Novel Integer Optimization Methods and their Applications in Biomass Supply Chain and Power Dominating Set

Abstract

Integer optimization (IO) problems arise in research areas and our daily life almost in every aspect. IO formulations and methods can be adopted to make optimal decisions for solution-searching and management with global optimization. Two main areas of applications of IO are studied in the dissertation. Not only the compact formulations for each problem are proposed, but also possible extensions with respect to solution approaches and illustrative case studies are presented. The first area studied in the dissertation is the application of IO to biomass supply chain. The IO is utilized to make various decisions when coordinating the flows in a biomass supply chain network. A typical biomass supply chain contains following five operational components: harvesting and collection, storage, transportation, pretreatment, and conversion. In the process of each component, there are some related classic optimization methods, including linear programming models, integer programming models, stochastic programming models, approximate approaches, etc. A detailed literature review on optimization methods for biomass supply chain is presented in this dissertation. Besides that, the uncertainties and challenges in a biomass supply chain and corresponding optimization methods to handle them are reviewed. Moreover, environmental and social issues arising in a biomass supply chain is also studied in the review. In latter work, a facility location problem is studied since the facility location decision is vital to a supply chain and has long-term influences on both cost and income. Geographic Information System (GIS) analysis is integrated into the optimization method. GIS analysis is used to identify the potential candidates which satisfy all the given criteria. Uncertainty coming from planting plan is also considered in the problem and the problem is formulated as a two-stage stochastic programming model. The second area studied in the dissertation is the application of IO to power systems, especially power dominating set problems. The IO has been applied in almost every aspect of the power system industry, including power system network design problem, unit commitment problem, and sensor placement problem. Phasor Measurement Unit (PMU) placement problem is studied in the following two manners. First, a multistage PMU placement problem is paid attention to due to the high expense of PMUs and budget limitation at each time period. The IO formulation is proposed to maximize the observation of the power system at each stage and guarantee the full observation at the last planning stage. In order to enhance the computational efficiency of the IO formulation, the problem is converted to a multistage network flow problem. Second, uncertain issues are taken into consideration and the probabilistic and reliable connected power dominating set problem is studied. In a power system, the placed PMUs in the power grid and transmission lines may not always function well. The power system health under contingencies is studied. Given pre-specified reliability level for each bus in the power system to be observed and known distribution of random events, the IO formulation is proposed to satisfy the reliability requirement and meet some other problem-specific restrictions at the same time. In the work, the connectivity of the subgraph constructed by PMUs is also guaranteed for better communication of PMUs and the reliability of the connectivity is also studied.