Can't use minimum() on constraint -MethodError: no method matching isless(...)

Specific Domains Optimization (Mathematical)
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1

I am trying to use minimum on a Julia Contraint but I get the following Method Error. I am 100% using the minimum() function is what causes the trouble. Any ideas on a work around?

LoadError: MethodError: no method matching isless(::GenericAffExpr{Float64,VariableRef}, ::GenericAffExpr{Float64,VariableRef})

for n = 1:numNeighborhoods
    @constraint(eModel, minimum(travelTimeMatrix[n,:].*openedRooms[:]) >= maxTravelTime[n])
end

The general idea is that at least one element of an array should be less than that max.

Thanks in advance

More complete snip of code:

using JuMP, Cbc, CSV

file = "Emergency.csv"

data_import = CSV.read(file, header=true)

travelTimeMatrix = Matrix{Int}(data_import[1:10,2:13])
maxTravelTime = Array{Int}(data_import[1:10,14])
emergencyRoomCost = Array{Int}(data_import[11,2:13])

numNeighborhoods = size(maxTravelTime,1)
numEmergencyRooms = size(emergencyRoomCost,1)

eModel = Model(Cbc.Optimizer)

@variable(eModel, openedRooms[1:numEmergencyRooms], binary=true)
@objective(eModel, Min, sum(openedRooms.*emergencyRoomCost))

for n = 1:numNeighborhoods
    @constraint(eModel, minimum(travelTimeMatrix[n,:].*openedRooms[:]) >= maxTravelTime[n])
end

stats = JuMP.optimize!(eModel)
result = JuMP.value.(openedRooms)

println(data_import)
println(result)
2

You cannot use arbitrary functions in a @constraint. Since you are using Cbc, you need to formulate a mixed-integer linear program with linear constraints.

for n = 1:numNeighborhoods
    @constraint(eModel, minimum(travelTimeMatrix[n,:].*openedRooms[:]) >= maxTravelTime[n])
end

# is equivalent to

@constraint(
    eModel, 
    [n = 1:numNeighborhoods, r=1:numEmergencyRooms], 
    travelTimeMatrix[n, r] * openedRooms[r] >= maxTravelTime[n],
)
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