Calculate the number of values greater than a certain value

Specific Domains Optimization (Mathematical)
2

It seems that your constraint

@constraint(model, [i = 1:numtime], -60 * time60[i] <= Q[i] - 60)

forces time60[i] to be 1 if Q[i] < 60. Let’s say that Q[i]=40. Then we have:

-60*time60[i]<=-20

If time60[i] is zero, then we have 0<=-20 which is false, so time60[i] must be one. Maybe this link would help: Conditional constraint if else in JuMP - #12 by odow? Your constraint could be something like:

for i in numtime
    if Q[i] >= 0
        @constraint(model,time60[i] == 1)
    end
end

If you really want to play with reformulations, how about (not sure if this covers all the cases, so take with a pinch of salt):

@constraint(model, [i = 1:numtime], -60 * time60[i] <= 60 - Q[i] )

Now if Q[i]<=60, then the right-hand side is non-negative and time60[i] can be either zero or one. If Q[i]>60 the right-hand side is negative and time60[i] must be one. We still need to make sure that for Q[i]<60 you get time60[i]=0. We can redo the second constraint as:

@constraint(model, [i = 1:numtime], Q[i] -60>= -60 * (1-time60[i]))

Now, if Q[i]>=60, the left-hand side is positive, so time60[i] can be either zero or one. But if Q[i] <60, then the left-hand side is negative. And for the constraint to be satisfied we need to push the right-hand side to its minimal value that can be attained only when time60[i]=0.