Decision Models in Skiable Areas - EPFL

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6 MODEL OF DEMAND IN A SKIABLE AREA 18 A lift on which a skier can sit down is more attractive than in the contrary case. Interpretation of the constants The constants related to the succession of two lifts passing par ”Les Ruinettes” are illustrated in Figure 9. Remarkable is the fact that the combination ”Médran-La Combe 2” is very unattractive and that ”Attelas 2” is for both preceding possibilities the most attractive choice. 4.00 3.00 2.00 1.00 0.00 -1.00 -2.00 -3.00 -4.00 Attelas 2 6.2 The Ski slope Model La Combe 2 Funispace Figure 9: Constants linked to ”Les Ruinettes” Médran 2 La Combe 1 As mentioned above, the ski slope model is not developed in this project. For the simulation, a equiprobable model is used. This means that each way from the end of the actual lift to the begin of the next lift has the same probability to be chosen: P(alternativei) = 6.3 Implementation in the code 1 # of alternatives ∀i (29) We have now seen the theory of discrete choice models, have developed a model and estimated the corresponding coefficients and parameters. Only the implementation in the code is missing. For this, we use the following algorithm: Supposing a skier is arriving at the end of a lift, then Médran 2 La Combe 1
7 CONCLUSIONS 19 • the alternatives, all reachable lifts, are determined • For all alternatives, the deterministic term of the utility function is determined as well as the probability that this alternative is chosen. This probability is determined after formula (16). • A uniformly random number between 0 and 1 is generated the corresponding alternative (the next lift) is determined. • Known the next lift, a way from the actual place to the next lift has to be chosen. For this anew a uniformly random number between 0 and 1 is generated and the way is chosen after formula (29) in the preceding section. Now, the skier knows where to go and the next time he is arriving at the end of a lift, the same procedure is used. 7 Conclusions With the Final Model we arrived at a satisfiable model with only significant attributes, parameters and constants. Some constants are not determinable with the actual set of data. But, it is probable that with a set covering the whole domain, the remaining constants could be estimated. The constants seems to be more important than we thought in the beginning. It is obvious that this model is just a first step to a model describing a lot of phenomena, observed in a skiable area. For example, our Final Model doesn’t change the values of the coefficients depending on time. But a model respecting time dependence is certainly more realistic than the Final Model. The possible improvements are explained in the next chapter. 8 Future objectives In this section, I like to suggest possible improvements of the Model. This are some hints, which has been concretized during this project or for which there was not enough time to treat it. • Time dependence: As mentioned in the previous section, it is probable that some coefficients are depending on time, because the skiers enter the skiable area in the morning and leave them in the afternoon. View that constants are very important in this models, I would propose a time dependence of the constants corresponding to the strategically places. • Altitude dependence: In my opinion, a higher situated lift is more attractive than one situated at the bottom of the area. First, because the conditions are often better in the altitude and second, in the altitude you have a better strategically position to reach rapidly a wished place in the area. Like in physics, the altitude is a potential energy. The skier has more freedom to choose his trip starting from an high situated place. So it is imageable to add an attribute corresponding to the altitude of the top of the lift in question. • Socio-economic aspects: It is also probable that a family shows up an other behavior than a singles skier, a bad skier than a good one, a young skier than an old one and so on. It would also be interesting if there is a difference between the behavior of the skiers and the snowborders.
Page 1 and 2: Decision Models in Skiable Areas Se
Page 3 and 4: 1 INTRODUCTION 3 1 Introduction Thi
Page 5 and 6: 3 METHODOLOGY - DISCRETE CHOICE MOD
Page 7 and 8: 3 METHODOLOGY - DISCRETE CHOICE MOD
Page 9 and 10: 6 MODEL OF DEMAND IN A SKIABLE AREA
Page 17: 6 MODEL OF DEMAND IN A SKIABLE AREA
Page 21 and 22: REFERENCES 21 References [1] Bierla
Page 23 and 24: REFERENCES 23 Appendix B: Detailed
Page 25: REFERENCES 25 Numéro Nom Capacité

Decision Models in Skiable Areas - EPFL

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