Tractable stochastic analysis in high dimensions via robust optimization

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 201-207).Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional financial contracts, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design and correct decoding in information theory are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks (Chapter 2) (b) designing multi-item, multi-bidder auctions with budget constraints, (Chapter 3) (c) characterizing the capacity region and designing optimal coding and decoding methods in multi-sender, multi-receiver communication channels (Chapter 4).by Chaithanya Bandi.Ph.D

Aggregate modeling in semiconductor manufacturing using effective process times

In modern manufacturing, model-based performance analysis is becoming increasingly important due to growing competition and high capital investments. In this PhD project, the performance of a manufacturing system is considered in the sense of throughput (number of products produced per time unit), cycle time (time that a product spends in a manufacturing system), and the amount of work in process (amount of products in the system). The focus of this project is on semiconductor manufacturing. Models facilitate in performance improvement by providing a systematic connection between operational decisions and performance measures. Two common model types are analytical models, and discrete-event simulation models. Analytical models are fast to evaluate, though incorporation of all relevant factory-fl oor aspects is difficult. Discrete-event simulation models allow for the inclusion of almost any factory-fl oor aspect, such that a high prediction accuracy can be achieved. However, this comes at the cost of long computation times. Furthermore, data on all the modeled aspects may not be available. The number of factory-fl oor aspects that have to be modeled explicitly can be reduced signiffcantly through aggregation. In this dissertation, simple aggregate analytical or discrete-event simulation models are considered, with only a few parameters such as the mean and the coeffcient of variation of an aggregated process time distribution. The aggregate process time lumps together all the relevant aspects of the considered system, and is referred to as the Effective Process Time (EPT) in this dissertation. The EPT may be calculated from the raw process time and the outage delays, such as machine breakdown and setup. However, data on all the outages is often not available. This motivated previous research at the TU/e to develop algorithms which can determine the EPT distribution directly from arrival and departure times, without quantifying the contributing factors. Typical for semiconductor machines is that they often perform a sequence of processes in the various machine chambers, such that wafers of multiple lots are in process at the same time. This is referred to as \lot cascading". To model this cascading behavior, in previous work at the TU/e an aggregate model was developed in which the EPT depends on the amount of Work In Process (WIP). This model serves as the starting point of this dissertation. This dissertation presents the efforts to further develop EPT-based aggregate modeling for application in semiconductor manufacturing. In particular, the dissertation contributes to: dealing with the typically limited amount of available data, modeling workstations with a variable product mix, predicting cycle time distributions, and aggregate modeling of networks of workstations. First, the existing aggregate model with WIP-dependent EPTs has been extended with a curve-fitting approach to deal with the limited amount of arrivals and departures that can be collected in a realistic time period. The new method is illustrated for four operational semiconductor workstations in the Crolles2 semiconductor factory (in Crolles, France), for which the mean cycle time as a function of the throughput has been predicted. Second, a new EPT-based aggregate model that predicts the mean cycle time of a workstation as a function of the throughput, and the product mix has been developed. In semiconductor manufacturing, many workstations produce a mix of different products, and each machine in the workstation may be qualified to process a subset of these products only. The EPT model is validated on a simulation case, and on an industry case of an operational Crolles2 workstation. Third, the dissertation presents a new EPT-based aggregate model that can predict the cycle time distribution of a workstation instead of only the mean cycle time. To accurately predict a cycle time distribution, the order in which lots are processed is incorporated in the aggregate model by means of an overtaking distribution. An extensive simulation study and an industry case demonstrate that the aggregate model can accurately predict the cycle time distribution of integrated processing workstations in semiconductor manufacturing. Finally, aggregate modeling of networks of semiconductor workstations has been explored. Two modeling approaches are investigated: the entire network is modeled as a single aggregate server, and the network is modeled as an aggregate network that consists of an aggregate model for each workstation. The accuracy of the model predictions using the two approaches is investigated by means of a simulation case of a re-entrant ow line. The results of these aggregate models are promising

Development of a Methodology for Hybrid Metamodeling of Hierarchical Manufacturing Systems Within a Simulation Framework

Industrial Engineering and Managemen