### A Pluto.jl notebook ###
# v0.14.5

using Markdown
using InteractiveUtils

# ╔═╡ 7845dc2e-5a8b-4a67-adb2-92df4b762df6
begin
	import Pkg
	Pkg.activate(mktempdir())
	Pkg.add([
		Pkg.PackageSpec(name="InteractiveUtils"),
		Pkg.PackageSpec(name="JuMP"),
		Pkg.PackageSpec(name="GLPK"),
		Pkg.PackageSpec(name="XLSX"),
		Pkg.PackageSpec(name="DataFrames"),
		Pkg.PackageSpec(name="Plots")
	])
	using InteractiveUtils, JuMP, GLPK, XLSX, DataFrames, Plots
end

# ╔═╡ 61e397ee-9fa5-4925-8505-b0bc9d7df0c3
md"## Coverage-based location problems"

# ╔═╡ 3b4e2c9c-21f3-4e84-983d-97ee73675840
md" To see the location of your notebook type `pwd()`"

# ╔═╡ 9e1cdd63-6a2d-4138-bb0b-1227ea448092
pwd()

# ╔═╡ b00d14b1-7f36-47fe-9206-25f0738ae044
df_ambulance = DataFrame(XLSX.readtable("Data/dataset.xlsx", "ambulance")...)

# ╔═╡ da8b7342-15cb-4515-9e74-487814689540
df_demand = DataFrame(XLSX.readtable("Data/dataset.xlsx", "demand")...)

# ╔═╡ ab3ea4bc-c3bb-462c-9529-1c4895548d88
plt = scatter(df_ambulance.:x, df_ambulance."y", xlabel = "x coordinate", ylabel = "y coordinate", grid = false, label = "Ambulance")

# ╔═╡ 58cd468c-9b7a-4d14-84fd-79b72c6b1c25
scatter!(df_demand.:x, df_demand."y", label = "Demand")

# ╔═╡ f35e03f4-2ba2-4471-b093-e66677057cf1
md"### Definition of a coverage"

# ╔═╡ c802dac0-d3bb-4e3a-88f0-2c81a1638b1b
begin
	for amb in eachrow(df_ambulance)
		r = 20
		th = Array(0:2*pi/100:2*pi+2*pi/100) # theta from 0 to 2pi 
		X = r*cos.(th) + ones(101,1)*amb.:x
		Y = r*sin.(th) + ones(101,1)*amb.:y
		plot!(plt, X,Y, c=:blue, legend=false)
	end
end

# ╔═╡ f60c5f40-395c-4e6f-ad41-c3b1c3fceaa2
plt

# ╔═╡ dc18dacb-9c5f-422d-9600-2494a7a693ba
md" ## How many ambulance should be located to cover all demands?"

# ╔═╡ cb3bc13c-68e5-40c7-932c-25f64933976e
md"""
### Step 1) Set the decision variable
"""

# ╔═╡ 07eea2bf-f092-4ec1-a82b-a43a63e9fb09
md"""
# 
$X_{i}: ~1~\text{if an ambulance is located at site}~i,~ 0~\text{otherwise}$
"""

# ╔═╡ aef7cb22-359c-4fe9-accd-7517f341cd4b
md"""
#### Step 2) Set the objective function
"""

# ╔═╡ 54088c2b-b4bc-4786-8a5a-e057c0ddc2f4
md"""
# 
$\min \sum_{i \in V}{X_i}$
"""

# ╔═╡ be9f41c6-64aa-4b97-a885-2c66a03ea8ce
md"""
#### Step 3) Set the constraint
"""

# ╔═╡ 766a9164-5959-4af6-ab6d-6da21f52cc9a
md"""
##### parameter
$a_{ij}:~ 1\text{if ambulance}~i~\text{can cover demand}~j,~ 0~\text{otherwise}$
"""

# ╔═╡ 7ae345b1-49e9-4a6a-94d5-7db7ce5a82ef
md"""
$\sum_{i}{a_{ij}\cdot X_{i}} \geq 1~~\forall j \in D$
$X_{i} \in \{0,1\} ~~\forall i \in V$
"""

# ╔═╡ ddeb045f-028f-4abc-b0bb-433818b6c31e
md"#### Exercise 1: Implement the formulation and find the solution"

# ╔═╡ 0b558788-94e9-43fb-9b1c-1c275a5bd2fe
md"-----
#### Exercise 2 : What if I can locate 3 ambulances only?
##### To where should I locate the ambulances to maximize the coverage?"

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