Re
First, when I give tests, I like to have a variety of sections...a matching section, a mutiple choice section, a true-false section, a short answer section, an essay section, etc. However, because this an open-book test, I don't see anything wrong with just short answer.
Second, I do not allow retakes unless many students did poorly. Basically, I feel that if many students did poorly, that there was probably something wrong with understanding...perhaps I didn't explain it well enough. When that happens, we review and I retest them, using a different test of course! I do not average the scores because when many do poorly, I feel it's more of a lack of understanding and that I might not have taught it as well I could.
You said the test was on material that they were suppose to read the night before. Did you go over it before the test? Could they have had some trouble understanding what they read? Could they not have read it? Even if they used their book, that still doesn't help if they didn't understand it and it doesn't help them as well if they hadn't read it prior to the test. Could you retest but review the material more in case there was some misunderstanding?
When I assign students to read a lesson from their book, I suggest that they took notes in their notebook. Then, I will occasionally give a pop quiz on it. Those students who took notes are allowed to use the notes for the quiz. Those who didn't can't. They know when I assign the reading that if they take notes and there's a quiz on the material, that they get to use the notes. It's a good tool for me because if the student took notes, I know for sure that he or she read it. It also helps them learn to take notes. I also think that taking notes helps to comprehend what the book is actually saying.