Problem 4: Model Establishment and Solution for Tourist Route Planning

5.4 Problem 4: Model Establishment and Solution

5.4.1 Model Preprocessing

(1) Walking Time between Attractions

In the process of maximizing the time spent visiting attractions, the walking speed of tourists and the distances between attractions are known. Therefore, distances are converted to time units to facilitate problem solving. As a result, the time it takes for tourists to reach each attraction at a constant speed has been determined[6]. In Problem 4, the walking speed of tourists is not a fixed value:

{1km/h < v < 3km/h

Based on the real-time visiting conditions of each attraction, the walking speed of the tourist group can be adjusted accordingly. Therefore, the time it takes for tourists to reach each attraction under variable speed is a fluctuating value:

t, = (8)

Problem 4 is developed from the previous problem of allocating routes to three tourist groups.

Similarly, based on the reality of this paper, the planning of tourist routes in tourist attractions must satisfy the condition that only one tourist group can be accommodated at each attraction (except for the Wetland Commercial Street). Therefore, based on integer programming, the following constraint can be obtained:

a1j + a2j + a3j = 1

j ∈ 7 (5)

Due to the time constraint, it is known that only one tourist group can be accommodated at each attraction (except for the Wetland Commercial Street) at the same time, which means that there can be a maximum of two waiting times at the same attraction. Therefore, the constraint on the multi-objective function of waiting time w in this problem can be obtained as follows:

w1j × a1j + w2j × a2j + w3j × a3j = 1 (9)

5.4.2 Model Establishment

Based on the above analysis, the problem of planning tourist routes within tourist attractions can be regarded as a classic multi-objective programming problem aiming to maximize the visiting time and minimize the waiting time.

Let the waiting time at each attraction be w and the total waiting time be W. The multi-objective optimization function is: max T_total, min W

From the above analysis, it can be concluded that:

〈(|T_total = t, xv |lW = wij xvij

Where:

(0 Visit the attraction vik =〈l1 Do not visit the attraction

Furthermore, combined with the time constraint conditions mentioned earlier, the multi-objective optimization function can be solved.

5.4.3 Model Solution

Using the above constraints (3), (6), and (7), combined with 0-1 integer programming, a multi-objective optimization model for the three tourist groups to maximize the visiting time and minimize the waiting time is established. Finally, Lingo is used to solve the model and obtain the results (see Appendix IV for the code). The selected routes for the three tourist groups with long visiting time and short waiting time are shown in the following table (Numbers ① to represent the 7 attractions including the Tourist Service Center and Sunshine Lawn):