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).
In the following, we will try to develop a mixed-integer programming (MIP) model for the
above problem. Our objective is to determine a specific drone model for each location with the
lowest total costs, while making sure 5G signals will cover the entire area. Let us first define
subscripts (下標)for this MIP model.
In the In the following, we will develop this MIP model onc equation at a time. **Please note**:
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
【題組】Question 1.1 (10%) Next, the drone model chosen for each location will determine that location's effective 5G-
covering area. Shown in the following figure, if drone model
is chosen for location
m , then D
m will equal radius
i ; but if a different drone model in drones
m is chosen, D
m could
have a different value. For each location m in the locations set, please develop an equation to
determine the real value of D
m.