Theses - Computation for Design and Optimization
http://hdl.handle.net/1721.1/39113
2014-04-18T06:10:39ZApproximation of the transient joint queue-length distribution in tandem networks
http://hdl.handle.net/1721.1/85470
Approximation of the transient joint queue-length distribution in tandem networks
Yamani, Jana H. (Jana Hashim)
This work considers an urban traffic network, and represents it as a Markovian queueing network. This work proposes an analytical approximation of the time-dependent joint queue-length distribution of the network. The challenge is to provide an accurate analytical description of between and within queue (i.e. link) dynamics, while deriving a tractable approach. In order to achieve this, we use an aggregate description of queue states (i.e. state space reduction). These are referred to as aggregate (queue-length) distributions. This reduces the dimensionality of the joint distribution. The proposed method is formulated over three different stages: we approximate the time-dependent aggregate distribution of 1) a single queue, 2) a tandem 3-queue network, 3) a tandem network of arbitrary size. The third stage decomposes the network into overlapping 3-queue sub-networks. The methods are validated versus simulation results. We then use the proposed tandem network model to solve an urban traffic signal control problem, and analyze the added value of accounting for time-dependent between queue dependency in traffic management problems for congested urban networks.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 95-97).
2013-01-01T00:00:00ZThe Markov chain Monte Carlo approach to importance sampling in stochastic programming
http://hdl.handle.net/1721.1/85220
The Markov chain Monte Carlo approach to importance sampling in stochastic programming
Ustun, Berk (Tevfik Berk)
Stochastic programming models are large-scale optimization problems that are used to facilitate decision-making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it involves the evaluation of a multidimensional integral whose integrand is an optimization problem. Accordingly, the recourse function is estimated using quadrature rules or Monte Carlo methods. Although Monte Carlo methods present numerous computational benefits over quadrature rules, they require a large number of samples to produce accurate results when they are embedded in an optimization algorithm. We present an importance sampling framework for multistage stochastic programming that can produce accurate estimates of the recourse function using a fixed number of samples. Our framework uses Markov Chain Monte Carlo and Kernel Density Estimation algorithms to create a non-parametric importance sampling distribution that can form lower variance estimates of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using numerical experiments in which we solve variants of the Newsvendor problem. Our results show that even a simple implementation of our framework produces highly accurate estimates of the optimal solution and optimal cost for stochastic programming models, especially those with increased variance, multimodal or rare-event distributions.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2012.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Cataloged from student-submitted PDF version of thesis.; Includes bibliographical references (pages 85-87).
2012-01-01T00:00:00ZSetting optimal production lot sizes and planned lead times in a job shop system
http://hdl.handle.net/1721.1/82419
Setting optimal production lot sizes and planned lead times in a job shop system
Yuan, Rong, S.M. Massachusetts Institute of Technology
In this research we model a job shop that produces a set of discrete parts in a make-to-stock setting. The intent of the research is to develop a planning model to determine the optimal operating tactics that minimize the relevant manufacturing costs subject to workload variability and capacity limits. We model the interplay of three key components in the job shop, namely, the production frequency for each part, the variability of production at each work station, and the level of parts inventory. We consider two operating tactics (decision variables): the production lot size for each part and the planned lead time for each work station. We model the relevant manufacturing costs, entailing production overtime costs and inventory-related costs (finished parts, work-in-process, and raw materials), as functions of these decision variables. We formulate a non-linear optimization model and implement it in the Excel Spreadsheet. We solve the model with the premium Excel Solver to determine the minimum-cost operating tactics. We test the model with both hypothetical and actual factory data from our research sponsor. The target factory processes 133 product parts on 59 work stations. The results are consistent with our intuition and demonstrate the potential value from optimizing over these tactics; these tests also provide some managerial insights on the application of these operating tactics.
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 73-75).
2013-01-01T00:00:00ZA scalable methodology for modeling cities as systems of systems
http://hdl.handle.net/1721.1/82418
A scalable methodology for modeling cities as systems of systems
Wachtel, Amanda M. (Amanda Marie)
As cities evolve in size and complexity, their component systems become more interconnected. Comprehensive modeling and simulation is needed to capture interactions and correctly assess the impact of changes. This thesis presents a methodology for modeling cities from a systems of systems perspective. The framework supplies general modeling guidelines and key steps. Also addressed are the importance of stakeholder interactions, creating the model structure, using smart city sensor data, and applying the methodology to larger, traditional cities. As an initial step, four city modeling including CityNet, CityOne, Sim City 4, and SoSAT software programs were evaluated from both a user and mathematical perspective. From the assessments, a list was developed of features critical to successful city modeling software including visualization, a streamlined user interface, accurate mathematics, the ability to specify systems and attributes, and the ability to model interconnections between systems. SoSAT was selected as the modeling tool for the case study, which involved modeling the Army's Base Camp Integration Laboratory. A model of the camp's baseline configuration was built and the camp was simulated for 30 days with results recorded at one hour intervals. 100 trials were run with averaged results presented by time intervals and for the total simulation time. Results were presented at all levels of structural aggregation. Two sensitivity analyses were conducted to analyze the impact of maintenance personnel and the frequency of potable water deliveries. Adding or subtracting a maintenance person impacted the availability of the generator systems that were being serviced, in turn impacting the performance of the micro grid. Extending the time between deliveries by 24 and 48 hours revealed two systems experienced resource depletions. Lastly, two technology insertions cases were conducted to assess the impact of adding a laundry water reuse system (LWRS) and a solar powered hot water heater (SHWH). The LWRS provided 70% of the laundry system's water needs, significantly reducing dependency upon deliveries. The SHWH was expected to decrease electricity consumption and increase fuel consumption. However, the reduction in energy demand meant fewer generators were needed to power the micro grid and both electricity and fuel consumption decreased.
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 144-146).
2013-01-01T00:00:00Z