I have a binary variable $\ v(s,c,h)\ $which takes value 1 if subject $\ s\ $is taught in classroom $\ c\ $in time slot $\ h\ $ and 0 otherwise.
I have a question about a type of constraint that I cannot completely understand. For example, every instructor teaches at most one subject every hour (time slot)
$\mathop{\LARGE\mathrm Σ}_{s\in\Omega_i}\mathop{\LARGE\mathrm Σ}_{c=1}^3 \ v(s,c,h) \le 1, \forall h$
where
$\Omega = \{s_1,s_2,...,s_8\}$
There are two teachers teaching the subjects below:
$\Omega_1 = \{s_1,s_2,s_8\}$ and $\Omega_2 = \{s_3,s_4,s_5,s_6,s_7\}$
I would like to ask: How do I develop this double summation?
So far I've got
$\mathop{\LARGE\mathrm Σ}_{s\in\Omega_i}v(s,c1,h) + v(s,c2, h) + v(s,c3,h)\le 1 \Rightarrow$
$v(s1,c1,h) + v(s2,c1,h) + ... + v(s8,c1,h) + v(s1,c2,h) + ... + v(s8,c2,h) + v(s1,c3,h) + ... + v(s8, c3,h) \le 1$
But what about h? What is its role, since there is no reference for it in summation? If I have a variable with 3 elements, shouldn't I have a triple summation or something? I am completely lost here. I would appreciate of you could explain to me what is going on here. Thank you in advance.
