Production Scheduling (Current Main Project)

The topic of interest concerns a modern industrial plant producing a large variety of composite biomaterials which are manufactured by combining and processing a substantial number of ingredients. Incoming orders are processed in real-time and slotted into a production schedule in order to meet the required delivery deadline. The scheduling problem is complicated because of numerous constraints, chief among them the availability of production lines, contamination and the limited storage capacity for intermediate or finished products. Solving this complicated scheduling problem currently requires comprehensive manual intervention by experienced planning experts. As a consequence, it is labor-intensive and lacks flexibility.

The goal of this project is to develop new algorithms to tackle the dynamic scheduling problem. Although this scheduling problem is linked to a concrete industrial installation, it can be seen as prototypical of a new class of challenges gaining prominence in the context of "smart industry". These problems are characterized by the availability of large amounts of real-time data quantifying nearly all aspects of the production and logistics process, the need to incorporate numerous, and often heterogeneous, constraints, and the requirement to enable on-the-fly flexibility. The project is the result of a public-private partnership between CWI and the company ENGIE.

Network Analysis via Markov Chains

Networks are everywhere, the study of which can lead to important insights. In this project networks are studied by performing a random walk over the network. This random walk can be modeled as a Markov chain. Using fundamental Markov chain concepts, such as ergodic projectors, Kemeny constants and deviation matrices, the network can be characterized and decomposed into natural clusters.

In particular, the long-term fraction of random walk visits to nodes give insight into the importance of nodes. An insight that is elaborated into Google's search engine to present satisfying and meaningful search results based on users' search terms. In one research theme we study Google's ranking approach and variants thereof in light of numerical efficiency and fairness.

In a second research theme the random walk is elaborated in a more advanced manner to decompose the original network into 'natural' clusters. This lead to Kemeny decomposition algorithm (KDA). KDA seems to provide promising results in various application domains such as in social networks and data clustering.

Numerical Computation of Markov Chains Measures

In this research project we study the various ways to efficiently calculate concepts such as ergodic projectors and deviation matrices for finite Markov multi-chains. In contrast to irreducible Markov chains, Markov multi-chains consist of multiple closed communicating classes of states together with transient states. These type of Markov multi-chains arise naturally when studying real-life networks. Both the theory and applications of the calculation methods are considered.

Robustness of Mathematical Models

In operations research the reality is often represented via a mathematical model for some parameter input. In practice, the parameter input follows from statistical analysis and is therefor of stochastic nature. In this research theme, the impact of parameter uncertainty in mathematical models is studied. Particular research questions are: What is the risk of ignoring parameter uncertainty in practice? By taking parameter uncertainty into account, what are robust solutions for the optimization of the considered model?