
## 2 The University Lecturer-Student Assignment Problem

The studied problem of assigning students to lecturers has to be solved by the Department Production and Operations Management of the University of Hohenheim on a recurring basis. Within a seminar, organized twice a year, each member of staff proposes a number of scientific topics for which students may apply. Depending on the number of applications, identical topics may be assigned to different students to increase the capacity of the seminar. It can be experienced that the acceptance of a particular topic and the corresponding motivation to work in it depends on the personal preferences students may have for particular subjects.

In the past the assignment of students to topics has been done **on a first-come-first-served basis,**
leading to a potential unsatisfying situation for some late **enrolling participants. Students have**
already before been given the possibility of articulating their preferences by ranking topics, but when assigning topics priority was given with respect to the **sequence in which the applications have** been received.

The concept currently under investigation allows each student i **to articulate his/her preferences**
by assigning nonnegative weights wij to each topic j **which correspond to a measure of utility**
associated with the assignment of a certain topic. For practical reasons, a total weight of Pj wij =
wmax **has been chosen and communicated to the applicants, a potential alternative however would be**
the normalization of the weight values. Applications are collected up to a certain deadline, and an optimization problem of maximizing the realized utility values is formulated and solved as follows.

$${\mathrm{max~UTILITY}}=\sum_{i=1}^{n}\sum_{j=1}^{m}w_{i j}\ x_{i j}$$
$$(1)$$

subject to

$$\sum_{i=1}^{n}x_{ij}\geq a_{j}\quad\forall j=1,\ldots,m$$ $$\sum_{i=1}^{n}x_{ij}\leq b_{j}\quad\forall j=1,\ldots,m$$ $$\sum_{j=1}^{m}x_{ij}=1\quad\forall i=1,\ldots,n$$ $$x_{ij}\in\{0,1\}\quad\forall i=1,\ldots,n,\ j=1,\ldots,m$$

Expression (1) maximizes the total utility associated with an assignment xij **of students** i to

$$\left({2}\right)$$
$$\left({\mathrm{3}}\right)$$
