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In this paper, we introduce the Maximum Diversity Assortment Selection Problem (MADASS), which is a generalization of the 2-dimensional Cutting Stock Problem (2CSP). Given a set of rectangles and a rectangular container, the goal of 2CSP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. In MADASS, we need to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as minimum or average normalized Hamming-Distance of all assortment pairs. The MADASS Problem was used in the 11th AIMMS-MOPTA Competition in 2019. The methods we describe in this article and the computational results won the contest.
In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2CSP literature.

In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP is to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2D-KP literature.

We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.