Abstract:
Decision optimization is widely used in many decision support and guidance systems (DSGS) to support business decisions such as procurement, scheduling and planning. In spite of rapid changes in customer requirements, the implementation of DSGS is typically rigid, expensive and not easily extensible, in stark contrast to the agile implementation of information systems based on the DBMS and SQL technologies. This dissertation introduces the Decision Guidance Query Language (DGQL) designed to (re-)use SQL programs for decision optimization with the goals of making DSGS implementation agile and intuitive, and leveraging existing investment in SQL- implemented systems. This dissertation addresses several related technical issues with DGQL: (1) how to annotate existing queries to precisely express the optimization semantics, (2) how to translate the annotated queries into equivalent mathematical programming (MP) formulations that can be solved efficiently using existing industrial solvers, and (3) how to develop specialized optimization algorithms for a class of multi- stage production problems modeled in DGQL.
The algorithms for the multi-stage production network utilize the fact that only part of the problem is dynamic, e.g., the demand for output products in a manufacturing process, whereas the rest of the problem is static, e.g., the connectivity graph of the assembly processes and the cost functions of machine assemblies. An online decomposition algorithm (ODA) is developed based on offline preprocessing of static assembly components to create an approximated cost function, which is used to decompose the original problem into smaller problems and significantly improve solution quality and time complexity. The preprocessing of each static assembly component involves discretizing assembly output, finding the corresponding optimal machine configuration, and constructing a piecewise linear approximation of the assembly cost function. An adaptive preprocessing algorithm (APA) is introduced that considers only a small percentage of the discretized points by classifying outputs based on their predicted machine configuration. An initial experimental evaluation suggests that (1) machine generated MP models introduce little or no degradation in performance as compared with expertly crafted models, (2) ODA, using offline preprocessing, leads to an order of magnitude improvement in quality of solutions and optimization time as compared to MILP, and (3) APA shows significant improvement in preprocessing time with no reduction in the quality of the online solution.
