Discrete and disjunctive optimization: Parallel strategies and applications in industrial scheduling

In this thesis, two main subjects are discussed. The first subject is distributed solving techniques for disjunctive and Mixed Integer (Non)Linear Programming and the second is the scheduling of operations in the process industry. Disjunctive optimization techniques have been considered as an alternative to methods based on mixed integer linear programming. This is especially the case in the chemical engineering community, where synthesis, planning and scheduling problems are commonly solved using mathematical programming techniques. Disjunctive programming might be used when traditional mathematical programming techniques will not exploit the structure of the problems. Some basic notes on disjunctive programming are given and discussed. The relation to mixed integer programming is explored and a structured way to express disjunctive problems are given. In an early stage of the work, it was recognized that disjunctive problems should be suitable for solving by a parallel solver. To test this assumption, a system for distributed solving over a computer network was developed. Some typical scheduling problems (machine sequencing) were solved using the system, and techniques for dynamic scaling of the algorithm were introduced to further improve the methods. Although the basic system was developed for linear systems, some brief tests using non-linear problems were also performed. In the second part of the thesis, where scheduling is discussed, new methods for solving the short-term scheduling problems are presented. Although there already exist a number of algorithms for solving such problems, methods for efficient solving of large scale problems are still scarce. The method is based on a mathematical programming approach, dividing the original problem into smaller sub-problems that are solved separately. The scheduling problems considered are typically found in the pharmaceutical and the paper-converting industries, but could easily be applied to other industries. Whereas many methods handle engineering aspects such as material balances, the formulations here concentrate on operational aspects.