2022 electrician cup question B analysis of emergency materials distribution under 5g network environment

B topic 5G The distribution of emergency materials under the network environment
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Some major emergencies often cause road blockage 、 damage 、 Closed and other unexpected situations , It will have a certain impact on people's daily life . In order to ensure people's normal life , It is particularly important to timely and accurately distribute emergency supplies . With the improvement of scientific and technological level and 5G The gradual popularity of the Internet , Unmanned aerial vehicles are more and more widely used ,“ Delivery vehicles + Unmanned aerial vehicle (uav) ” The distribution mode of has gradually become a new and effective way of distribution .

“ Delivery vehicles + Unmanned aerial vehicle (uav) ” The distribution mode of refers to ： In the process of material distribution , When the delivery vehicle delivers to a certain place , Drones can also be delivered to nearby feasible locations , And return to the delivery vehicle to reload the materials after the delivery 、 Replace the battery . This distribution mode can greatly improve the distribution efficiency of emergency supplies , It can also solve the material distribution under complex road conditions , Avoid secondary injury caused by secondary disasters .

In the process of emergency material distribution , The delivery vehicle can release the drone at a certain place , Then go to other places Delivery . The delivery vehicle can arrive at a place before the UAV and wait for the UAV to be received , It can also arrive later than UAV Place recycling drones . UAV can distribute to a place during a flight , Can also be based on Deliver to multiple locations according to the actual situation . After completing a flight, the UAV can return to the distribution vehicle to replace the battery , Then deliver again . Distribution vehicles and unmanned aerial vehicles cooperate to complete the distribution of emergency supplies at all locations , return Return to the starting point , This is called the completion of an overall delivery .

The time required to complete an overall distribution is the main consideration of the distribution personnel , It is calculated according to the time from the departure of the distribution vehicle and UAV to the return to the departure place . In the delivery process , It does not consider the time for delivery vehicles and unmanned aerial vehicles to load and unload materials , At the same time, the residence time of distribution vehicles and UAVs at each distribution point is not considered .

In order to complete the material distribution task as soon as possible , Please solve the following problems according to the data given in the attachment ： 1. chart 1 give 14 Locations , The solid line represents the route between the locations . If at present all

The emergency supplies are concentrated in No 9 Locations , The maximum load capacity of the delivery vehicle is 1000 kg , Take delivery vehicles （ Drones are not involved ） Distribution mode of . Please attach 1, Establish a mathematical model to complete one-time overall distribution , And the optimal scheme is given .

\2. chart 2 The medium solid line represents the route that both vehicles and UAVs can take , The dotted line indicates that only UAVs can

The route we took . Emergency supplies are still concentrated in No 9 Locations , The maximum load capacity of the delivery vehicle is 1000 kg , take “ Delivery vehicles + Unmanned aerial vehicle (uav) ” Distribution mode of . Please attach 2, Establish a mathematical model to complete one-time overall distribution , And the optimal scheme is given .

\3. If the problem 2 The maximum load capacity of the distribution vehicle in is 500 kg , Other conditions remain the same . Please attach 2, Establish a mathematical model to complete one-time overall distribution , And the optimal scheme is given .

\4. chart 3 There is 30 Locations , It is planned to set up two emergency material concentration sites , If the maximum load capacity of the delivery vehicle is 500 kg , take “ Delivery vehicles + Unmanned aerial vehicle (uav) ” Distribution mode of . Please attach 3, Establish a mathematical model to complete one-time overall distribution , Determine the best location of the two emergency material concentration sites .

notes ：

\1. Assume that before the distribution of emergency supplies 5G The network can cover the whole distribution area .

\2. Ignore the influence of the weight of the UAV , The maximum payload of the UAV is 50 kg ; Delivery vehicles

The average driving speed is 50 km / Hours , The average flight speed of UAV is 75 km / Hours ; UAV list

The longest flight time is 70 minute .

\3. Each emergency material concentration location is limited to one distribution vehicle , Only one drone can be carried .

\4. The runnable programs of all mathematical models are provided in the appendix of the paper .

chart 1 problem 1 Connection diagram of various points

chart 2 problem 2、 problem 3 Connection diagram of various points

chart 3 problem 4 Connection diagram of various points