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IMMC 2023 Problem A (Greater China, Autumn) (English 简体 繁體)
Smart delivery of books for campus library
Background
The university has started the construction of a smart campus system. In order to facilitate teachers
and students to borrow books, and return books in a timely manner, the school library has launched
a smart module for books delivery and distribution. The smart system uses delivery robots for
receiving the returned books and distributing the borrowed books. The specifications are as follows:
1. Teachers and students in each building should put the books that need to be returned to library
at the depository in the door foyer of the building, and report their borrowing needs (see
Table 2). The book depository of each building is only allowed to store the returned or
borrowed books of the building teachers or students reside;
2. The existing delivery robots A and B respectively set off from the charging station (no
books were loaded before departure), arrive at various buildings, bring the returned books
back to the library, and then set off again to collect and return books or distribute loaned
books;
3. Under this exercise scenario, each delivery robot acts independently; it is not required to
consider the time spent in collecting books from the building depository for each robot,
either exchanging books when the two robots encounter on the way;
4. After completing the tasks ordered by the library, the delivery robots must return to their
respective starting stations for recharging.
The location of each building and actual distance of each road are shown in Figure 1 and Table 2,
respectively. Each delivery robot can load up to 10 books. The average driving speed of delivery
robot A is 8 km/h, and the average driving speed of robot B is 10 km/h.
Tas k s
1. Considering only the situation of returning books without borrowing, the delivery robots start
from the charging station respectively. Please establish a suitable mathematical model so that
the delivery robots can complete the task of returning the book in the shortest time, and finally
return to the initial station. Please illustrate the specific route and total riding time for each
delivery robot.
2. If the situation of returning books and borrowing books in Table 1 is comprehensively
considered, the delivery robots still start from their respective charging stations and can load
the books for borrowing after arriving at the library. During the driving process, you can
choose to collect the returned books while distributing the borrowed books. Please establish a
suitable mathematical model to guide the delivery robots to complete the tasks of collecting
returned books and distributing borrowed books in an optimal way, and finally return to the
initial stations. Please illustrate the specific route and total riding time for each delivery robot.
