The map you see above is of ‘De Berkenplas’ amusement park. This was originally a nature park located by the river A, a few small lakes, and a hill with the sonorous name ‘De Berkenberg’. The ‘Berkenplas’ restaurant formed part of the park.
A few years ago a businessman bought the nature park in order to turn it into
an amusement park. As its natural state could not be disturbed to any great
extent, the number of major attractions had to be kept limited. There is however
space for adding a number of small attractions.
When planning the lay out of the amusement park, the fact that some people want
spectacular attractions (which often don’t last very long), while others will
come for quiet recreation was taken into account. Because the distances in the
park are rather large, and in order to give people the opportunity to easily
see much of the landscape, it was decided to build a small railway line. Because
of the natural obstacles of the landscape, this railway had to be a single track
railway. It goes without saying that there are stations at the major attractions.
In addition to the railway lines there are also footpaths (see the map).
The major attractions to bring in the people are:
The proprietor wants the best synchronization possible between the flows of visitors to and from the attractions and the train timetable. He wants to keep the irritation of visitors caused by waiting for a train or for an attraction to a minimum. Satisfied visitors are a good advert for friends and acquaintances. That is why he wants a train standing ready at the entrance as often as possible so that people can get on as soon as they arrive.
The gates open at 10:00 a.m.
After 21:00 no further visitors are allowed. The park closes at 22:00.
Peak times (expectation):
11:00 – 12:00
14:00 – 15:00
18:00 – 19:00.
Management expects twice as many people during peak hours as during the other
times.
Number of visitors (expectation): 5000 per day.
Exercise 1
Design the optimum timetable (for one day) for the three trains in the park.
Take all the above information into account and also other aspects that you
consider relevant. Also specify the starting times of the attractions.
You can also indicate where to place the minor attractions in order better to
control the flows of visitors. Give clear justification in your solutions.
Exercise 2
Management is considering (while keeping the timetable unchanged) taking measures
to be able to better handle the people at the entrance preparing for future
growth. They are thus considering building an extra landing stage for the boat
(at the entrance) or buying two new carriages for the train but they are also
open to other suggestions.
Advise the management in this respect.
After one year a study was done among a representative group of ‘active’ visitors. These are visitors who want to go on the four major attractions (the restaurant is left out of consideration here). They were asked which three attractions they would most like to visit and in what order they should be visited in. The result is given in the table below.
Cx-C-A | 60 | C-Cx-A | 81 | A-Cx-C | 8 | O-Cx-C | 84 |
Cx-C-O | 10 | C-Cx-O | 9 | A-Cx-O | 22 | O-Cx-A | 36 |
Cx-A-C | 17 | C-A-Cx | 30 | A-C-Cx | 18 | O-C-Cx | 36 |
Cx-A-O | 18 | C-A-O | 30 | A-C-O | 27 | O-C-A | 24 |
Cx-O-C | 147 | C-O-Cx | 75 | A-O-Cx | 38 | O-A-Cx | 10 |
Cx-O-A | 98 | C-O-A | 75 | A-O-C | 37 | O-A-C | 10 |
(F.e..: 60 people first preferred Cx, then C, then A) | Total | 1000 |
The above data can be processed into ‘transition matrices’. These matrices have the following form:
From | ||||||
---|---|---|---|---|---|---|
I | Cx | C | A | O | ||
To | Cx | |||||
C | ||||||
A | ||||||
O |
As you can see we do not assume that after the third attraction people will go back to the Entrance (exit). Try completing such a matrix in a sensible way and show the significance of such matrices for management when they as much as possible want to take the desires of the public into account, of course without discarding economic considerations. (With thanks to the ‘Nationaal Veenpark Barger-Compascuum).