申論題

1. (35% in total)
         Consider this situation which could become real in the near future: We have a number of predetermined(事先決定的)Iocationsfrom which 5G signals will be emitted (發射) by using air- borne autono mous drones(空中無人機).Of course,we wish to cover the entire area with 5G. There are a number of companies manufacturing various drone models. These drone models have different weight-lifting(載重) capabilities, which means they can carry different 5G equipment into the air to cover a different area size.Naturally, if a drone model can carry more weight, it is also more expensive to purchase. Moreover, for those predetermined locations to emit 5G signals, each of them can only deploy some of the drone models due to various reasons/considerations (that is, a drone model that is OK for one location may not be OK for another location). 

We will only use the above already defined subscripts, sets, parameters, and decision variables.' In

other words,“在模型中禁止使用任何自行定義的符號,無論是下標、參數、決策變數等”

**Please also note**: We only want to develop a lincar MIP model(必需是線性 MIP模型).

First, since each location must bave a drone model (which is OK for that location) to send 5G

signals, we obviously will need this constraint in the model: locations .

ie drenes

Question 1.2(10%) To make sure that SG signals will cover the entire area, we must enforce a specific overlap(特 定程度的重疊) on the two areas covered by any two nearby locations. Shown in the following figure, if m and n are two such locations, then the sum of D_mand D_n must be at least 1.5 times of the distance between the two locations (no matter the drone model used in each location to emit 5G signals). Please develop an equation to enforce that requirement in the model.