Decision Models in Skiable Areas - EPFL

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6 MODEL OF DEMAND IN A SKIABLE AREA 10 which the decision maker is ending at. Let also be LD the lift which the decision maker is considered to chose. The set SLD is the set of ski slopes leaving from the top of LD. Then the six attributes are: • The first attribute is the information about the most difficult level of the pistes on the different ways from O to D: Maxmax D O = max w∈W D O max i=1,...,k lsi , where w = s1 ∪ s2 ∪ . . . sk (20) • The second attribute is the minimum level you have to master for skiing form O to D. Minmax D O = min w∈W D O max i=1,...,k lsi , where w = s1 ∪ s2 ∪ . . . sk (21) • The MaxLD attribute is the value of the highest level of the ski slopes leaving from the top of LD MaxLD (22) = max ls s∈SLD • The MinLD attribute is contrary to the MaxLD attribute the lowest level of ski slopes leaving from the top of LD. MinLD = min ls s∈SLD • The next attribute is a binary value and it is about the protection against the weather of the considered lift LD and noted P rotLD . It counts true (”1”) if the skier is protected against weather on the lift, and false (”0”) otherwise. This attribute coincide in the particular case of Verbier with the attribute which describes if the skier have to put off his skis or snowboard. This means that at every lift with a weather protection you have to put off your skis or snowboard. (23) • The last attribute describes the possibility to have a seat or not while using the lift LD. It is also a binary value and noted SeatsLD. Note: A such coding of the ski slope level makes the hypothesis that a black ski slope is considered two times more difficult than a blue one. This hypothesis is accepted in the Basic Model such as the first approach to improve the Basic Model. The second Approach respect the fact, that a black ski slope has not to be two times more difficult than a red one. The deterministic term In the Basic Model, the deterministic term is only depending of the alternatives and not from the decision maker itself. Also the constants has been omitted. As described in section 3.4.1 it has the following form: Va(xa) = � βkxa(k) (24) or with the particular attributes and alternative LD k VLD (xLD ) = β1Maxmax D O + β2Minmax D O + β3MaxLD + β4MinLD (25) + β5P rotLD + β6SeatsLD (26) where the same notation is used as above. In further sections, we pose
6 MODEL OF DEMAND IN A SKIABLE AREA 11 Name Value Std err t-test Max 0.48 0.07 6.80 Maxmax -0.27 0.06 -4.73 Min -2.00 0.18 -11.29 Minmax -1.76 0.07 -26.63 Protection 0.78 0.08 10.15 Sieges 1.05 0.13 8.00 Figure 2: Results of the Basic Model β1 = Maxmax β2 = Minmax β3 = Max β4 = Min β5 = Prot β6 = Seats The random term In the basic model, a Multinominal Logit Model is used. Note: In this model (Basic Model), the following hypothesis are supposed: • Homogeneity: The behavior of all skiers is supposed to be equal. There is no distinction between different types of skiers. • Independence of time: The behavior of a skier is supposed the same at 10 am than at 3 pm. • A black level ski slope is considered two times more difficult than a red level one. 6.1.2 Analysis of the Basic Model The coefficient estimation using the data’s is done with the programm Biogeme 1 . It’s a programm allowing to estimate the coefficients by maximum of likelihood. It returns the estimated values of the coefficients, a signification test value for each coefficient and the correlation between the coefficients. The results of the estimation of the basic model is shown in Figure 2 where all coefficients satisfies the signification test (t-test). A further analysis, assuming that the coefficients are random variables, shows that the hypothesis that Minmax D O and P rotD are random variables can not be rejected. This is the motivation for the next section and leads to an other model, where these two attributes are supposed depending on time. In this paragraph, a explication for the signs of the coefficients is searched • Maxmax has a negative sign. This would mean that a more difficult way between to lifts is less attractive. This can not be explained and is the motivation for the second approach in section 6.1.4 • Minmax has a negative sign, which can be interpreted that the skiers appreciates more a low level of the minimal difficulty of the ways between to lifts. • Max has a positive sign. This means that a high level of the attribute ”Max” (MaxLD = maxs∈SL D ls) is more attractive, which is comprehensible. 1 This is a programme developed by M. Bierlaire which allows to estimate the coefficients of a Multinominal Logit Model (such as Cross-Nested and GEV-Models)
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Page 3 and 4: 1 INTRODUCTION 3 1 Introduction Thi
Page 5 and 6: 3 METHODOLOGY - DISCRETE CHOICE MOD
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Page 19 and 20: 7 CONCLUSIONS 19 • the alternativ
Page 21 and 22: REFERENCES 21 References [1] Bierla
Page 23 and 24: REFERENCES 23 Appendix B: Detailed
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