It is a complex sentence as it contains a subordinate clause. 'After the supplies are delivered' does not make sense on its own as a sentence,so you need to add the 'we will decorate the room' for the sentence to make sense.
A complex sentence is a type of sentence consisting of an independent clause (a clause that expresses a complete thought) and a dependent clause (a clause that can not stand alone as a sentence because it does not express a complete thought). In this type of sentence, the dependent clause is often introduced by a coordinating conjunction such as when (like in the sentence given), after, while, because, since, if and until, which also indicate the subordination of the clause to the independent clause.
The sentence provided is structured like a complex sentence: It has a dependent clause:<em> After the supplies are delivered</em>, and a dependent clause: <em>we will decorate the room.</em>
The first one is the correct way to use it, since it separates the parts of the sentence into fragments that can still be understood without changing the meaning of the entire sentence.
