2. Each elevator can reach its maximum capacity within the waiting time (20 seconds) on the basement floor, and office workers can get in and out of the elevator within the corresponding stay time (10 second) on each floor. The rest of the time, such as the time when the elevator opens and closes the door, is ignored.
3. When the elevator descends, there is no one inside, and the elevator directly returns to the lowest floor from the original target floor.
The elevator runs at a constant speed, and the acceleration when starting and stopping is ignored.
When no one is using the elevator, the elevator should stand by on the ground floor.
6. The elevator can only transport employees whose target floor is in the work area, and cannot transport other employees, even if they are on standby.
2. Variable description
Time required for Tk elevator to complete work in one mode (k= 1, …, 6)
The time when the elevator stops at the ground floor
B. Time required for the elevator to stop at each floor (except the lowest floor)
The highest target floor for elevator operation
M number of people to be transported on each floor
Unit transport capacity of elevator
Five, the elevator speed
3. Enumeration and analysis of problems
3. 1. 1 We assume that only one elevator is working.
Case 1 If there are two people on each floor when an elevator is running, then the time required for the elevator to complete all transportation tasks and return to the lowest floor for standby:
Ta = 30 * (20+2 * 3 *10+5 *10) = 3900 seconds =65 minutes.
Case 2 If all the people in the elevator are working on the same floor when the elevator runs for the first time, the time required for the elevator to complete all the transportation tasks and return to the lowest floor for standby:
TB = ∑ 6 * [20+2 * 3 * (n-1)+10] = 2340 seconds =39 minutes.
3. 1.2 Assume that the working modes of the three elevators are exactly the same (that is, A, B and C rise and fall together and open and close together).
Then, in the case of 1 of 3. 1, Tc=3900/3= 1300 seconds =2 1.67 minutes; 3. Case 2 of1.1,Td=2340/3=780 seconds = 13 minutes.
3. 1.3 Assume that elevator A only works on floors 1, 7 and 8, elevator B only works on floors 1, 9 10, and elevator C only works on floors 1,1. Three elevators are running at the same time, but they are all on the ground floor after their respective tasks are completed.
Case 1 Suppose there are five people on each floor when elevators A and B run for the first time, then the time required for elevators to complete all transportation tasks and return to the lowest floor for standby:
Te =12 * (20+2 * 3 * 9+20) =1128 seconds = 18.8 minutes.
Note: As the elevators are connected in parallel, in fact, the running time of A is 984 seconds (16.4 minutes), and that of C is 540 seconds (9 minutes), where T5 refers to the longest time consumption of the elevator group in this working mode.
Case 2 Assuming that when the elevator runs for the first time, everyone in the elevator is working on the same floor, then the time required for the elevator to complete all transportation tasks and return to the lowest floor for standby:
TF = 6 * [(20+2 * 3 * 8+10)+(20+2 * 3 * 9+10)] = 972 seconds = 16.2 minutes.
Note: Again, this is the maximum time consumption calculated by B. A and C work in this mode for 828 seconds (13.8 minutes) and 540 seconds (9 minutes) respectively. 4. Overview of the problem
User's satisfaction with elevator operation includes both physiological and psychological satisfaction [2]. Physiological satisfaction generally includes: the acceleration of the elevator in the process of starting and stopping will not make people feel uncomfortable, and the number of stops during the operation of the elevator will be as few as possible. Psychological satisfaction includes: the shortest waiting time and the shortest elevator ride time. Therefore, it is necessary to find a balance between users' physical satisfaction and psychological satisfaction in order to get the best satisfaction.
But the running speed of the elevator has been given in the original question, and the acceleration when the elevator starts and stops is ignored in this paper. Therefore, this paper only needs to care about the elevator operation scheme, so that users can wait as little as possible at the bottom and stop as little as possible on the way, which can meet the requirements.
In the third part above, by comparison, it can be found that when three elevators are running at the same time, stopping step by step saves more time than stopping step by step (compare the time required in case 1 and case 2 in one working mode). The file [1] gives a complete proof of the time saving of grouped stops. Therefore, when the stops of each group of elevators are connected together, the shortest waiting time can be obtained, which is the optimal scheme.
From this, we get the expression of the time required for the elevator to completely transport the employees on each floor during the grouping operation:
tk = m *[a+2v *(p- 1)+b *(p-6)]/n
Therefore, the answer to the question 1 "How long will it take to send these people to the corresponding office floor" is the arbitrary result of the third part. The answer to question 2, "How to dispatch elevators to make the total time for office workers to reach the corresponding floors as little as possible", is TD =13minutes 3. 1.2 or TF =16.2minutes 3. 1.3.
Question 3 "Give a concrete and practical elevator operation scheme" is the scheme of 3. 1.3: A elevator only works on floors 1, 7 and 8, B only works on floors 1, 9, 10, and C only works on floors 1,/.
4.5. Thinking about the problem
In solving the problem, this paper has made too many constraints, which makes the problem tend to be simple. However, in real life, it is impossible for all people to be on the same target floor during a trip of the elevator. After an elevator transports a specific group of people, it can continue to cooperate to transport employees on other floors. This is why there are two answers to the second question in this paper.
Because I think the correct answer to this question is really 13 minutes, and it is really only required that three elevators lift at the same time, and all employees in the elevators work on the same floor. However, if the number of floors increases, people in elevators do not work on the same floor, and the number of elevator groups increases, the corresponding method of 3. 1.3 is more feasible.