Analytical evaluation of the output variability in production systems with general Markovian structure

Performance evaluation models are used by companies to design, adapt, manage and control their production systems. In the literature, most of the effort has been dedicated to the development of efficient methodologies to estimate the first moment performance measures of production systems, such as the expected production rate, the buffer levels and the mean completion time. However, there is industrial evidence that the variability of the production output may drastically impact on the capability of managing the system operations, causing the observed system performance to be highly different from what expected. This paper presents a general methodology to analyze the variability of the output of unreliable single machines and small-scale multi-stage production systems modeled as General Markovian structure. The generality of the approach allows modeling and studying performance measures such as the variance of the cumulated output and the variance of the inter-departure time under many system configurations within a unique framework. The proposed method is based on the characterization of the autocorrelation structure of the system output. The impact of different system parameters on the output variability is investigated and characterized. Moreover, managerial actions that allow reducing the output variability are identified. The computational complexity of the method is studied on an extensive set of computer experiments. Finally, the limits of this approach while studying long multi-stage production lines are highlighted. © 2013 Springer-Verlag Berlin Heidelberg

Factory Models for Manufacturing Systems Engineering

We review MIT research in manufacturing systems engineering, and we describe current and possible future research activities in this area. This includes advances in decomposition techniques, optimization, token-based control systems analysis, multiple part types, inspection location, data collection and several other topics.Singapore-MIT Alliance (SMA

Serial production line performance under random variation:Dealing with the ‘Law of Variability’

Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation

The asymptotic variance of departures in critically loaded queues

We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load rho equals 1, and prove that the asymptotic variance rate satisfies lim_t Var D(t)/t = lambda (1 - 2/pi) (c_a2 + c_s2) where lambda is the arrival rate and c_a2 and c_s2 are squared coefficients of variation of the inter-arrival and service times respectively. As a consequence, the departures variability has a remarkable singularity in case rho equals 1, in line with the BRAVO effect (Balancing Reduces Asymptotic Variance of Outputs) which was previously encountered in the finite-capacity birth-death queues. Under certain technical conditions, our result generalizes to multi-server queues, as well as to queues with more general arrival and service patterns. For the M/M/1 queue we present an explicit expression of the variance of D(t) for any t

Variance of the output in a deterministic two-machine line

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1995.Includes bibliographical references (p. 133-134).by Maria Carrascosa.M.S

Production Systems with Deteriorating Product Quality : System-Theoretic Approach

Manufacturing systems with perishable products are widely seen in practice (e.g., food, metal processing, etc.). In such systems, the quality of a part is highly dependent on its residence time within the system. However, the behavior and properties of these systems have not been studied systematically, and, therefore, is carried out in this dissertation. Specifically, it was assumed that the probability that each unfinished part is of good quality is a decreasing function of its residence time in the preceding buffer. Then, in the framework of serial production lines with machines having Bernoulli and geometric reliability models, closed-form formulas for performance evaluation in the two-machine line case were derived, and develop an aggregation-based procedure to approximate the performance measures in M\u3e2-machine lines. In addition, the monotonicity properties of these production lines using numerical experiments were studied. A case study in an automotive stamping plant is described to illustrate the theoretical results obtained. Also, Bernoulli serial lines with controlled parts released was analyzed for both deterministic and stochastic releases. Finally, bottleneck analysis in Bernoulli serial lines with deteriorating product quality were studied

On the distribution of throughput of transfer lines

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 86-107A transfer line corresponds to a manufacturing system consisting of a number of work stations in series integrated into one system by a common transfer mechanism and a control system. There is a vast literature on the transfer lines. However, little has been done on the transient analysis of these systems by making use of the higher order moments of their performance measures due to the difficulty in determining the evolution of the stochastic processes under consideration. This thesis examines the transient behavior of relatively short transfer lines and derives the distribution of the performance measures of interest. The proposed method based on the analytical derivation of the distribution of throughput is also applied to the systems with two-part types. An experiment is designed in order to compare the results of this study with the state-space representations and the simulation. They are also interpreted from the point of view of the line behavior and design issue. Furthermore, extensions are briefly discussed and directions for future research are suggested.Deler, BaharM.S

Performance Evaluation of Remanufacturing Systems

Implementation of new environmental legislation and public awareness has increased the responsibility on manufacturers. These responsibilities have forced manufacturers to begin remanufacturing and recycling of their goods after they are disposed or returned by customers. Ever since the introduction of remanufacturing, it has been applied in many industries and sectors. The remanufacturing process involves many uncertainties like time, quantity, and quality of returned products. Returned products are time sensitive products and their value drops with time. Thus, the returned products need to be remanufactured quickly to generate the maximum revenue. Every year millions of electronic products return to the manufacturer. However, only 10% to 20% of the returned products pass through the remanufacturing process, and the remaining products are disposed in the landfills. Uncertainties like failure rate of the servers, buffer capacity and inappropriate preventive maintenance policy would be highly responsible the delays in remanufacturing. In this thesis, a simulation based experimental methodology is used to determine the optimal preventive maintenance frequency and buffer allocation in a remanufacturing line, which will help to reduce the cycle time and increase the profit of the firm. Moreover, an estimated relationship between preventive maintenance frequency and MTBF (Mean Time Between Failure) is presented to determine the best preventive maintenance frequency for any industry. The solution approach is applied to a computer remanufacturing and a cell phone remanufacturing industry. Analysis of variance and regression analysis are performed to denote the influential factors in the remanufacturing line, and optimization is done by using the regression techniques and ANOVA results