A dual exterior point simplex type algorithm for the minimum cost network flow problem

A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree)

The Role and relevance of mathematics in the maritime industry

Maritime activities occupy more than three-quarters of the world space and provide a huge occupational industry for mankind. Of late, ship construction and usage including space management onboard the vessels and the ports have brought about a great dependency on mathematical principles or models such as time series, linear programming and queuing theories among others. These models, however, hardly come in the form of direct mathematics but rather embedded in technology which, again, is built on the advancement of mathematics. This study was aimed at investigating the relevance (utility value) of mathematics in the changing trends of Maritime Business, Education and Training. The paper discusses the various domains of occupational practice where maritime education and training practitioners encounter the use and application of mathematics. It also identifies specific types or areas of mathematics applicable to and/or by Maritime Business, Education and Training practitioners in their day to day activities. The paper concludes by making recommendations for curriculum considerations on issues bordering on the mathematics teaching and learning for Maritime Business, Education and Trainin

Optimizing Inventory for Profitability and Order Fulfillment Improvement

Despite the extensive research on inventory management, few studies have investigated the optimization of inventory classification and control policies for maximizing the net present value of profit and order fulfillment performance. This dissertation aims to fill the gaps, and consists of two main essays. Essay One (Chapter 1) presents a new multi-period optimization model to explicitly address nonstationary demand, arbitrary review periods, and SKU-specific lead times, with the objective of maximizing the net present value of profit. A real-world application and computational experiments show that the optimal dynamic inventory classification and control decisions obtained from the model significantly reduce both safety stock and base stock levels compared to a multi-criteria inventory classification scheme and the traditional ABC approach. Essay Two (Chapter 2) examines two order-based fulfillment performance measures: the order fill rate, defined as the percentage of orders that are completely filled from available inventory; and the average customer-order fill rate, defined as the mean percentage of total units in a customer order that can be filled from on-hand inventory. Novel optimization models are developed to maximize the order fulfillment performance. Computational results indicate that a commonly used item-based measure in general does not adequately indicate order-based performance, and the tradeoffs between profit and order-based measures vary with inventory investment. This research contributes to the existing literature by providing new approaches to optimize inventory classification and control policies with various performance criteria. It also provides practitioners with a viable way to manage inventory with nonstationary demand, general review periods and lead times, and further allows companies to quantity the tradeoffs of different performance measures

Integrated network flow model for a reliability assessment of the national electric energy system

Electric energy availability and price depend not only on the electric generation and transmission facilities, but also on the infrastructure associated to the production, transportation, and storage of coal and natural gas. As the U.S. energy system has grown more complex and interdependent, failure or degradation on the performance of one or more of its components may possibly result in more severe consequences in the overall system performance. The effects of a contingency in one or more facilities may propagate and affect the operation, in terms of availability and energy price, of other facilities in the energy grid. In this dissertation, a novel approach for analyzing the different energy subsystems in an integrated analytical framework is presented, by using a simplified representation of the energy infrastructure structured as an integrated, generalized, multi-period network flow model. The model is capable of simulating the energy system operation in terms of bulk energy movements between the different facilities and prices at different locations under different scenarios. Assessment of reliability and congestion in the grid is performed through the introduction and development of nodal price-based metrics, which prove to be especially valuable for the assessment of conditions related to changes in the capacity of one or more of the facilities. Nodal price-based metrics are developed with the specific objectives of evaluating the impact of disruptions and of assessing capacity expansion projects. These metrics are supported by studying the relationship between nodal prices and congestion using duality theory. Techniques aimed at identifying system vulnerabilities and conditions that may significantly impact availability and price of electrical energy are also developed. The techniques introduced and developed through this work are tested using 2005 data, and special effort is devoted to the modeling and study of the effects of hurricanes Katrina and Rita in the energy system. In summary, this research is a step forward in the direction of an integrated analysis of the electric subsystem and the fossil fuel production and transportation networks, by presenting a set of tools for a more comprehensive assessment of congestion, reliability, and the effects of disruptions in the U.S. energy grid

Economic efficiencies of the energy flows from the primary resource suppliers to the electric load centers

The economic efficiency of the electric energy system depends not only on the performance of the electric generation and transmission subsystems, but also on the ability to produce and transport the various forms of primary energy, particularly coal and natural gas. However, electric power systems have traditionally been developed and operated without a conscious awareness of the energy system-wide implications, namely the consideration of the integrated dynamics with the fuel markets and infrastructures. This has been partly due to the difficulty of formulating models capable of analyzing the large-scale, complex, time-dependent, and highly interconnected behavior of the integrated energy system. In this dissertation, a novel approach for studying the movements of coal, natural gas, and electricity in an integrated fashion is presented. Conceptually, the model developed is a simplified representation of the national infrastructures, structured as a generalized, multiperiod network composed of nodes and arcs. Under this formulation, fuel supply and electricity demand nodes are connected via a transportation network and the model is solved for the most efficient allocation of quantities and corresponding prices for the mutual benefits of all. The synergistic action of economic, physical, and environmental constraints produces the optimal pattern of energy flows. Key data elements are derived from various publicly available sources, including publications from the Energy Information Administration, survey forms administered by the Federal Energy Regulatory Commission, and databases maintained by the Environmental Protection Agency. The results of different test cases are analyzed to demonstrate that the decentralized level of decision-making combined with imperfect competition may be preventing the realization of potential cost savings. An overall optimization at the national level shows that there are opportunities to better utilize low cost generators, curtailing usage of higher cost units and increasing electric power trade, which would ultimately allow customers to benefit from lower electricity prices. In summary, the model developed is a simulation tool that helps build a better understanding of the complex dynamics and interdependencies of the coal, natural gas, and electricity networks. It enables public and private decision makers to carry out comprehensive analyses of a wide range of issues related to the energy sector, such as strategic planning, economic impact assessment, and the effects of different regulatory regimes

A tool for sourcing decisions

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (leaf 61).by Miguel Manuel Miciano.S.M