Conference Agenda

In sports, two key planning challenges are the scheduling of games / matches and the assignment of officiating staff to such games / matches. Addressing any of these usually requires accounting for very specific characteristics of, e.g., the sport, the level of play or the mode of competition. Consequently, decision support tools need to be tailored to these requirements rather than allowing for a one-size-fits-all solution.

This research is dedicated to the problem of assigning officiating crews to American football games in North Rhine-Westphalia (NRW), Germany. An amateur league system in terms of both competition and officiating, there are several hundred games per season in need of officiating crews that have to meet certain league-dependent requirements while accounting for each official’s availability.

Being out of reach for exact approaches, two heuristic algorithms – an adaptive large neighborhood search and a mixed-integer programming-based decomposition procedure – are proposed to tackle the problem and support the planning authorities who primarily rely on expert knowledge at this point.

Computational tests on real-world instances demonstrate substantial improvements over said expert solutions for both heuristics.

Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them - such as recycling centers - fairness between the usage of facilities becomes especially important. We develop a series of optimization models for the allocation of populations of users to such recycling centers such that access for users is balanced with a fair utilization of facilities. The optimality conditions of the underlying nonconvex quadratic models state the precise balance between accessibility and fairness. We define new classes of fairness and a metric to quantify the extent to which fairness is achieved in both optimal and suboptimal allocations.

Within the state of Bavaria in Germany, such centers have closed in the last few decades. Using mobility survey data we show how selective closures of these centers can still lead to high levels of recycling access. Our analysis ensures that even when 20% of facilities are closed smartly, the median travel distance by residents to their assigned recycling center increases by only 450 m. Additionally, we find Bavaria suffers from disparity in recycling patterns in rural and urban regions, both in terms of motivation to recycle and the locations of the facilities. We promote a policy that favors retention of recycling centers in rural regions by reserving 75% of open facilities to be in rural areas, while selectively closing facilities in urban regions, to remove these regional differences.

This work is based on two recently published articles.

Organizing lab groups in a University of Applied Sciences is a challenging task that is often done by manually assigning students to groups. For sufficiently large cohorts of students, the optimal allocation is often not reached, which is achieved by minimizing the teaching effort of instructors and minimizing the occupancy of laboratories.

In this contribution, an integer programming approach is employed to allocate students to lab groups across the Faculty of Mechanical Engineering, while minimizing the total number of groups needed. The algorithm particularly addresses the challenge of the availability of professors and laboratories, aligning the availability of students from four different bachelor programs with their personal preferences for certain weekdays, which they provide in advance. Additionally, the flexibility or restrictions required by part-time and dual study programs in terms of lab participation are integrated into the model.

The developed algorithm uses an iterative procedure that checks all relevant constraints in each iteration using IP. If the constraints lead to an infeasible solution, the less important constraints are dropped until a feasible solution is found. The choice of an objective function ensures minimal teaching effort and lab usage, but does not take advantage of group sizes. In a second iterative process, all group sizes are equalized as long as the problem is feasible.

The example computes 862 lab group assignments with a solution vector of 32,344 components, 7944 inequalities and 346 equality constraints to model the lab group assignment.