I teach a class with about $N=290$ students who will be taking an exam next week. The exam consists of two sections ($A$ and $B$) each with 6 essay questions. Students must answer one essay question from each section of the exam and each answer must be written in a separate exam book. Because each answer is written in a separate book, I think this essentially means that there are $2N$ essays spread out over 12 questions that need to be marked (but I will keep the two sections in case I am wrong). The distribution of the number of answers for each question tends to be non uniform such that for each section one or two questions are very popular and one or two question are very unpopular.
There will be $M=7$ people marking the exam. Assuming I have the number of times each question $a_i$ and $b_i$, for $i=1,...6$ where $\sum_ia_i=N$ and $\sum_ib_i=N$ is answered, how do I group the essays such that each group has approximately the same number of essays and questions to mark and that the number of unique questions in each group is nearly minimized. If there is variation in the number essays and questions in each group, ideally groups with more questions would have fewer essays.
Can this problem be solved in general?