Browsing by Subject "Benders decomposition"
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Item Benders decomposition and an IP-based heuristic for selecting IMRT treatment beam angles(2014-12) Lin, Sifeng; Bard, Jonathan F.To optimize the beam angle and fluence map in Intensity Modulated Radiation Therapy (IMRT) planning, we apply Benders decomposition as well as develop a two-stage integer programming-based heuristic. Benders decomposition is first implemented in the traditional manner by iteratively solving the restricted master problem, and then identifying and adding the violated Benders cut. We also implemented Benders decomposition using the “lazy constraint” feature included in CPLEX. In contrast, our two-stage heuristic first seeks to find a good solution by iteratively eliminating the least used angles in the linear programming relaxation solution until the size of the formulation is manageable. In the second stage of the heuristic, the solution is improved by applying local branching. The various methods were tested on real patient data in order to investigate their effectiveness and runtime characteristics. The results indicated that implementing Benders using the lazy constraint usually led to better feasible solutions than the traditional approach. Moreover, the LP rounding heuristic was seen to generate high-quality solutions within a short amount of time, with further improvement obtained with the local branching search.Item Dynamic and Robust Capacitated Facility Location in Time Varying Demand Environments(2010-07-14) Torres Soto, JoaquinThis dissertation studies models for locating facilities in time varying demand environments. We describe the characteristics of the time varying demand that motivate the analysis of our location models in terms of total demand and the change in value and location of the demand of each customer. The first part of the dissertation is devoted to the dynamic location model, which determines the optimal time and location for establishing capacitated facilities when demand and cost parameters are time varying. This model minimizes the total cost over a discrete and finite time horizon for establishing, operating, and closing facilities, including the transportation costs for shipping demand from facilities to customers. The model is solved using Lagrangian relaxation and Benders? decomposition. Computational results from different time varying total demand structures demonstrate, empirically, the performance of these solution methods. The second part of the dissertation studies two location models where relocation of facilities is not allowed and the objective is to determine the optimal location of capacitated facilities that will have a good performance when demand and cost parameters are time varying. The first model minimizes the total cost for opening and operating facilities and the associated transportation costs when demand and cost parameters are time varying. The model is solved using Benders? decomposition. We show that in the presence of high relocation costs of facilities (opening and closing costs), this model can be solved as a special case by the dynamic location model. The second model minimizes the maximum regret or opportunity loss between a robust configuration of facilities and the optimal configuration for each time period. We implement local search and simulated annealing metaheuristics to efficiently obtain near optimal solutions for this model.Item Relay Network Design in Logistics and Telecommunications: Models and Solution Approaches(2011-08-08) Kewcharoenwong, PanitanStrategic network design has significant impacts on the operational performance of transportation and telecommunications industries. The corresponding networks are typically characterized by a multicommodity ow structure where a commodity is defined by a unique origin-destination pair and an associated amount of ow. In turn, multicommodity network design and hub location models are commonly employed when designing strategic networks in transportation and telecommunications applications. In this dissertation, these two modeling approaches are integrated and generalized to address important requirements in network design for truckload transportation and long-distance telecommunications networks. To this end, we first introduce a cost effective relay network design model and then extend this base model to address the specific characteristics of these applications. The base model determines relay point (RP) locations where the commodities are relayed from their origins to destinations. In doing this, we explicitly consider distance constraints for the RP-RP and nonRPRP linkages. In truckload transportation, a relay network (RP-network) can be utilized to decrease drivers' driving distances and keep them within their domiciles. This can potentially help alleviate the high driver turnover problem. In this case, the percentage circuitry, load-imbalance, and link-imbalance constraints are incorporated into the base model to control related performance metrics that are affected by the distance constraints. When compared to the networks from other modeling approaches, the RP-network is more effective in controlling drivers' tour lengths and capable of controlling the empty mileage to low levels without adding a large amount of additional travel distance. In telecommunications, an RP-network can be beneficial in long-distance data transfers where the signals' delity must be improved/regenerated at RPs along their travel paths. For this setting, we extend the base model to include fixed link setup costs and capacities. From our computational results, our models provide better network configuration that is cost effective and facilitates a better service quality (shorter delays and better connectivity). Concerning methodology, we develop effcient exact solution algorithms based on Benders decomposition, Lagrangean decomposition, and Lagrangean relaxation. The performance of the typical solution frameworks are enhanced via numerous accelerating techniques to allow the solution of large-sized instances in reduced solution times. The accelerating techniques and solution approaches are transferable to other network design problem settings with similar characteristics.