An Efficient Extension of Network Simplex Algorithm

In this paper, an efficient extension of network simplex algorithm is presented. In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by Network Simplex Algorithm (NSA) and NSA+, which extended the standard NSA. The algorithms are based on graph model and their performances are at least 100 times faster than traditional simplex algorithm for Linear Programs. Many random data are generated and fed to the model for 50 vehicles. We compared results of NSA and NSA+ for the static automated vehicle scheduling problem. The results show that NSA+ is significantly more efficient than NSA. It is found that, in practice, NSA and NSA+ take polynomial time to solve problems in this application

On finding paths and flows in multicriteria, stochastic and time-varying networks

This dissertation addresses two classes of network flow problems in networks with multiple, stochastic and time-varying attributes. The first problem class is concerned with providing routing instructions with the ability to make updated decisions as information about travel conditions is revealed for individual travelers in a transportation network. Three exact algorithms are presented for identifying all or a subset of the adaptive Pareto-optimal solutions with respect to the expected value of each criterion from each node to a desired destination for each departure time in the period of interest. The second problem class is concerned with problems of determining the optimal set of a priori path flows for evacuation in capacitated networks are addressed, where the time-dependent and stochastic nature of arc attributes and capacities inherent in these problems is explicitly considered. The concept of Safest Escape is formulated for developing egress instructions. An exact algorithm is proposed to determine the pattern of flow that maximizes the minimum path probability of successful arrival of supply at the sink. While the Safest Escape problem considers stochastic, time-varying capacities, arc travel times, while time-varying, are deterministic quantities. Explicit consideration of stochastic and time-varying travel times makes the SEscape problem and other related problems significantly more difficult. A meta-heuristic based on the principles of genetic algorithms is developed for determining optimal path flows with respect to several problems in dynamic networks, where arc traversal times and capacities are random variables with probability mass functions that vary with time. The proposed genetic algorithm is extended for use in more difficult, stochastic, time-varying and multicriteria, capacitated networks, for which no exact, efficient algorithms exist. Several objectives may be simultaneously considered in determining the optimal flow pattern: minimize total time, maximize expected flow and maximize the minimum path probability of successful arrival at the sink (the objective of the SEscape problem). Numerical experiments are conducted to assess the performance of all proposed approaches