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Tourist carrying capacity
Annals cf Tounrm Ruearch. Vol 18, pp 295-311, Printed in the USA. All rights reserved.
1991 CopyrIght
0
0160.7383191 $3.00 + 00 1991 Pergamon Press plc and J Jafari
TOURIST CARRYING CAPACITY A Fuzzy Approach Elio Canestrelli Pa010 Costa
University
of Venice,
Italy
Abstract: This paper discusses the concept of tourist-carrying capacity of an urban cultural destination and presents a model for determining its optimal level. The model is then made operational within a “fuzzy” linear programming approach that is tested in the case of the historical center of Venice. The “fuzziness” of the model makes it possible to take into account the distribution of benefits and costs from tourism between the touristdependent and the tourist-independent resident populations who confront different categories of tourists and day-trippers. Keywords: tourist-carrying capacity, cultural tourism, urban tourism, fuzzy linear programming, Venice. R&urn& La capacitt de charge touristique: une approche floue. Cet article discute du concept de capacit6 de charge touristique vis-i-vis d’une destination culturelle urbaine et prisente un modsle pour diterminer son niveau optimal. Le modile est rendu optratif par sa traduction dans un schema de programmation 1inCaire ‘You” qui est appliquC au cas du centre-ville historique de Venise. La flexibilit6 du modkle rend possible une evaluation de la distribution des avantages et des co&s, provenant de cattgories diffbrentes de touristes et d’excursionnistes, entre deux sousgroupes de population: la population vtnitienne qui vit de tourisme et celle qui vit h Venise malgrt le tourisme. Mots-cl&: capacit6 de charge touristique, tourisme culturel, tourisme urbain, programmation lintaire floue, Venise.
INTRODUCTION One of the major changes recently noted in the evolution of world tourist demand seems to be represented by the shift from “sun and beach” holidays to more active and special interest ones (Edwards 1987; WTO 1987). This trend will affect some tourist destinations more than others, and it is possible that many cultural destinations will face increasing pressure. This is already happening in many urban historical centers, such as the historical center of Venice, whose case is discussed in this paper. In 1952, more than 500,000 tourists spent 1.2 million bed-nights in Elio Canestrelli is Professor of Financial Mathematics at the University of Venice. His major areas of interest are mathematical programming, control theory, and fuzzy set theory. Paolo Costa is Professor of Economic Programming and Director of the School of Tourism Economics and Management (Dipartimento di Scienze Economiche, Ca’Foscari 30123 Venice, Italy). His major fields of interest also include input-output analysis and regional and urban economics. 295
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TOURIST CARRYING CAPACITY
the historical center of Venice. These figures have grown to 1.13 million tourist arrivals in 1987, with 2.49 million bed-nights spent in hotel and nonhotel accommodations (APT di Venezia 1988). But Venice is also the destination of a huge number of day-trippers who come from home, or from other tourist destinations (both the Adriatic beaches and the Alpine mountain areas), or from hotel accommodations located in the Veneto region. In 1987 alone, Venice was visited by 4.9 million daytrippers (Menetto 1988). Tourists and day-trippers compete for the “use” of the historical center of Venice (which has a nonexpandable surface area of only about 700 ha and is made of buildings that are protected from any alteration by special national legislation), with a resident population of 83,000 inhabitants and more than 47,000 commuters coming daily to Venice for reasons of work or study. In 1951, the historical center of Venice had a population of 175,000 inhabitants, which has been declining ever since. This process, at least during the last decade, has also been fueled by the “crowding-out” of the competitors for space activated by tourism (Costa 1990; Prud’homme 1986). It is, therefore, possible that the current quantity of visitors (a total of 6.04 million people in 1987) has already passed the tourist-carrying capacity of Venice. If Venice can be seen nowadays as an extreme case, it deserves some attention because it suffers from problems that will be shared by many other cultural tourist destinations in the very near future. This paper discusses the concept of carrying capacity of tourist destinations and suggests a way of making it operational within a “fuzzy” linear programming approach that is tested in the case of the historical center of Venice. A “crisp” linear programming approach to the same problem has been outlined in Costa and van der Borg (1988) and discussed in Costa (1988). CARRYING
CAPACITY
OF A DESTINATION
Tourists consume both public goods (or services coming from zeroprice common-property goods) and commodities and services produced and distributed by supporting facilities. Since the resource-based tourist attractions are usually nonreproducible and treated as commonproperty goods (if not strictly public goods), their (zero or negligible) price plays no role in their allocation. The maximum number of their users is first of all defined with reference to congestion: a reduction in the quality of the visitor’s experience that shows up when the intensity of use approaches the capacity limit of the tourist attraction. The concept of carrying capacity is defined (see Fisher and Krutilla 1972:420) both in ecological terms, as the maximum number of visitors that can be accommodated by a given destination under conditions of maxinurm stress, and in economic terms as the maximum number of visitors that can be accommodated at a constant quality of their experthue. Therefore, carrying capacity is in reference to the ultimate upper bound in the number of potential visitors in a resource-based attraction subsystem. However, it is quite possible that the whole tourist destination is constrained by the capacity of some other subsystem (one of those pertaining to the facilities that cater to visitor needs), regardless
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of whether or not these supporting subsystems are based on reproducible resources and are technically expandable. Unfortunately, the expansion of these supporting facilities in an urban tourist destination is not always socially desirable. Possible adverse impacts on the physical, economic, and social environments, as perceived by the resident population, are among limiting factors. This situation can be better understood by analogy to the conditions for the optimal use of a wild area, like a forest, from the economics of outdoor recreation. According to Fisher and Krutilla (1972) the criterion for optimal use of a resource-based recreational attraction is given by the maximization of:
+I) = B(q) - C(q) with
C(q) = Gk) + G&l) + G(q),
(2)
where : q c C, C, C,
= net benefits =b enefits (net of congestion disutilities) = use level of the recreational attraction = costs = cost of damage to ecological environment = current expenditures = capital expenditures (i.e., the relevant interest charges)
which is achieved in this case by differentiating setting equal to zero: d?r dB -=---dq
dq
dC, dq
dC,,, -----_() dq
and depreciation
with respect to q, and
dC, dq
The optimum use level of the recreation resource, q” in Figure 1, is higher than qm, the use level at which costs (both ecological and/or operational) begin to become relevant, and lower than qM, the use level at which total benefits would reach their maximum. With a few more assumptions, this approach can be used to determine the carrying capacity of a tourist destination that, like the historical center of Venice, is experiencing a growing demand pressure. The first assumption concerns the possibility of separating benefits and costs accruing to two mutually exclusive population subgroups. The plausibility of this assumption becomes evident, for example, ifas in the case of Venice discussed later-it is ascertainable that a relevant part of the resident population nei&r directly ROTindirectl,, gets any substantial part of its income, or any other possible benefit, from tourist activities. This is equivalent to saying- using the basic/service categorization of the urban economic base theory (Tiebout 1956)-that tourism does not account for the whole economic base of the city under
TOURIST CARRYING CAPACITY
UseLevels
q”
Figure 1. Optimal Use of a Recreation Resource
consideration. While all “service” activities are, by definition, dependent on “basic” activities and interdependent with other “service” activities, “basic” activities depend only on their export markets and are not necessarily affected by other “basic” activities. In the Venetian case, port activities (at least those handling commodities) and governmental activities (at least those connected with the role of Venice as a regional capital) are only two examples of activities that are not at all dependent on tourism. In the Italian institutional framework, the separability of the two population subgroups is made still more credible by the fact that local governments do not get their finance from taxes proportional to local income or property, but from funds transferred from the national government independently from any variation in local income. Within this first assumption, the “willingness to pay” of tourists can be easily translated into revenues and incomes accruing only to the “tourist-dependent population” who supplies those priced goods and services that complement the zero-price, resource-based tourist attractions and the resident population whose income is indirectly dependent on the activity of the “front-line” tourist suppliers. As for the costs, if the separability of the two population subgroups is accepted, it should not be difficult also to accept the possibility of a clear-cut distinction between costs borne by each subgroup. If one paraphrases the model of Fisher and Krutilla (1972), this second assumption can be specified by assuming that current and capital expenditures from tourism expansion, C,(q) and C,(q) of equation (2), are borne by both subgroups. In Venice, for example, tourist trash disposal is largely subsidized by the “nontourism-dependent” popula-
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299
tion, since it has been shown that the direct “tourist-dependent population” pays for only 17% of the cost of this service (Costa 1990). While the “nontourism-dependent” population is the sole group bearing Cdq) of equation (2)-the cost of damage to the ecological environment in the model of Fisher and Krutilla (1972). In this case, it can be thought of as corresponding to the opportunity costs from tourism expansion. These are the costs coming from the difficulty to expand activities different from tourism when enlarging capacities of tourist supporting facilities make use of increasing shares of the local stock of primary resources (land, buildings, accessibility, etc.). In the literature on Venice, this process is labeled as the “crowding-out” process (Prud’homme 1986). If the costs incurred by the “tourist-dependent population” are deducted from the corresponding benefits, it is possible to define an aggregate cost curve that represents only those costs borne by the “nontourist-dependent” population. ?The third assumption concerns the effects of a growing pressure of demand. In the recreational resource model, the demand curve represented in Figure 1 is such that any increase in demand will lower the willingness to pay for the marginal user. For each user, it is hypotheothers on a wilsized, “an increase in the probability of encountering derness outing is attended by diminished utility obtained from the outing” (Fisher and Krutilla 1972:421). This is equivalent to the assumption that each user has a demand curve that slopes downward and to the right, and that the aggregate demand curve will also slope downward and to the right. Any increase in the number of visitors will correspond to a movement along the aggregate demand curve and, as a consequence, to a reduction in the willingness to pay for the marginal user. If, as it has been ascertained in Venice (Costa 1990), a huge increase in the number of visitors (both tourists and day-trippers), and consequently in the level of congestion, is accompanied with price increases for all tourist commodities, this cannot be represented by movements along the aggregate demand curve. Successive rightward shifts of this curve, caused by a substitution of low-sensitive-to-congestion visitors for high-sensitive-to-congestion ones, have to be assumed. Within this third assumption, it is possible for the tourists’ willingness to pay to remain stable or even to increase, in spite of increasing congestion levels and of a consequent deterioration in the quality of a visitor’s experience. This can be described by successive shifts to the right of the marginal benefit curve of Figure 1, with corresponding shifts of q,u. Sooner or later, these movements of the marginal benefit curve will make operational the level of q’ of “ecological” carrying capacity. Any further rightward shift of the marginal benefit curve will only lead, at the margin, to an increase in the willingness to pay for a visit under conditions of maximum stress. The model for the determination of the level of optimal use of a tourist destination is represented in Figure 2, where curves B,, B,, B,, etc., depict successive net marginal benefits for the “tourist-dependent population” (benefits actually paid by visitors to the “tourist-dependent population” net of tourist costs incurred by this population subgroup) and the MC curve describes marginal tourist costs mainly borne by the “nontourist-dependent population.”
300
TOURIST CARRYING CAPACITY
qrn
%l
%Eq*
%3
Use Levels Figure 2. Optimal Use-Level of a Tourist Destination
It should be clear that because of the existence of these two different interest groups, the optimal level of use, q”, is not an equilibrium point. While the “tourist-dependent population” will try to push the carrying capacity limit toward q*, where its net benefits would be maximized, the “nontourist-dependent population” will try to keep the carrying capacity level as near to qmas possible in order to minimize its touristic costs. The actual level of use, q, which is allowed to vary between q,,,and q*, will result from the composition of the forces exerted by the two population subgroups, if its determination is not handled by extra-market devices in the public sector. In the latter case, the determination of the optimal tourist-carrying capacity should be defined by the public authority through a decision process characterized by two sets of control variables. First are those defining the capacity of each supporting facility (hotels, restaurants, parking lots, etc.) that would be set near qmor at q* as defined according to the opposing aspirations of the two population subgroups. Second sets of control variables are those describing the mix of potential users: separate categories of tourists and daytrippers who yield different “benefits” and exert distinct levels of pressure on different facilities. Since the measure of constraints (capacity of each supporting facility) has to be purposely set to vary within given intervals (qtm, q’* for each facility i), this problem can easily be translated into a linear-programming or into a “fuzzy” linear programming (FLP) problem.
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LINEAR
AND COSTA
301
PROGRAMMING
A linear programming problem which deals with fuzzy sets becomes a fuzzy linear programming (FLP) problem. A set A of the universe X is said to be fuzzy if its characteristic function is replaced by a membership function whose valuation set is allowed to be the real interval [0,11. A = ((x, pA(x)), x E X) with pa: X+[O,l] pA(x) is called th e membership function of fuzzy set A because the closer the value of pLA(x)is to 1, the more x belongs to A (Dubois and Prade 1980). In the fuzzy realm a classical integer number, such as 5, is replaced by the set of integers “more or less equal to 5.” In this case, if p(x) = 0, x is not equal to 5, if p(x) = 1, x is fully equal to 5, while if 0 < p(x) < 1, x is equal to 5 at some “degree of possibility” p(x). The most frequent formulations of an FLP problem are (a) find a fuzzy vector solution x that maximizes cx subject to fuzzy inequality constraints ai x C 5: b, max cx subject to: a, x <
x >
= b,
(i =
1,2,
. . . ,772)
=o
(4)
where c,a, . . . a, are crisp vectors while x and b are fuzzy; and (b) find a crisp optimal solution x that maximizes the objective function cx subject to fuzzy inequality constraints six < = 6, . max cx subject to: ai x <
= 6,
(i = 1,2,
. . .
. .m)
XL0 where vectors c,a, . . . a,,, and In the application described the type (a) according to the Following Bellman and Zadeh mize can be usefully replaced Therefore, the goal z = cx is is:
P”(X) =
i
b are fuzzy. next, the paper solves a FLP problem of approach suggested by Chanas (1983). (1970) the concept of a goal to maxiby the concept of a goal to achieve. a fuzzy set whose membership function
0 if cx < 6,, - p0 1 - t if cx = 6, - pa (0 5 1 5 1) 1
if cx
>
(5)
b,,
(6)
where b, is the “aspiration level” for the objective function value, (6, pO) defines the minimum acceptable level of cx, and t measures the degree of nonsatisfaction of the aspiration level b,. The membership function of each fuzzy constraint b, is defined in the same way as:
302
TOURIST
CAPACITY
if a,x > b, + pt a,x = b, + tp, (0 I
0
t if
1 -
/4(x) =
CARRYING
1
t 5
1)
(7)
if a,x < b,
where t measures the degree of violation of the “aspiration level” for the ith constraint, b,, and (b, ,+ pi) is the maximum admissible value for the same constraint. Given the membership function of each constraint, it is possible to define a unique membership function for the whole set of constraints as: k(x) A “fuzzy decision” ship function is:
=
minbl(x>, CL?(~), ..
44x)1.
(8)
is then defined by a fuzzy set D whose member-
b(x)
=
minb-4x>,14x)1.
(9)
Given these definitions, the FLP problem becomes x0, which maximizes pD(x) i.e., finding x” such as:
one of calculating
(10)
kdx”> = max h(x). Such an FLP problem can be translated programming (LP) (Chanas 1983):
into a parametric
linear
max f = cx, subject to: six % 6, + Q,, (1 = 1, 2, x20
. ,m)
(11)
which allows studying the effects on the objective function z of different grades 8 of constraint violation (for the solution of such a parametric LP problem, see, e.g., Van De Panne 1975). For each admissible value of 8, equation (11) d e f mes a value x0 and then a 2” (0) = cx” (6) also contingent upon 8. Choosing an “aspiration level,” b,, and its maximally acceptable violation pO, it becomes possible to define a membership function oft” such as: 0
P&w)
=
if,?(O)
1 - t ifpI 1 if r’(0)
< b,, - p. = b,, - tpo (0 I > b,,
t s
1)
(12)
and then to interpret 2” as a fuzzy set, while it is easy to see from equation (8) and equation (11) that:
pcle) = 1 - 8.
(13)
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AND COSTA
For each possible 8, a solution x0 is obtained, if one exists, which both maximizes the objective function t in equation (1 l), with an associated value of the membership function pLFin equation (12) and verifies the set of constraints at a degree of satisfaction 1 - 8 according to equation (13). The degree of satisfaction of this decision is given by &e)
= min [CL&@)),
cL@)l.
(14)
A graph representing the three membership functions contingent upon 0 (pp, pc, and, see equation (14), pg) describes a complete “fuzzy decision” of the problem. APPLICATION
OF THE
FLP APPROACH
To
VENICE
Problem Formulation
The determination of the optimal level of tourist use of Venice is pursued here by solving (as an illustrative application of the FLP approach) a stylized “Venice problem” where: l The Basilica of St. Mark has been assumed to represent the whole system of nonreproducible resources that attract tourists to Venice. Since all tourists or day-trippers, with the exception of some repeat visitors, will almost certainly visit St. Mark’s, its use level under condition of stress can be set to determine the “ecological” tourist carrying capacity of the whole historical center. l Six tourist supporting facilities (see Table 1) have been identified as relevant, because they cater to the basic needs of visitors (sleeping, eating, parking and moving within Venice, etc.), because each one could constrain the whole tourist capacity of the historical city, and because their expansion would impose actual and/or opportunity costs to the “nontourist-dependent” population. l Three types of visitors have been identified to compete for the “tourist use” of Venice and to yield net benefits for the “touristdependent” population. With three types of visitorstourists using hotel accommodation (TH), tourists using nonhotel accommodations (TNH), and day-trippers (DT)the objective function of our fuzzy linear programming problem can be written as: maxr
= c,TH
+ c,TNH
+ csDT
(15)
where t represents total per diem outlays (which are assumed to be a good proxy for the net benefits paid by Venice visitors to the “touristdependent population” in spite of income leakages to residents outside Venice), and c,, c2, and cg are coefficients representing average daily per capita tourist outlay for each type of visitor. The value of this objective function (for which an aspiration level, b,, is defined by the “tourist-dependent population” together with its minimum acceptable level, 6, - p,, has to comply with some constraints of the form:
304
TOURIST
Table 1. Determination
CARRYING
CAPACITY
of the Tourist Carying Fuzzy LP Formulation
Capacity
of Venice
Max z = 221.00 TH + 85.40 TNH + 149.00 DT Subject To: 1. HB 1.0 TH IS 9000 + e 2000 2. NHB 1.0 TNH 5 1600 + 8 2400 3. L 1.0 TH + 0.75 TNH + 0.5 DT 5 25000 + e 15000 4. P 0.33 TH + 0.33 TNH + 0.75 DT 5 15000 + e 15000 5. T 1.0 TH + 1.0 TNH + 2.0 DT 5 30000 + e 10000 6. WD 2.3 TH + 2.0 TNH + 1.5 DT 5 30000 + e 30000 7. SMV 0.4 TH + 0.3 TNH + 0.7 DT 5 10000 + e 5000 TH>O. TNHzO, DmO and we<1
WhWX?: TH TNH DT HB NHB L P T WD SMV
= = = = = = = = = =
daily number of tourists usmg hotel accommodation daily number of tourists using non-hotel accommodation daily number of day-trippers number of beds available in hotel accomodations number of beds available in non-hotel accommodations number of lunches which can be served daily by Venetian restaurants or coffee shops number of coach and car parking places offered at Venetian terminals daily number of trips offered to visitors on selected routes of the local water transport system capacity of solid waste disposal maximum number of daily visits to the Saint Mark’s Basilica
a, x 22 6, + t?p,
with x = (TH,TNH,DTJ
and x 1
0,
where 6, is the “aspiration level”- optimal, according to the “nontourist population”for the carrying capacity of the ith facility used by visitors to Venice; (b, + p,) is the value, to be considered insuperableat which the capacity expansion of the ith facility becomes unbearable for the population of Venice; ai is the vector of coefficients measuring the level of daily use of facility i by each category of visitors; and 13E [O,l] is the degree of violation of constraint b, toward 6, + p,. The FLP problem to be solved for the determination of the tourist carrying capacity of the historical center of Venice is outlined in Table 1. Model Calibration
.
The coefficients of the objective function are average per capita, per diem 1984 outlays of each category of visitors (in thousand of 1984 lire), according to a local survey conducted by CoSES (1986). As for the aspiration level of the objective function and its minimum acceptable level, they have been set equal, respectively, to 4.5 and 3 billion lire per day (in 1984 prices). According to official sources, there are 11,000 beds in hotels located within Venice, and, assuming a highly satisfactory rate of occupancy of 80%, the aspiration level for their use has been set equal to 9,000. These beds can be used only by TH tourists who have been assigned a coefficient equal to 1. There are 4,000 beds in nonhotel accommodations (rooms in private apartments, hostels, etc.). According to the
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305
normal rate of occupancy of this type of accommodation (50% of the hotel bed occupancy rate on an all-year-round basis for Venice), its aspiration level has been set equal to 1,600; these beds are used by TNH tourists with a coefficient equal to 1. The number of meals that can be served at lunch time to tourists and day-trippers in Venice is about 40,000. It has been assumed that restaurants, pizza shops, and coffee shops can serve 27,500 meals two times a day from noon to 2:00 PM, with 15,000-20,000 meals reserved for commuters (students or working people). The increasing number of tourist restaurants and coffee shops is one of the most evident signs of the “crowding-out” of nontourist activity currently at work in Venice. If the maximum capacity in this area is estimated at 40,000 meals a day, a reasonable aspiration level can be set at 25,000 (the capacity level in operation only 5 years ago). All TH tourists take a lunch meal (coefficient l), while this service is assumed to be bought by three TNH tourists out of four (coefficient 0.75) and by one day-tripper out of two. The center of Venice can be reached by train or ship, but cannot be reached by car or bus. Visitors to Venice have to leave their cars or coaches at specific parking areas from where they will reach the center of Venice either on foot or by public boat (vupo~e~to).Since nontourist visitors will compete with tourists and day-trippers for parking space, one can assume that tourists can rely on an average daily availability of parking space for 30,000 persons. The aspiration level for this constraint (a level that would guarantee a comfortable accessibility to Venice for residents and commuters) has been set equal to 15,000 persontourists have been given a parking places. The TH and TNH coefficient equal to 0.33, since only one out of three tourists reaches Venice by car and almost none by coach. The DT has been given a coefficient 0.75, since 75% of day-trippers reach Venice by car or coach. The capacity of the Venetian water transportation system currently used by tourists and day-trippers has been estimated at 40,000 personrides a day. This is a use level that puts some stress on nontourist riders: The aspiration level has then been set equal to 30,000 tourist-rides a day. Every day-tripper has been supposed to ride the vaporetb twice a day (a coefficient equal to 2 .O for DT), while TH and TNH tourists are assumed to use it only once a day. The current capacity of solid waste disposal serving tourists and daytrippers has been estimated at 60,000 kg. per day; its aspiration level has been set equal to 30,000 kg per diem. It has been assumed that TH tourists produce 2.3 kg per day of garbage (like each Venetian resident), while each TNH tourist’s trash production has been set equal to 2 .O kg and the day-trippers’ is equal to 1.5 kg. St. Mark’s Basilica has been considered to represent the tourist attraction that no visitor will miss during his or her stay in Venice. Its physical capacity, or its use level under condition ofstress, has been estimated at 15,000 persons per day. An aspiration level that would avoid excessive wear and tear to the monument (like the effects of excessive temperature and humidity on the golden mosaics induced by visitor
306
TOURIST
CARRYING
CAPACITY
congestion) has been set equal (according to the office in charge of the church maintenance) to 10,000 visitors a day. Since the average length of stay of a TH tourist is a little more than 2 days and one of a TNH tourist is a little less than 3 days, TH has been given a 0.4 coefficient, TNH a 0.3 coefficient, and DT a coefficient equal to 0.7 (allowing for a share of 30 % visitors on consecutive day trips). Model Solution
The FLP problem formulated in Table 1 has been solved for different value of 19(i.e., for different grades of violation of the opposing aspiration levels): one for the objective function, which represents the interests of the “tourist-dependent population,” and those for the set of constraints which represent the interests of the “nontourist-dependent population” of Venice. If local public authorities can influence the degree of admissible violation, they will affect the objective function (the benefits) as well as the degree of violation of the various constraints or the costs. The values for t, TH, TNH, and DT corresponding to selected values of 0 are presented in Table 2 and Figure 3. Those selected are the values of 8 for which there is a change in number and quality of the actually active constraints. As can be seen in Figure 3, for 0 I 0 < 0.27 the solution is constrained by the availability of capacity for solidwaste disposal and for visits to St. Mark’s, while no TNH tourist would be “admitted” to Venice. For 0.27 I 0 < 0.5, few TNH visitors would be admitted, while the number of beds in hotel accommodations joins the set of active constraints. Numbers of beds both for TH and TNH visitors, together with St. Mark’s capacity, are the constraints active for 0.5 I 0 C 0.57. When 8 L 0.57, the capacity for urban water transportation substitutes for St. Mark’s capacity as the third active constraint. While the capacity for solid waste disposal is the most stringent constraint for 0 < 6 < 0.27, this role is played by St. Mark’s capacity for 0.27 < 8 < 0.57 and by hotel bed capacity fore > 0.57. The solution for 8 = 0 is the one that represents the achievement of the aspiration level for all constraints and then of the “nontourist-
Table 2. Determination
Different
Z
cl 0.000000 0.269164 0.501087 0.572368 1.000000 WbeIX e Z TH TNH DT
2935644 3710869 4081114 4180031 4635100
of the Tourist Carrying Capacity for Venice
FLP Solutions
TH
TNH
5941 9538 10002 10145 11000
0 2803 2974 4000
0
for 0 z 0 2 1 DT 10891 10758 10948 11303 12500
PF
= = = = = =
degree of constraint violation value of the objective function (see Table 1) (see Table 1) (see Table 1) (see Table 1) value of the membershnp functmn of Z Isee equation
PC
=
value of the membership
functmn
PF
PC
0.000000 0.473926 0.720743 0.786687 1.000000
1.000000 0.730836 0.498913 0.427632 0.000000
(12)l
of the set of constraints
[see equations
(8) and (13)I
CANESTRELLI
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307
-r
Active Constraints Duel Prices) HE (146) T (75)
0
42
W
46
Degree of ConstraintsViolation
-9-m
0.8
1
+~-A-=
Figure 3. Optimal Mix of Visitors
dependent population.” But the solution for 19 = 1 defines a situation of “ecological” maximum capacity, a situation that corresponds to the maximum tolerance level for the violation of each constraint and to the achievement of the aspiration level of the “tourist-dependent population.” For all intermediate levels of 0, both “tourist-dependent” and “nontourist-dependent” populations will only partially achieve their aspiration levels. According to the calculations in Table 2, the optimum amount of daily receipts from tourist and day-tripper outlays would vary from a value of little less than 2.94 billion lire (0 = 0) to a value of 4.64 billion lire (0 = 1). The corresponding extreme annual totals (1,073 and 1,694 billion lire) are not very far from the value estimated by CoSES (1986) for the year 1984 (1,400 billion lire), but it would come from a completely different mix of visitors. Having defined the aspiration level for the value of the objective function .z (4.5 billion lire a day in this case), together with its maximum acceptable level (3.0 billion a day), it is possible to compute pF, the membership function of z(0) defined by equation (12). Combining the “constraint” membership function, pLcgiven in equation (13), with the “objective function” one, pF given in equation (12), it becomes possible to represent /.L~given in equation (14), and the graph of “ . . . an optimal and satisfying compromise between aspirations and violations. . . . ” (Carlsson and Korhonen 1986), as noted in Table 2 and Figure 4. This figure shows that when 0 grows from 0 to 1, the degree of satisfaction of the nontourist-dependent population decreases linearly from 1 to 0, while the degree of satisfaction of the touristdependent population is equal to 0 for 0 I 0 I 0.022, shows piece-
308
TOURIST
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CAPACITY
0 0
42 _.- Tourism -dependent
44 Parameter +
46
0,s
1
Non -Tourism -depend
Figure 4. Fuzzy Decision Diagram
wise linear increases for 0.022 I 0 I 0.873, and remains equal to its maximum level, 1, for 0.873 I 8 I 1. In this case, a fuzzy decision process would suggest the compromising choice corresponding to 8 = 0.39. Both the tourist-dependent population and the nontourist-dependent population would enjoy the same degree of satisfaction. The “optimal” solution could become a stable one if, taking into account the relative size of the two population subgroups, some form of compensation could pass from the tourist-dependent population to the nontourist-dependent one. The long-run optimality of this solution is much more questionable if the aspiration level for each constraint is to be interpreted as the level that guarantees the conservation of nonreproducible resources and a long-run consistency between tourism and other residential and productive activities in the local community. A continuous violation of these aspiration levels, as implied by 6 = 0.39, is likely to strengthen the “crowding-out” of nontourist activities (a process already working in Venice). The features of the fuzzy optimal solution are described in Table 3. The “optimal solution” would admit to Venice 9,780 tourists who use hotel accommodations (with a rate of bed-occupancy of 89%), 1,460 tourist in nonhotel accommodations, and a daily maximum of 10,857 day-trippers. While this “optimal” number of tourists exceeds the actual one, the “optimal” number of day-trippers is below actual values. If the 4.1 million day-trippers who visited Venice in 1984 had been evenly distributed over each day of the year, there would have been 11,233 day-trippers per diem. As a matter of fact, CoSES (1986) has estimated
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Table 3. Determination of the Tourist Carrying Capacity for Venice FLP Solutions for 0 = 0.39 Objective Function Value 3903783.00 Variable a Value TH TNH DT How HB NHB L P T WD shw a For the definition
9780.000000 1460.211000 10857.050000
Slack or Surplus .ooOooo 1075.789000 14546.320000 8997.940000 945.684000 .oooooo .oooooo of variables
and the problem
Reduced Cost .oooOoo .oooooo .ooOOoo Dual Prices 112.953700 .OOoooo .oooooo .oooooo .oooooo 15.873690 178.842100 formulation
see Table 1
that an average of 37,500 day-trippers a day arrived during the month of August 1984, reaching a daily maximum of 80,000. The underrepresentation of TH tourists (and the overrepresentation of day-trippers) is confirmed by the postoptimization analysis (see Table 3). This shows that the second most stringent constraint, after the capacity of St. Mark’s Basilica, is the availability of hotel beds. The limits to visitor pressure that Venice has successfully made operational against tourists have been bypassed by day-trippers. The postoptimization analysis also shows (see the “dual prices” column in Table 3) that, since the chosen 0 = 0.39 is within the range 0.27 < 0 < 0.57, the most stringent constraint would be the maximum number of daily visits to St. Mark’s Basilica (this role would be played by the capacity of solid waste disposal for 0 < 9 < 27 and by the number of hotel beds for 8 > 0.57). The capacity of St. Mark’s, unfortunately, cannot be loosened without endangering the very source of tourist attraction to Venice. CONCLUSIONS Carrying capacity of a tourist destination is a concept that first has to be defined with reference to the quality of the tourist experience. When the tourist destination is a city, the quality of life of the resident population has also to be taken into consideration, by distinguishing between the tourist-dependent and the nontourist-dependent populations. While the tourist-dependent population will be ready to stand some costs in order to maximize the touristic benefits, the nontourist-dependent population will try to keep the tourist-carrying capacity at a level that does not make it bear unwanted costs. The optimal level of use of an urban tourist destination can be found by solving an FLP problem that takes into consideration the opposing aspirations of the two populations. The aspiration level of the touristdependent population - which is assumed to be the upper limit of the objective function to maximize-is likely to reach the level of “ecologi-
310
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CAPACITY
cal” carrying capacity. But the aspiration level of the nontourist-dependent population -which constrains the maximization of the objective function-is the one that fully guarantees the conservation of nonreproducible resources and a long-run consistency between tourism and other residential and productive activities in the local community. The fuzzy solution will be given by the levels of tourist use contingent on possible degrees of violation of the opposing aspiration levels. The illustrative application of the model to Venice shows promising results, even if some model assumptions need to be further verified, and the model calibration could be refined with the availability of pieces of information whose collection was beyond the scope of this work. When the model is made fully operational, by contrasting its “optimal solution” with the actual situation, it can be used in illuminating the decision-making process of the public authority. They would accommodate strategic questions such as the long-run consistency of tourism pressure on Venice, conservation of its most visited monuments, the survival of its other residential and productive functions, and the overrepresentation of day-trippers versus the underrepresentation of tourists using hotel accommodations. 00 Ackrwwledlments-This study has been financially supported by the Italian Ministry of Public Education (1988, 60% and 40% research funds granted to both Authors). The authors gratefully acknowledge many useful comments made by the anonymous referees and those on previous versions of this paper made by Jan van der Borg (Tinbergen Instituut, Rotterdam), Paul Cheshire (University of Reading), Karl Gustav Lijfgren (Umea University), Enrico Marelli (Universith Bocconi, Milano), Steiner Strom (Oslo University), Ira Sohn (Montclair College, New Jersey), and other participants in seminars held at Bocconi University (Milan), the University of Malta, the University of Venice, and Erasmus University (Rotterdam).
REFERENCES APT di Venezia. 1988 I1 movimento turistico nel comune di Venezia, Venezia: APT di Venezia Bellman, A. E., and L. A. Zadeh 1970 Decision Making in a Fuzzy Environment. Management Science 17(4):141164. Carlsson, C., and P. Korhonen 1986 A Parametric Approach to Fuzzy Linear Programming. Fuzzy Sets and Systems 20: 17-30. Chanas, S. 1983 The Use of a Parametric Programming in Fuzzy Linear Programming. Fuzzy Sets and Systems 11(3):243-251. CoSES 1986 Background Documentation on Tourism in Venice, a Report for the O.C.D.E. Venice: CoSES. Costa, Pa010 1988 Measuring the Carrying Capacity of a Major Cultural Tourism Destination: The Case of Venice. European Workshop on “Cultural Tourism in Mediterranean Islands,” Malta: University of Malta. 1990 11 turismo a Venezia e l’ipotesi Venetiaexpo 2000. Politica de1 turismo 7( 1):724. Costa, Paolo, and Jan van der Borg 1988 Un modello lineare per la programmazione de1 turismo, CoSES Informazioni 18(32/33):21-26. Dubois, D., and H. Prade 1980 Fuzzy Sets and Systems: Theory and Applications. New York: Academic Press.
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Edwards, Anthony 1987 Choosing Holiday Destinations. London: Economist Intelligent Unit. Fisher, Anthony C., and John V. Krutilla 1972 Determination of Optimal Capacity of Resource-based Recreation Facilities. Natural Resources Journal 12:417-444. Menetto, Luciano 1988 “Stimati” turisti. Una stima degli arrivi turistici a Venezia nel 1987. CoSES informazioni 18(31):29-30. Prud’homme, Remy 1986 Le tourisme et le developpement de Venise. Moteur ori frein? Paris: Institut d’urbanisme de Paris, Universite Paris XII. Tiebout, Charles T. 1956 The Urban Economic Base Reconsidered. Land Economics 32(1):95-99. Van De Panne, C. 1975 Methods for Linear and Quadratic Programming. Amsterdam: North-Holland Elsevier. World Tourism Organisation Seminar on the Development of International 1987 Basic Introductory Report, Tourism in Europe by the Year 2000. Madrid: WTO. Submitted 25 September 1989 Revised version submitted 12 April 1990 Accepted 7 May 1990 Refereed anonymously Coordinating Editor: Geoffrey Wall
1991 CopyrIght
0
0160.7383191 $3.00 + 00 1991 Pergamon Press plc and J Jafari
TOURIST CARRYING CAPACITY A Fuzzy Approach Elio Canestrelli Pa010 Costa
University
of Venice,
Italy
Abstract: This paper discusses the concept of tourist-carrying capacity of an urban cultural destination and presents a model for determining its optimal level. The model is then made operational within a “fuzzy” linear programming approach that is tested in the case of the historical center of Venice. The “fuzziness” of the model makes it possible to take into account the distribution of benefits and costs from tourism between the touristdependent and the tourist-independent resident populations who confront different categories of tourists and day-trippers. Keywords: tourist-carrying capacity, cultural tourism, urban tourism, fuzzy linear programming, Venice. R&urn& La capacitt de charge touristique: une approche floue. Cet article discute du concept de capacit6 de charge touristique vis-i-vis d’une destination culturelle urbaine et prisente un modsle pour diterminer son niveau optimal. Le modile est rendu optratif par sa traduction dans un schema de programmation 1inCaire ‘You” qui est appliquC au cas du centre-ville historique de Venise. La flexibilit6 du modkle rend possible une evaluation de la distribution des avantages et des co&s, provenant de cattgories diffbrentes de touristes et d’excursionnistes, entre deux sousgroupes de population: la population vtnitienne qui vit de tourisme et celle qui vit h Venise malgrt le tourisme. Mots-cl&: capacit6 de charge touristique, tourisme culturel, tourisme urbain, programmation lintaire floue, Venise.
INTRODUCTION One of the major changes recently noted in the evolution of world tourist demand seems to be represented by the shift from “sun and beach” holidays to more active and special interest ones (Edwards 1987; WTO 1987). This trend will affect some tourist destinations more than others, and it is possible that many cultural destinations will face increasing pressure. This is already happening in many urban historical centers, such as the historical center of Venice, whose case is discussed in this paper. In 1952, more than 500,000 tourists spent 1.2 million bed-nights in Elio Canestrelli is Professor of Financial Mathematics at the University of Venice. His major areas of interest are mathematical programming, control theory, and fuzzy set theory. Paolo Costa is Professor of Economic Programming and Director of the School of Tourism Economics and Management (Dipartimento di Scienze Economiche, Ca’Foscari 30123 Venice, Italy). His major fields of interest also include input-output analysis and regional and urban economics. 295
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the historical center of Venice. These figures have grown to 1.13 million tourist arrivals in 1987, with 2.49 million bed-nights spent in hotel and nonhotel accommodations (APT di Venezia 1988). But Venice is also the destination of a huge number of day-trippers who come from home, or from other tourist destinations (both the Adriatic beaches and the Alpine mountain areas), or from hotel accommodations located in the Veneto region. In 1987 alone, Venice was visited by 4.9 million daytrippers (Menetto 1988). Tourists and day-trippers compete for the “use” of the historical center of Venice (which has a nonexpandable surface area of only about 700 ha and is made of buildings that are protected from any alteration by special national legislation), with a resident population of 83,000 inhabitants and more than 47,000 commuters coming daily to Venice for reasons of work or study. In 1951, the historical center of Venice had a population of 175,000 inhabitants, which has been declining ever since. This process, at least during the last decade, has also been fueled by the “crowding-out” of the competitors for space activated by tourism (Costa 1990; Prud’homme 1986). It is, therefore, possible that the current quantity of visitors (a total of 6.04 million people in 1987) has already passed the tourist-carrying capacity of Venice. If Venice can be seen nowadays as an extreme case, it deserves some attention because it suffers from problems that will be shared by many other cultural tourist destinations in the very near future. This paper discusses the concept of carrying capacity of tourist destinations and suggests a way of making it operational within a “fuzzy” linear programming approach that is tested in the case of the historical center of Venice. A “crisp” linear programming approach to the same problem has been outlined in Costa and van der Borg (1988) and discussed in Costa (1988). CARRYING
CAPACITY
OF A DESTINATION
Tourists consume both public goods (or services coming from zeroprice common-property goods) and commodities and services produced and distributed by supporting facilities. Since the resource-based tourist attractions are usually nonreproducible and treated as commonproperty goods (if not strictly public goods), their (zero or negligible) price plays no role in their allocation. The maximum number of their users is first of all defined with reference to congestion: a reduction in the quality of the visitor’s experience that shows up when the intensity of use approaches the capacity limit of the tourist attraction. The concept of carrying capacity is defined (see Fisher and Krutilla 1972:420) both in ecological terms, as the maximum number of visitors that can be accommodated by a given destination under conditions of maxinurm stress, and in economic terms as the maximum number of visitors that can be accommodated at a constant quality of their experthue. Therefore, carrying capacity is in reference to the ultimate upper bound in the number of potential visitors in a resource-based attraction subsystem. However, it is quite possible that the whole tourist destination is constrained by the capacity of some other subsystem (one of those pertaining to the facilities that cater to visitor needs), regardless
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of whether or not these supporting subsystems are based on reproducible resources and are technically expandable. Unfortunately, the expansion of these supporting facilities in an urban tourist destination is not always socially desirable. Possible adverse impacts on the physical, economic, and social environments, as perceived by the resident population, are among limiting factors. This situation can be better understood by analogy to the conditions for the optimal use of a wild area, like a forest, from the economics of outdoor recreation. According to Fisher and Krutilla (1972) the criterion for optimal use of a resource-based recreational attraction is given by the maximization of:
+I) = B(q) - C(q) with
C(q) = Gk) + G&l) + G(q),
(2)
where : q c C, C, C,
= net benefits =b enefits (net of congestion disutilities) = use level of the recreational attraction = costs = cost of damage to ecological environment = current expenditures = capital expenditures (i.e., the relevant interest charges)
which is achieved in this case by differentiating setting equal to zero: d?r dB -=---dq
dq
dC, dq
dC,,, -----_() dq
and depreciation
with respect to q, and
dC, dq
The optimum use level of the recreation resource, q” in Figure 1, is higher than qm, the use level at which costs (both ecological and/or operational) begin to become relevant, and lower than qM, the use level at which total benefits would reach their maximum. With a few more assumptions, this approach can be used to determine the carrying capacity of a tourist destination that, like the historical center of Venice, is experiencing a growing demand pressure. The first assumption concerns the possibility of separating benefits and costs accruing to two mutually exclusive population subgroups. The plausibility of this assumption becomes evident, for example, ifas in the case of Venice discussed later-it is ascertainable that a relevant part of the resident population nei&r directly ROTindirectl,, gets any substantial part of its income, or any other possible benefit, from tourist activities. This is equivalent to saying- using the basic/service categorization of the urban economic base theory (Tiebout 1956)-that tourism does not account for the whole economic base of the city under
TOURIST CARRYING CAPACITY
UseLevels
q”
Figure 1. Optimal Use of a Recreation Resource
consideration. While all “service” activities are, by definition, dependent on “basic” activities and interdependent with other “service” activities, “basic” activities depend only on their export markets and are not necessarily affected by other “basic” activities. In the Venetian case, port activities (at least those handling commodities) and governmental activities (at least those connected with the role of Venice as a regional capital) are only two examples of activities that are not at all dependent on tourism. In the Italian institutional framework, the separability of the two population subgroups is made still more credible by the fact that local governments do not get their finance from taxes proportional to local income or property, but from funds transferred from the national government independently from any variation in local income. Within this first assumption, the “willingness to pay” of tourists can be easily translated into revenues and incomes accruing only to the “tourist-dependent population” who supplies those priced goods and services that complement the zero-price, resource-based tourist attractions and the resident population whose income is indirectly dependent on the activity of the “front-line” tourist suppliers. As for the costs, if the separability of the two population subgroups is accepted, it should not be difficult also to accept the possibility of a clear-cut distinction between costs borne by each subgroup. If one paraphrases the model of Fisher and Krutilla (1972), this second assumption can be specified by assuming that current and capital expenditures from tourism expansion, C,(q) and C,(q) of equation (2), are borne by both subgroups. In Venice, for example, tourist trash disposal is largely subsidized by the “nontourism-dependent” popula-
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tion, since it has been shown that the direct “tourist-dependent population” pays for only 17% of the cost of this service (Costa 1990). While the “nontourism-dependent” population is the sole group bearing Cdq) of equation (2)-the cost of damage to the ecological environment in the model of Fisher and Krutilla (1972). In this case, it can be thought of as corresponding to the opportunity costs from tourism expansion. These are the costs coming from the difficulty to expand activities different from tourism when enlarging capacities of tourist supporting facilities make use of increasing shares of the local stock of primary resources (land, buildings, accessibility, etc.). In the literature on Venice, this process is labeled as the “crowding-out” process (Prud’homme 1986). If the costs incurred by the “tourist-dependent population” are deducted from the corresponding benefits, it is possible to define an aggregate cost curve that represents only those costs borne by the “nontourist-dependent” population. ?The third assumption concerns the effects of a growing pressure of demand. In the recreational resource model, the demand curve represented in Figure 1 is such that any increase in demand will lower the willingness to pay for the marginal user. For each user, it is hypotheothers on a wilsized, “an increase in the probability of encountering derness outing is attended by diminished utility obtained from the outing” (Fisher and Krutilla 1972:421). This is equivalent to the assumption that each user has a demand curve that slopes downward and to the right, and that the aggregate demand curve will also slope downward and to the right. Any increase in the number of visitors will correspond to a movement along the aggregate demand curve and, as a consequence, to a reduction in the willingness to pay for the marginal user. If, as it has been ascertained in Venice (Costa 1990), a huge increase in the number of visitors (both tourists and day-trippers), and consequently in the level of congestion, is accompanied with price increases for all tourist commodities, this cannot be represented by movements along the aggregate demand curve. Successive rightward shifts of this curve, caused by a substitution of low-sensitive-to-congestion visitors for high-sensitive-to-congestion ones, have to be assumed. Within this third assumption, it is possible for the tourists’ willingness to pay to remain stable or even to increase, in spite of increasing congestion levels and of a consequent deterioration in the quality of a visitor’s experience. This can be described by successive shifts to the right of the marginal benefit curve of Figure 1, with corresponding shifts of q,u. Sooner or later, these movements of the marginal benefit curve will make operational the level of q’ of “ecological” carrying capacity. Any further rightward shift of the marginal benefit curve will only lead, at the margin, to an increase in the willingness to pay for a visit under conditions of maximum stress. The model for the determination of the level of optimal use of a tourist destination is represented in Figure 2, where curves B,, B,, B,, etc., depict successive net marginal benefits for the “tourist-dependent population” (benefits actually paid by visitors to the “tourist-dependent population” net of tourist costs incurred by this population subgroup) and the MC curve describes marginal tourist costs mainly borne by the “nontourist-dependent population.”
300
TOURIST CARRYING CAPACITY
qrn
%l
%Eq*
%3
Use Levels Figure 2. Optimal Use-Level of a Tourist Destination
It should be clear that because of the existence of these two different interest groups, the optimal level of use, q”, is not an equilibrium point. While the “tourist-dependent population” will try to push the carrying capacity limit toward q*, where its net benefits would be maximized, the “nontourist-dependent population” will try to keep the carrying capacity level as near to qmas possible in order to minimize its touristic costs. The actual level of use, q, which is allowed to vary between q,,,and q*, will result from the composition of the forces exerted by the two population subgroups, if its determination is not handled by extra-market devices in the public sector. In the latter case, the determination of the optimal tourist-carrying capacity should be defined by the public authority through a decision process characterized by two sets of control variables. First are those defining the capacity of each supporting facility (hotels, restaurants, parking lots, etc.) that would be set near qmor at q* as defined according to the opposing aspirations of the two population subgroups. Second sets of control variables are those describing the mix of potential users: separate categories of tourists and daytrippers who yield different “benefits” and exert distinct levels of pressure on different facilities. Since the measure of constraints (capacity of each supporting facility) has to be purposely set to vary within given intervals (qtm, q’* for each facility i), this problem can easily be translated into a linear-programming or into a “fuzzy” linear programming (FLP) problem.
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LINEAR
AND COSTA
301
PROGRAMMING
A linear programming problem which deals with fuzzy sets becomes a fuzzy linear programming (FLP) problem. A set A of the universe X is said to be fuzzy if its characteristic function is replaced by a membership function whose valuation set is allowed to be the real interval [0,11. A = ((x, pA(x)), x E X) with pa: X+[O,l] pA(x) is called th e membership function of fuzzy set A because the closer the value of pLA(x)is to 1, the more x belongs to A (Dubois and Prade 1980). In the fuzzy realm a classical integer number, such as 5, is replaced by the set of integers “more or less equal to 5.” In this case, if p(x) = 0, x is not equal to 5, if p(x) = 1, x is fully equal to 5, while if 0 < p(x) < 1, x is equal to 5 at some “degree of possibility” p(x). The most frequent formulations of an FLP problem are (a) find a fuzzy vector solution x that maximizes cx subject to fuzzy inequality constraints ai x C 5: b, max cx subject to: a, x <
x >
= b,
(i =
1,2,
. . . ,772)
=o
(4)
where c,a, . . . a, are crisp vectors while x and b are fuzzy; and (b) find a crisp optimal solution x that maximizes the objective function cx subject to fuzzy inequality constraints six < = 6, . max cx subject to: ai x <
= 6,
(i = 1,2,
. . .
. .m)
XL0 where vectors c,a, . . . a,,, and In the application described the type (a) according to the Following Bellman and Zadeh mize can be usefully replaced Therefore, the goal z = cx is is:
P”(X) =
i
b are fuzzy. next, the paper solves a FLP problem of approach suggested by Chanas (1983). (1970) the concept of a goal to maxiby the concept of a goal to achieve. a fuzzy set whose membership function
0 if cx < 6,, - p0 1 - t if cx = 6, - pa (0 5 1 5 1) 1
if cx
>
(5)
b,,
(6)
where b, is the “aspiration level” for the objective function value, (6, pO) defines the minimum acceptable level of cx, and t measures the degree of nonsatisfaction of the aspiration level b,. The membership function of each fuzzy constraint b, is defined in the same way as:
302
TOURIST
CAPACITY
if a,x > b, + pt a,x = b, + tp, (0 I
0
t if
1 -
/4(x) =
CARRYING
1
t 5
1)
(7)
if a,x < b,
where t measures the degree of violation of the “aspiration level” for the ith constraint, b,, and (b, ,+ pi) is the maximum admissible value for the same constraint. Given the membership function of each constraint, it is possible to define a unique membership function for the whole set of constraints as: k(x) A “fuzzy decision” ship function is:
=
minbl(x>, CL?(~), ..
44x)1.
(8)
is then defined by a fuzzy set D whose member-
b(x)
=
minb-4x>,14x)1.
(9)
Given these definitions, the FLP problem becomes x0, which maximizes pD(x) i.e., finding x” such as:
one of calculating
(10)
kdx”> = max h(x). Such an FLP problem can be translated programming (LP) (Chanas 1983):
into a parametric
linear
max f = cx, subject to: six % 6, + Q,, (1 = 1, 2, x20
. ,m)
(11)
which allows studying the effects on the objective function z of different grades 8 of constraint violation (for the solution of such a parametric LP problem, see, e.g., Van De Panne 1975). For each admissible value of 8, equation (11) d e f mes a value x0 and then a 2” (0) = cx” (6) also contingent upon 8. Choosing an “aspiration level,” b,, and its maximally acceptable violation pO, it becomes possible to define a membership function oft” such as: 0
P&w)
=
if,?(O)
1 - t ifpI 1 if r’(0)
< b,, - p. = b,, - tpo (0 I > b,,
t s
1)
(12)
and then to interpret 2” as a fuzzy set, while it is easy to see from equation (8) and equation (11) that:
pcle) = 1 - 8.
(13)
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For each possible 8, a solution x0 is obtained, if one exists, which both maximizes the objective function t in equation (1 l), with an associated value of the membership function pLFin equation (12) and verifies the set of constraints at a degree of satisfaction 1 - 8 according to equation (13). The degree of satisfaction of this decision is given by &e)
= min [CL&@)),
cL@)l.
(14)
A graph representing the three membership functions contingent upon 0 (pp, pc, and, see equation (14), pg) describes a complete “fuzzy decision” of the problem. APPLICATION
OF THE
FLP APPROACH
To
VENICE
Problem Formulation
The determination of the optimal level of tourist use of Venice is pursued here by solving (as an illustrative application of the FLP approach) a stylized “Venice problem” where: l The Basilica of St. Mark has been assumed to represent the whole system of nonreproducible resources that attract tourists to Venice. Since all tourists or day-trippers, with the exception of some repeat visitors, will almost certainly visit St. Mark’s, its use level under condition of stress can be set to determine the “ecological” tourist carrying capacity of the whole historical center. l Six tourist supporting facilities (see Table 1) have been identified as relevant, because they cater to the basic needs of visitors (sleeping, eating, parking and moving within Venice, etc.), because each one could constrain the whole tourist capacity of the historical city, and because their expansion would impose actual and/or opportunity costs to the “nontourist-dependent” population. l Three types of visitors have been identified to compete for the “tourist use” of Venice and to yield net benefits for the “touristdependent” population. With three types of visitorstourists using hotel accommodation (TH), tourists using nonhotel accommodations (TNH), and day-trippers (DT)the objective function of our fuzzy linear programming problem can be written as: maxr
= c,TH
+ c,TNH
+ csDT
(15)
where t represents total per diem outlays (which are assumed to be a good proxy for the net benefits paid by Venice visitors to the “touristdependent population” in spite of income leakages to residents outside Venice), and c,, c2, and cg are coefficients representing average daily per capita tourist outlay for each type of visitor. The value of this objective function (for which an aspiration level, b,, is defined by the “tourist-dependent population” together with its minimum acceptable level, 6, - p,, has to comply with some constraints of the form:
304
TOURIST
Table 1. Determination
CARRYING
CAPACITY
of the Tourist Carying Fuzzy LP Formulation
Capacity
of Venice
Max z = 221.00 TH + 85.40 TNH + 149.00 DT Subject To: 1. HB 1.0 TH IS 9000 + e 2000 2. NHB 1.0 TNH 5 1600 + 8 2400 3. L 1.0 TH + 0.75 TNH + 0.5 DT 5 25000 + e 15000 4. P 0.33 TH + 0.33 TNH + 0.75 DT 5 15000 + e 15000 5. T 1.0 TH + 1.0 TNH + 2.0 DT 5 30000 + e 10000 6. WD 2.3 TH + 2.0 TNH + 1.5 DT 5 30000 + e 30000 7. SMV 0.4 TH + 0.3 TNH + 0.7 DT 5 10000 + e 5000 TH>O. TNHzO, DmO and we<1
WhWX?: TH TNH DT HB NHB L P T WD SMV
= = = = = = = = = =
daily number of tourists usmg hotel accommodation daily number of tourists using non-hotel accommodation daily number of day-trippers number of beds available in hotel accomodations number of beds available in non-hotel accommodations number of lunches which can be served daily by Venetian restaurants or coffee shops number of coach and car parking places offered at Venetian terminals daily number of trips offered to visitors on selected routes of the local water transport system capacity of solid waste disposal maximum number of daily visits to the Saint Mark’s Basilica
a, x 22 6, + t?p,
with x = (TH,TNH,DTJ
and x 1
0,
where 6, is the “aspiration level”- optimal, according to the “nontourist population”for the carrying capacity of the ith facility used by visitors to Venice; (b, + p,) is the value, to be considered insuperableat which the capacity expansion of the ith facility becomes unbearable for the population of Venice; ai is the vector of coefficients measuring the level of daily use of facility i by each category of visitors; and 13E [O,l] is the degree of violation of constraint b, toward 6, + p,. The FLP problem to be solved for the determination of the tourist carrying capacity of the historical center of Venice is outlined in Table 1. Model Calibration
.
The coefficients of the objective function are average per capita, per diem 1984 outlays of each category of visitors (in thousand of 1984 lire), according to a local survey conducted by CoSES (1986). As for the aspiration level of the objective function and its minimum acceptable level, they have been set equal, respectively, to 4.5 and 3 billion lire per day (in 1984 prices). According to official sources, there are 11,000 beds in hotels located within Venice, and, assuming a highly satisfactory rate of occupancy of 80%, the aspiration level for their use has been set equal to 9,000. These beds can be used only by TH tourists who have been assigned a coefficient equal to 1. There are 4,000 beds in nonhotel accommodations (rooms in private apartments, hostels, etc.). According to the
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normal rate of occupancy of this type of accommodation (50% of the hotel bed occupancy rate on an all-year-round basis for Venice), its aspiration level has been set equal to 1,600; these beds are used by TNH tourists with a coefficient equal to 1. The number of meals that can be served at lunch time to tourists and day-trippers in Venice is about 40,000. It has been assumed that restaurants, pizza shops, and coffee shops can serve 27,500 meals two times a day from noon to 2:00 PM, with 15,000-20,000 meals reserved for commuters (students or working people). The increasing number of tourist restaurants and coffee shops is one of the most evident signs of the “crowding-out” of nontourist activity currently at work in Venice. If the maximum capacity in this area is estimated at 40,000 meals a day, a reasonable aspiration level can be set at 25,000 (the capacity level in operation only 5 years ago). All TH tourists take a lunch meal (coefficient l), while this service is assumed to be bought by three TNH tourists out of four (coefficient 0.75) and by one day-tripper out of two. The center of Venice can be reached by train or ship, but cannot be reached by car or bus. Visitors to Venice have to leave their cars or coaches at specific parking areas from where they will reach the center of Venice either on foot or by public boat (vupo~e~to).Since nontourist visitors will compete with tourists and day-trippers for parking space, one can assume that tourists can rely on an average daily availability of parking space for 30,000 persons. The aspiration level for this constraint (a level that would guarantee a comfortable accessibility to Venice for residents and commuters) has been set equal to 15,000 persontourists have been given a parking places. The TH and TNH coefficient equal to 0.33, since only one out of three tourists reaches Venice by car and almost none by coach. The DT has been given a coefficient 0.75, since 75% of day-trippers reach Venice by car or coach. The capacity of the Venetian water transportation system currently used by tourists and day-trippers has been estimated at 40,000 personrides a day. This is a use level that puts some stress on nontourist riders: The aspiration level has then been set equal to 30,000 tourist-rides a day. Every day-tripper has been supposed to ride the vaporetb twice a day (a coefficient equal to 2 .O for DT), while TH and TNH tourists are assumed to use it only once a day. The current capacity of solid waste disposal serving tourists and daytrippers has been estimated at 60,000 kg. per day; its aspiration level has been set equal to 30,000 kg per diem. It has been assumed that TH tourists produce 2.3 kg per day of garbage (like each Venetian resident), while each TNH tourist’s trash production has been set equal to 2 .O kg and the day-trippers’ is equal to 1.5 kg. St. Mark’s Basilica has been considered to represent the tourist attraction that no visitor will miss during his or her stay in Venice. Its physical capacity, or its use level under condition ofstress, has been estimated at 15,000 persons per day. An aspiration level that would avoid excessive wear and tear to the monument (like the effects of excessive temperature and humidity on the golden mosaics induced by visitor
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congestion) has been set equal (according to the office in charge of the church maintenance) to 10,000 visitors a day. Since the average length of stay of a TH tourist is a little more than 2 days and one of a TNH tourist is a little less than 3 days, TH has been given a 0.4 coefficient, TNH a 0.3 coefficient, and DT a coefficient equal to 0.7 (allowing for a share of 30 % visitors on consecutive day trips). Model Solution
The FLP problem formulated in Table 1 has been solved for different value of 19(i.e., for different grades of violation of the opposing aspiration levels): one for the objective function, which represents the interests of the “tourist-dependent population,” and those for the set of constraints which represent the interests of the “nontourist-dependent population” of Venice. If local public authorities can influence the degree of admissible violation, they will affect the objective function (the benefits) as well as the degree of violation of the various constraints or the costs. The values for t, TH, TNH, and DT corresponding to selected values of 0 are presented in Table 2 and Figure 3. Those selected are the values of 8 for which there is a change in number and quality of the actually active constraints. As can be seen in Figure 3, for 0 I 0 < 0.27 the solution is constrained by the availability of capacity for solidwaste disposal and for visits to St. Mark’s, while no TNH tourist would be “admitted” to Venice. For 0.27 I 0 < 0.5, few TNH visitors would be admitted, while the number of beds in hotel accommodations joins the set of active constraints. Numbers of beds both for TH and TNH visitors, together with St. Mark’s capacity, are the constraints active for 0.5 I 0 C 0.57. When 8 L 0.57, the capacity for urban water transportation substitutes for St. Mark’s capacity as the third active constraint. While the capacity for solid waste disposal is the most stringent constraint for 0 < 6 < 0.27, this role is played by St. Mark’s capacity for 0.27 < 8 < 0.57 and by hotel bed capacity fore > 0.57. The solution for 8 = 0 is the one that represents the achievement of the aspiration level for all constraints and then of the “nontourist-
Table 2. Determination
Different
Z
cl 0.000000 0.269164 0.501087 0.572368 1.000000 WbeIX e Z TH TNH DT
2935644 3710869 4081114 4180031 4635100
of the Tourist Carrying Capacity for Venice
FLP Solutions
TH
TNH
5941 9538 10002 10145 11000
0 2803 2974 4000
0
for 0 z 0 2 1 DT 10891 10758 10948 11303 12500
PF
= = = = = =
degree of constraint violation value of the objective function (see Table 1) (see Table 1) (see Table 1) (see Table 1) value of the membershnp functmn of Z Isee equation
PC
=
value of the membership
functmn
PF
PC
0.000000 0.473926 0.720743 0.786687 1.000000
1.000000 0.730836 0.498913 0.427632 0.000000
(12)l
of the set of constraints
[see equations
(8) and (13)I
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-r
Active Constraints Duel Prices) HE (146) T (75)
0
42
W
46
Degree of ConstraintsViolation
-9-m
0.8
1
+~-A-=
Figure 3. Optimal Mix of Visitors
dependent population.” But the solution for 19 = 1 defines a situation of “ecological” maximum capacity, a situation that corresponds to the maximum tolerance level for the violation of each constraint and to the achievement of the aspiration level of the “tourist-dependent population.” For all intermediate levels of 0, both “tourist-dependent” and “nontourist-dependent” populations will only partially achieve their aspiration levels. According to the calculations in Table 2, the optimum amount of daily receipts from tourist and day-tripper outlays would vary from a value of little less than 2.94 billion lire (0 = 0) to a value of 4.64 billion lire (0 = 1). The corresponding extreme annual totals (1,073 and 1,694 billion lire) are not very far from the value estimated by CoSES (1986) for the year 1984 (1,400 billion lire), but it would come from a completely different mix of visitors. Having defined the aspiration level for the value of the objective function .z (4.5 billion lire a day in this case), together with its maximum acceptable level (3.0 billion a day), it is possible to compute pF, the membership function of z(0) defined by equation (12). Combining the “constraint” membership function, pLcgiven in equation (13), with the “objective function” one, pF given in equation (12), it becomes possible to represent /.L~given in equation (14), and the graph of “ . . . an optimal and satisfying compromise between aspirations and violations. . . . ” (Carlsson and Korhonen 1986), as noted in Table 2 and Figure 4. This figure shows that when 0 grows from 0 to 1, the degree of satisfaction of the nontourist-dependent population decreases linearly from 1 to 0, while the degree of satisfaction of the touristdependent population is equal to 0 for 0 I 0 I 0.022, shows piece-
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0 0
42 _.- Tourism -dependent
44 Parameter +
46
0,s
1
Non -Tourism -depend
Figure 4. Fuzzy Decision Diagram
wise linear increases for 0.022 I 0 I 0.873, and remains equal to its maximum level, 1, for 0.873 I 8 I 1. In this case, a fuzzy decision process would suggest the compromising choice corresponding to 8 = 0.39. Both the tourist-dependent population and the nontourist-dependent population would enjoy the same degree of satisfaction. The “optimal” solution could become a stable one if, taking into account the relative size of the two population subgroups, some form of compensation could pass from the tourist-dependent population to the nontourist-dependent one. The long-run optimality of this solution is much more questionable if the aspiration level for each constraint is to be interpreted as the level that guarantees the conservation of nonreproducible resources and a long-run consistency between tourism and other residential and productive activities in the local community. A continuous violation of these aspiration levels, as implied by 6 = 0.39, is likely to strengthen the “crowding-out” of nontourist activities (a process already working in Venice). The features of the fuzzy optimal solution are described in Table 3. The “optimal solution” would admit to Venice 9,780 tourists who use hotel accommodations (with a rate of bed-occupancy of 89%), 1,460 tourist in nonhotel accommodations, and a daily maximum of 10,857 day-trippers. While this “optimal” number of tourists exceeds the actual one, the “optimal” number of day-trippers is below actual values. If the 4.1 million day-trippers who visited Venice in 1984 had been evenly distributed over each day of the year, there would have been 11,233 day-trippers per diem. As a matter of fact, CoSES (1986) has estimated
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Table 3. Determination of the Tourist Carrying Capacity for Venice FLP Solutions for 0 = 0.39 Objective Function Value 3903783.00 Variable a Value TH TNH DT How HB NHB L P T WD shw a For the definition
9780.000000 1460.211000 10857.050000
Slack or Surplus .ooOooo 1075.789000 14546.320000 8997.940000 945.684000 .oooooo .oooooo of variables
and the problem
Reduced Cost .oooOoo .oooooo .ooOOoo Dual Prices 112.953700 .OOoooo .oooooo .oooooo .oooooo 15.873690 178.842100 formulation
see Table 1
that an average of 37,500 day-trippers a day arrived during the month of August 1984, reaching a daily maximum of 80,000. The underrepresentation of TH tourists (and the overrepresentation of day-trippers) is confirmed by the postoptimization analysis (see Table 3). This shows that the second most stringent constraint, after the capacity of St. Mark’s Basilica, is the availability of hotel beds. The limits to visitor pressure that Venice has successfully made operational against tourists have been bypassed by day-trippers. The postoptimization analysis also shows (see the “dual prices” column in Table 3) that, since the chosen 0 = 0.39 is within the range 0.27 < 0 < 0.57, the most stringent constraint would be the maximum number of daily visits to St. Mark’s Basilica (this role would be played by the capacity of solid waste disposal for 0 < 9 < 27 and by the number of hotel beds for 8 > 0.57). The capacity of St. Mark’s, unfortunately, cannot be loosened without endangering the very source of tourist attraction to Venice. CONCLUSIONS Carrying capacity of a tourist destination is a concept that first has to be defined with reference to the quality of the tourist experience. When the tourist destination is a city, the quality of life of the resident population has also to be taken into consideration, by distinguishing between the tourist-dependent and the nontourist-dependent populations. While the tourist-dependent population will be ready to stand some costs in order to maximize the touristic benefits, the nontourist-dependent population will try to keep the tourist-carrying capacity at a level that does not make it bear unwanted costs. The optimal level of use of an urban tourist destination can be found by solving an FLP problem that takes into consideration the opposing aspirations of the two populations. The aspiration level of the touristdependent population - which is assumed to be the upper limit of the objective function to maximize-is likely to reach the level of “ecologi-
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cal” carrying capacity. But the aspiration level of the nontourist-dependent population -which constrains the maximization of the objective function-is the one that fully guarantees the conservation of nonreproducible resources and a long-run consistency between tourism and other residential and productive activities in the local community. The fuzzy solution will be given by the levels of tourist use contingent on possible degrees of violation of the opposing aspiration levels. The illustrative application of the model to Venice shows promising results, even if some model assumptions need to be further verified, and the model calibration could be refined with the availability of pieces of information whose collection was beyond the scope of this work. When the model is made fully operational, by contrasting its “optimal solution” with the actual situation, it can be used in illuminating the decision-making process of the public authority. They would accommodate strategic questions such as the long-run consistency of tourism pressure on Venice, conservation of its most visited monuments, the survival of its other residential and productive functions, and the overrepresentation of day-trippers versus the underrepresentation of tourists using hotel accommodations. 00 Ackrwwledlments-This study has been financially supported by the Italian Ministry of Public Education (1988, 60% and 40% research funds granted to both Authors). The authors gratefully acknowledge many useful comments made by the anonymous referees and those on previous versions of this paper made by Jan van der Borg (Tinbergen Instituut, Rotterdam), Paul Cheshire (University of Reading), Karl Gustav Lijfgren (Umea University), Enrico Marelli (Universith Bocconi, Milano), Steiner Strom (Oslo University), Ira Sohn (Montclair College, New Jersey), and other participants in seminars held at Bocconi University (Milan), the University of Malta, the University of Venice, and Erasmus University (Rotterdam).
REFERENCES APT di Venezia. 1988 I1 movimento turistico nel comune di Venezia, Venezia: APT di Venezia Bellman, A. E., and L. A. Zadeh 1970 Decision Making in a Fuzzy Environment. Management Science 17(4):141164. Carlsson, C., and P. Korhonen 1986 A Parametric Approach to Fuzzy Linear Programming. Fuzzy Sets and Systems 20: 17-30. Chanas, S. 1983 The Use of a Parametric Programming in Fuzzy Linear Programming. Fuzzy Sets and Systems 11(3):243-251. CoSES 1986 Background Documentation on Tourism in Venice, a Report for the O.C.D.E. Venice: CoSES. Costa, Pa010 1988 Measuring the Carrying Capacity of a Major Cultural Tourism Destination: The Case of Venice. European Workshop on “Cultural Tourism in Mediterranean Islands,” Malta: University of Malta. 1990 11 turismo a Venezia e l’ipotesi Venetiaexpo 2000. Politica de1 turismo 7( 1):724. Costa, Paolo, and Jan van der Borg 1988 Un modello lineare per la programmazione de1 turismo, CoSES Informazioni 18(32/33):21-26. Dubois, D., and H. Prade 1980 Fuzzy Sets and Systems: Theory and Applications. New York: Academic Press.
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Edwards, Anthony 1987 Choosing Holiday Destinations. London: Economist Intelligent Unit. Fisher, Anthony C., and John V. Krutilla 1972 Determination of Optimal Capacity of Resource-based Recreation Facilities. Natural Resources Journal 12:417-444. Menetto, Luciano 1988 “Stimati” turisti. Una stima degli arrivi turistici a Venezia nel 1987. CoSES informazioni 18(31):29-30. Prud’homme, Remy 1986 Le tourisme et le developpement de Venise. Moteur ori frein? Paris: Institut d’urbanisme de Paris, Universite Paris XII. Tiebout, Charles T. 1956 The Urban Economic Base Reconsidered. Land Economics 32(1):95-99. Van De Panne, C. 1975 Methods for Linear and Quadratic Programming. Amsterdam: North-Holland Elsevier. World Tourism Organisation Seminar on the Development of International 1987 Basic Introductory Report, Tourism in Europe by the Year 2000. Madrid: WTO. Submitted 25 September 1989 Revised version submitted 12 April 1990 Accepted 7 May 1990 Refereed anonymously Coordinating Editor: Geoffrey Wall