Initial commit for the capacitated facility location

src/examples/csp/capacitated_facility_location.jl

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+#######################################################################################################################################
+#
+# This example was pulled from JuMP's Facility Location problem
+#
+# Link: https://jump.dev/JuMP.jl/stable/tutorials/linear/facility_location/#Capacitated-facility-location
+#
+# The objective is to minimize the cost of serving clients  by also determining whether to open a facility or not. It also takes
+# into account the client demands and facility capacities
+#
+#######################################################################################################################################
+import Random
+import LinearAlgebra
+import Plots
+include("../../JuliaCP.jl")
+using .JuliaCP
+
+Random.seed!(6789)
+
+## Upper bound used for the random number integer generation for facility & client locations
+LOCATION_UPPER_BOUND = 100
+NUMBER_OF_CLIENTS = 12
+NUMBER_OF_FACILITIES = 5
+MAX_NUMBER_OF_FACILITIES_ASSIGNED = 1
+
+## Generate the client locations
+x_client, y_client = rand(1:LOCATION_UPPER_BOUND, NUMBER_OF_CLIENTS), rand(1:LOCATION_UPPER_BOUND, NUMBER_OF_CLIENTS)
+x_facility, y_facility = rand(1:LOCATION_UPPER_BOUND, NUMBER_OF_FACILITIES), rand(1:LOCATION_UPPER_BOUND, NUMBER_OF_FACILITIES)
+
+## Fixed cost of opening the facilites
+facilities_opening_cost = ones(Int, NUMBER_OF_FACILITIES)
+
+## The distance between a client and each facility
+distances = zeros(Int, NUMBER_OF_CLIENTS, NUMBER_OF_FACILITIES)
+
+for c in 1:NUMBER_OF_CLIENTS
+    for f in 1:NUMBER_OF_FACILITIES
+        distance = LinearAlgebra.norm([x_client[c] - x_facility[f], y_client[c] - y_facility[f]], 2)
+        distances[c, f] = floor(Int, distance)
+    end
+end
+
+## Demands from each client
+demands = rand(1:5, NUMBER_OF_CLIENTS)
+
+## Capacities for each facility
+capacities = rand(12:20, NUMBER_OF_FACILITIES)
+
+## Define the solver
+solver = Engine.LearnieCP()
+
+## Variable definition
+## Shows whether a facility is open or closed
+y = [Engine.BoolVar(solver) for _ in 1:NUMBER_OF_FACILITIES]
+
+## Holds the assignment of a client to a facility
+x = Matrix{Engine.BoolVar}(undef, NUMBER_OF_CLIENTS, NUMBER_OF_FACILITIES)
+
+for c in 1:NUMBER_OF_CLIENTS
+    for f in 1:NUMBER_OF_FACILITIES
+        ## Whether client c is assigned to facility f
+        x[c, f] = Engine.BoolVar(solver)
+
+        ## A client can only be assigned to a facility if it's open
+        Engine.post(solver, Engine.LessOrEqual{Integer}(x[c, f], y[f]))
+    end
+
+    ## A client can only be assigned to 1 facility
+    Engine.post(solver, Engine.Sum{Integer}(x[c, :], MAX_NUMBER_OF_FACILITIES_ASSIGNED))
+end
+
+## Cost of opening a facility
+facility_cost = [y[f] * facilities_opening_cost[f] for f in 1:NUMBER_OF_FACILITIES]
+
+## Compute the cost of assigning a client to facility (this is the cost to be minimized)
+client_cost = Vector{Engine.AbstractVariable{Integer}}()
+for c in 1:NUMBER_OF_CLIENTS
+    for f in 1:NUMBER_OF_FACILITIES
+        ## Multiply the distance between the client & facility with the decision of whether the client was connected to 
+        ## the facility or not
+        push!(client_cost, distances[c, f] * x[c, f])
+    end
+end
+
+##