Dynamic setup scheduling and flow control in manufacturing systems

We propose a method for flow control of parts in a manufacturing system with machines that require setups. The setup scheduling problem is investigated in the context of a multilevel hierarchy of discrete events with distinct frequencies. The higher level of the hierarchy calculates a target trajectory in the surplus/backlog space of the part types which must be tracked at the level of setups. We consider a feedback setup scheduling policy which usescorridors in the surplus/backlog space of the part types to determine the timing of the set-up changes in order to guide the trajectory in the desired direction. An interesting case in which the trajectory leads to a target point (e.g., a hedging point) is investigated in detail. It is shown that in this case the surplus/backlog trajectory at the setup level can lead to a limit cycle. Conditions for linear corridors which result in a stable limit cycle are determined.     

Design of linear equalizers optimized for the structural similarity index.

We propose an algorithm for designing linear equalizers that maximize the structural similarity (SSIM) index between the reference and restored signals. The SSIM index has enjoyed considerable application in the evaluation of image processing algorithms. Algorithms, however, have not been designed yet to explicitly optimize for this measure. The design of such an algorithm is nontrivial due to the nonconvex nature of the distortion measure. In this paper, we reformulate the nonconvex problem as a quasi-convex optimization problem, which admits a tractable solution. We compute the optimal solution in near closed form, with complexity of the resulting algorithm comparable to complexity of the linear minimum mean squared error (MMSE) solution, independent of the number of filter taps. To demonstrate the usefulness of the proposed algorithm, it is applied to restore images that have been blurred and corrupted with additive white gaussian noise. As a special case, we consider blur-free image denoising. In each case, its performance is compared to a locally adaptive linear MSE-optimal filter. We show that the images denoised and restored using the SSIM-optimal filter have higher SSIM index, and superior perceptual quality than those restored using the MSE-optimal adaptive linear filter. Through these results, we demonstrate that a) designing image processing algorithms, and, in particular, denoising and restoration-type algorithms, can yield significant gains over existing (in particular, linear MMSE-based) algorithms by optimizing them for perceptual distortion measures, and b) these gains may be obtained without significant increase in the computational complexity of the algorithm.     

Optimal average cost manufacturing flow controllers: convexity anddifferentiability

The authors consider the control of a production facility consisting of a single workstation with multiple failure modes and part types using a continuous flow control model. Technical issues concerning the convexity and differentiability of the differential cost function are investigated. It is proven that under an optimal control policy the differential cost is C¹ on attractive control switching boundaries     

Optimal manufacturing flow controllers: zero-inventory policies andcontrol switching sets

A continuous-flow control model of a single workstation with multiple failure modes and part types is considered. Although the general model is intractable, properties of the optimal control policy are identified that can be used to help formulate heuristic policies. Control switching sets are described and shown to have a threshold form. For a single machine with two part-types, conditions are found under which no inventory is held, analogous to the single-part-type result of Bielecki and Kumar (1988)     

Utility experience with real time rates

The structure of electric utilities is undergoing far-reaching changes as new and expanded service options are added. The concepts of unbundling or of priority service are expanding the options open to customers. Spot pricing, or real-time pricing of electricity, provides the economic structure for many of these new service options. It is frequently stated that customers cannot adapt to real-time prices. The authors identify the elements of real-time rates and existing rate structures in the United States and other OECD countries which incorporate these dimensions     

Sequential DOE via dynamic programming

The paper considers a sequential Design Of Experiments (DOE) scheme. Our objective is to maximize both information and economic measures over a feasible set of experiments. Optimal DOE strategies are developed by introducing information criteria based on measures adopted from information theory. The evolution of acquired information along various stages of experimentation is analyzed for linear models with a Gaussian noise term. We show that for particular cases, although the amount of information is unbounded, the desired rate of acquiring information decreases with the number of experiments. This observation implies that at a certain point in time it is no longer efficient to continue experimenting. Accordingly, we investigate methods of stochastic dynamic programming under imperfect state information as appropriate means to obtain optimal experimentation policies. We propose cost-to-go functions that model the trade-off between the cost of additional experiments and the benefit of incremental information. We formulate a general stochastic dynamic programming framework for design of experiments and illustrate it by analytic and numerical implementation examples.     

The Costs of Wheeling and Optimal Wheeling Rates

Wheeling is the transmission of electrical energy from a buyer to a seller through a transmission network owned by a third party. This paper provides a theoretically sound, yet practical to implement, basis for setting wheeling rates. These wheeling rates are based on marginal costs (determined by losses and effects of line flow and voltage magnitude constraints) adjusted up or down as necessary to account for embedded capital costs (i.e. revenue reconciliation). Simple numerical examples are provided to illustrate interesting phenomena such as negative wheeling rates which yield positive net revenue. Comparisons with present day wheeling rates show that major differences exist. The wheeling rates of this paper yield a "no lose" situation for the buying, selling and wheeling utilities.     

Near optimal manufacturing flow controller design

Flow control of flexible manufacturing systems (FMSs) addresses an important real-time scheduling requirement of modern manufacturing facilities, which are prone to failures and other controllable or stochastic discrete events affecting production capacity, such as change of setup and maintenance scheduling. Flow controllers are useful both in the coordination of interconnected flexible manufacturing cells through distributed scheduling policies and in the hierarchical decomposition of the planning and scheduling problem of complex manufacturing systems. Optimal flow-control policies are hedging-point policies characterized by a generally intractable system of stochastic partial differential equations. This article proposes a near optimal controller whose design is computationally feasible for realistic-size systems. The design exploits a decomposition of the multiple-part-type problem to many analytically tractable one-part-type problems. The decomposition is achieved by replacing the polyhedra production capacity sets with inscribed hypercubes. Stationary marginal densities of state variables are computed iteratively for successive trial controller designs until the best inscribed hypercubes and the associated optimal hedging points are determined. Computational results are presented for an illustrative example of a failureprone FMS.     

Adaptation in Convolutionally Coded MIMO-OFDM Wireless Systems Through Supervised Learning and SNR Ordering

Multiple-input–multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) wireless systems use link adaptation to exploit the dynamic nature of wireless environments. Link adaptation maximizes throughput while maintaining target reliability by adaptively selecting the modulation order and coding rate. Link adaptation is extremely challenging, however, due to the difficulty in predicting error rates in OFDM with binary convolutional codes, bit interleaving, MIMO processing, and real channel impairments. This paper proposes a new machine-learning framework that exploits past observations of the error rate and the associated channel-state information to predict the best modulation order and coding rate for new realizations of the channel state without modeling the input–output relationship of the wireless transceiver. Our approach is enabled through our new error-rate expression that is only parameterized by postprocessing signal-to-noise ratios (SNRs), ordered over subcarriers and spatial streams. Using ordered SNRs, we propose a low-dimensional feature set that enables machine learning to increase the accuracy of link adaptation. An IEEE 802.11n simulation study validates the application of this machine-learning framework in real channels and demonstrates the improved performance of SNR ordering as it compares with competing link-quality metrics.      

An Inequality for Nearly Log-Concave Distributions With Applications to Learning

We prove that given a nearly log-concave distribution, in any partition of the space to two well separated sets, the measure of the points that do not belong to these sets is large. We apply this isoperimetric inequality to derive lower bounds on the generalization error in learning. We further consider regression problems and show that if the inputs and outputs are sampled from a nearly log-concave distribution, the measure of points for which the prediction is wrong by more than epsi₀ and less than epsi₁ is (roughly) linear in epsi₁-epsi₀, as long as epsi₀ is not too small, and epsi₁ not too large. We also show that when the data are sampled from a nearly log-concave distribution, the margin cannot be large in a strong probabilistic sense