An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

MPEC approach for solving preventive maintenance scheduling of power units in a market environment

Yearly preventive maintenance scheduling of generating units in a restructured power system is one of the most important problems that have to be solved in modern power systems. In this paper, a bilevel approach is used for modelling of the preventive maintenance scheduling problem. The upper level of this bilevel problem represents the revenue function of power units owned by a generation company (GENCO), whereas the lower-level problem represents the market-clearing process and is usually called the independent system operator (ISO) level. This bilevel problem is then formulated as a mathematical program with equilibrium constraints (MPEC) using the primal–dual theorem, which converts the problem into a single-level mixed-integer non-linear optimization problem that can be solved using programming software. Various case studies are conducted using the IEEE reliability test system (RTS) and the obtained results are compared.