27.01 0

8 350 3.82 0

9 600 6.55 0

10 1035 11.29 0

11 130 1.42 Equation (13)

12 1647 17.97 0

13 5502 60.02 0

14 1978 21.58 0

15 660 7.20 Equation (14)

16 664 7.24 0

17 1071 11.68 0

18 2196 23.96 0

19 8250 90.00� Equation (15)

20 2723 29.71 Equation (16)

21 504 5.50 0

22 620 6.76 0

23 1840 20.07 Equation (17)

24 1608 17.54 0

25 1092 11.91 0

26 896 9.77 0

�Venue 19 is selected as a reference to calculate fixed time budget for other venues.

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where

Tð20; t�Þ ¼� ¡ 2:5ðt� ¡ 12:2Þ2 þ 10 10:2�t��14:2

0 t� < 10:2; t� > 14:2(16)

Tð23; t�Þ ¼� ¡ 5ðt� ¡ 11:5Þ2 þ 20 9:5�t��13:5

0 t� < 9:5; t� > 13:5(17)

where t� is the time when the visitor reached the exhibit.

Because most tourists walked through the zoo, we assumed an average travel speed v

of 0.7 m/s. The distance matrix of the road network dij was derived from the shortest dis-

tance between any two exhibits. We then designed a branch-and-bound algorithm in

MATLAB to implement the problem. The branch-and-bound algorithm, which narrows

down candidate solutions by defining upper and lower bounds of the optimal solution, is

widely used for solving NP-hard problems and is credited for its high computational effi-

ciency (Laporte, Riera-Ledesma, & Salazar-Gonz�alez, 2003). By plugging these variablesinto custom codes in MATLAB, the most efficient route can be derived, representing the

most enjoyable tour route.

4.2. Results

Results were derived according to the following route planning scenarios to show that the

TSPWT method is more efficient compared to the classic TSP.

Figure 2. The waiting time at different exhibits based on different times of arrival.

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Scenario A: Suppose a tourist enters the zoo from E1 at 10:00 am. Out of personal

preference, this tourist has chosen ten exhibits (1, 3, 7, 8, 9, 10, 14, 15, 19, and 22) for

this visit, and plans to leave from E1.

This scenario was tested using the two routing methods: one is a classic TSP route

where the total travel distance is minimized, and the other is a TSPWT route where total

time cost is minimized because the waiting time of the activities themselves was factored

into the equation. The two routes are plotted in Figure 3, highlighting the selected exhibits

and routes.

Figure 3. The optimal route for visiting exhibits in Scenario A following (a) the classic TSP and(b) the TSPWT.

216 H. Xu et al.

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TSP: E1-14-7-8-9-3-1-10-22-19-15-E1

TSPWT: E1-19-22-10-1-7-8-9-3-14-15-E1

An interesting observation can be drawn from comparing these two routes. The differ-

ence becomes apparent on the second stop in front of exhibit 7 on the TSP route and

exhibit 19 on the TSPWT route. Because there is typically a long waiting time for patrons

at exhibit 19, whereas exhibit 7 has no waiting time, stopping by exhibit 19 at a later time

will dramatically increase the waiting time at exhibit 19. As shown in Figure 2, visitors of

exhibit 19 start to wait for entry at 10:42 am. Therefore, a patron would be wise to visit

exhibit 19 first by following the TSPWT method.

Evidenced by the efficiency of the TSPWT method, the total time cost for completing

activities on the TSP route comes to 6.284 hours, whereas the TSPWT route is shortened

to 5.821 hours, indicating a slight reduction of approximately 27.8 minutes or 7.4%.

Also, the paths of two optimal routes are for the most part different. This suggests that the

inclusion of waiting time does not only necessarily give rise to a difference in the total

time cost, but it also may result in a different route for navigating the exhibits.

Scenario B: Suppose a tourist wishes to find the most optimal time to visit the zoo.

The tourist enters the zoo from E1. The time of arrival is chosen from 8:00 am and 12:00

pm with an increment of 15 minutes. This tourist has chosen to visit the top ten most pop-

ular exhibits (15, 23, 19, 20, 4, 11, 3, 24, 6, and 18), and plans to exit from E1.

Table 2. A comparison of the total time cost for TSP and TSPWT in Scenario B.

Startingtime(am, tv0) TSP Route

Total timecost of

TSP (hrs) TSPWT route

Total timecost of

TSPWT (hrs)

Timereduction

(minutes and %)

8:00 E1-15-24-23-19-20-18-3-4-6-11-E1

5.980 E1-15-24-23-20-19-18-3-4-6-11-E1

5.898 4.9(1.36%)

8:15 5.970 5.872 5.8(1.63%)

8:30 5.987 5.878 6.5(1.82%)

8:45 6.210 E1-23-24-20-19-18-3-4-6-11-15-E1

5.875 20 (5.39%)

9:00 6.577 5.890 41.3(10.45%)

9:15 6.868 E1-23-24-19-20-18-3-4-6-11-15-E1

5.939 55.8(13.53%)

9:30 7.045 6.088 57.4(13.59%)

9:45 7.140 6.269 52.3(12.2%)

10:00 7.222 6.398 49.5(11.41%)

10:15 7.248 6.481 50(10.57%)

10:30 7.224 6.524 42(9.70%)

10:45 7.162 6.567 35.6(8.29%)

11:00 7.068 E1-11-6-4-3-18-20-19-23-24-15-E1

6.488 34.8(8.20%)

11:15 6.945 6.345 36(8.64%)

11:30 6.800 6.185 36.9(9.04%)

11:45 6.635 6.049 35.2(8.84%)

12:00 pm 6.454 5.967 29.2(7.54%)

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In this scenario, as the starting time of the tour is not fixed, the factor of the tourist’s

personal preferences would dictate the starting time of the zoo tour in order to avoid pos-

sible congestion and excessive waiting. Given this scenario, results of tour route optimi-

zation were obtained via the TSP and TSPWT respectively. The results in terms of the

optimal route and total time cost are given in Table 2, which is further interpreted graphi-

cally in Figure 4, illustrating the changing nature of the total time cost by starting time of

the trip.

Following the figure, it can be noted that the total time cost increases at first, followed

by a decrease at 11 am. The largest increase occurs at a starting time of 10:15 am for TSP

route and 10:45 am for TSPWT route, respectively. The best routing strategy can be dis-

cerned at the starting time of 8:15 am on the TSPWT route, where an optimal total time

cost of 5.872 hours was derived with the reduction of total time cost of approximately

1.63% compared to the TSP route. This suggests that visitors arriving at the zoo earlier

(before 8:30 am) can avoid crowds and excessive lines. This result confirms our

Figure 4. (a) A comparison of the total tour time for TSP and TSPWT and (b) time reduction ofTSPWT routing compared with TSP in Scenario B.

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observation that a patron visiting the zoo at mid-day would encounter excessive lines and

congestion, making the trip less time efficient. Figure 4(b) illustrates the time saved from

the TSPWT route compared to the classic TSP route, which further corroborates the

improved efficiency of the TSPWT method, particularly in the middle of the day when

tourists are faced with excessive waiting times. This analysis of different routing strate-

gies can be helpful for park managers in coordinating the best walking tour by the time of

day and offering guidance for tourists.

5. Conclusion and discussion

The enjoyment of park tours is influenced by many factors, among which waiting time is

considered a critical choice criterion (Moutinho, 1988). The waiting at park venues

involves much uncertainty that may increase the anxiety of visitors while deteriorating

the experience gained from the tour. One way to ameliorate this uncertainty is to devise a

reasonable walking route for individual visitor to follow. This optimized route, which

shortens the overall tour time, is one way to promote efficiency and provide visitors with

the satisfaction expected from a tour.

As the waiting times at park venues are difficult to capture, this study conducted a

case study in the Beijing Zoo to characterize the temporal pattern of waiting times at dif-

ferent animal exhibits by time of day. To solve this problem, this study extended the clas-

sic TSP method to incorporating flexible and fixed time budgets for each venue en route

in order to determine the best route that minimizes the total time cost. The problem called

TSPWT is of significance for many real-world settings where people have only a set

amount of time to spend on activities and the uncertainty of this time budget greatly influ-

ences the overall efficiency of travel. Two scenarios in the case study corroborate impor-

tant conclusions for studying the logistical routing of park tours that: (1) visitors start the

trip in the early morning can avoid crowds whereas visiting at mid-day would encounter

the longest wait and (2) the shortest tour route may not necessarily be the most efficient;

strategically scheduling the visit to popular exhibits in their off-peak hours could effec-

tively shorten overall tour time.

The TSPWT was found to be very useful for improving the efficiency of route plan-

ning when waiting times vary by time of day. More importantly, this inclusion of a time

budget extends the classic TSP method and allows it to more realistically reflect individu-

alized tourism planning. Tourists have different perceptions of time-frame and their

scheduling of activities in tours is impinged by personal-specific temporal constraints

(Poria, Butler, & Airey, 2003). A key aspect of improving their touring experience is to

customize trips that better accommodate individuals’ needs while maximizing travel effi-

ciency. The TSPWT is capable of accounting for these constraints by incorporating spa-

tio-temporal variables of individual tourists. The case of Beijing Zoo demonstrates

examples that different routing strategies could be derived based on the priority of exhib-

its, the starting time, and the entrance of the tour. These strategies could further raise con-

cerns about not only the efficiency but also the safety issue manifested by operational

management of tourism, such as how to avoid congestion and reduce waiting during peak

visiting hours.

Although preliminary, this study is significant because it tackles many real-world tour

routing problems when the uncertainty of time budget is expected from activities. It

should be noted that this study has some limitations that could be addressed in future stud-

ies. First, the TSPWT model has yet to take individual differences of visitors into account,

such as personal attributes (e.g., gender, age, etc.) that may affect their expected time

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budgets and travel speed (Chen & Kwan, 2012; Lee & Joh, 2010). Second, the variation

of time cost was modeled in the study from selected weekend days at the zoo. However,

the difference between weekdays and weekends and temporal variation by day of week

should be investigated in future studies (Chen & Clark, 2013). Third, from the perspective

of a park administrator, the goal of coordinating walking tours is not to maximize the time

efficiency of a single visitor but to improve the overall efficiency for all visitors. Directing

visitors onto the same route simultaneously would likely create congestion. Utilizing

global optimization strategies to maximize the overall time efficiency while considering

the uncertainty of waiting times would be a valuable study in the future (Chen, Chen, Li,

& Chen, 2013). Solution to the abovementioned uncertainties for variable time cost pre-

diction and related adverse impacts calls for real-time attainment of time budgets instead

of selected case modeling. One solution involves portable equipment installed with loca-

tion-based service such as GPS and smartphones that can function as a receiver to acquire

real-time park information, including availability and waiting time at each exhibit (Bee-

coa et al., 2013; Chen & Yang, 2014). This information can be analyzed to derive an opti-

mal touring route and timing for the visitor by employing the TSPWT algorithm. When

this real-time park information becomes available, it is expected that the proposed

TSPWT method can be customized for individual visitors to create a more efficient and

enjoyable tour.

Acknowledgement

This work was supported by National Natural Science Foundation of China [grant number41371489].

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Notes on contributors

Haiying Xu is a PhD candidate in the College of Resources Science and Technology at BeijingNormal University, Beijing, China. Her research interests include city traffic demand managementand emergency management.

Qiang Li is a professor in the College of Resources Science and Technology at Beijing NormalUniversity, Beijing, China. Her research interests include city traffic demand management, regionalplanning and resource management.

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Xiang Chen is an assistant professor in the Department of Emergency Management at ArkansasTech University, Russellville, AR, USA. His research interests are GIS applications for transporta-tion, emergency management, and food science.

Jin Chen is a professor in the Academy of Disaster Reduction and Emergency Management atBeijing Normal University, Beijing, China. His research interests include resources and environ-ment remote sensing, emergency management.

Jingting Guo is a master in Academy of Disaster Reduction and Emergency Management atBeijing Normal University, Beijing, China. She majors in Cartography and Geographic InformationEngineering.

Yu Wang is a research assistant in Beijing Research Center of Urban System Engineering Beijing,China. Her research interests include public safety and emergency management.

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