SOLVER_NL = IpoptSolver()

m4 = Model(solver = SOLVER_NL)

N,T = 10,12
to=10
@variable(m4, y[i=1:N, t=1:T])

@objective(m4, Min, sum(y[i,to] for i=1:N))
for t=to+1:T
@constraint(m4,sum(y[i,t] for i=1:N)==0)
end
for i=1:N
    @constraint(m4,sum(y[i,t] for t=d[i]:f[i])==w[i])
    @constraint(m4,sum(y[i,t] for t=1:(d[i]-1))==0)
    @constraint(m4,sum(y[i,t] for t=(f[i]+1):T)==0)
end
for t=1:T
    @constraint(m4,sum(y[i,t] for i=1:N) <=x_ub)
    @constraint(m4,sum(y[i,t] for i=1:N) >=0)
end
for i=1:N,t=1:T
    @constraint(m4,y[i,t]>=0)
end