We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby ...eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.
We address inventory decisions in the context of the “reorder-point, order-quantity” policy in infinite-horizon, stochastic lead-time demand inventory systems in which the parameters may be ...non-stationary. We develop a heuristic policy based on the simple economic order quantity (
EOQ) model and the one-period newsvendor model. Using illustrative numerical examples, we demonstrate that our simple and easy-to-understand heuristic policy performs nearly as well as the optimal policy derived from complicated mathematical procedures. Our heuristic policy is simple, easy-to-implement, and flexible in that it can be easily adapted to situations when the parameters of the inventory system may change. Analytical modeling under non-stationary parameters would be extremely complex and the derivation of closed form optimal policies is mathematically intractable in most cases. In such cases, practitioners will find our heuristic policy an attractive option.
The theory of quantum information provides a common language which links disciplines ranging from cosmology to condensed-matter physics. For example, the delocalization of quantum information in ...strongly-interacting many-body systems, known as quantum information scrambling, has recently begun to unite our understanding of black hole dynamics, transport in exotic non-Fermi liquids, and many-body analogs of quantum chaos. To date, verified experimental implementations of scrambling have dealt only with systems comprised of two-level qubits. Higher-dimensional quantum systems, however, may exhibit different scrambling modalities and are predicted to saturate conjectured speed limits on the rate of quantum information scrambling. We take the first steps toward accessing such phenomena, by realizing a quantum processor based on superconducting qutrits (three-level quantum systems). We implement two-qutrit scrambling operations and embed them in a five-qutrit teleportation algorithm to directly measure the associated out of-time-ordered correlation functions. Measured teleportation fidelities, Favg = 0.568 +- 0001, confirm the occurrence of scrambling even in the presence of experimental imperfections. Our teleportation algorithm, which connects to recent proposals for studying traversable wormholes in the laboratory, demonstrates how quantum information processing technology based on higher dimensional systems can exploit a larger and more connected state space to achieve the resource efficient encoding of complex quantum circuits.
Encoder-decoder networks with attention have proven to be a powerful way to solve many sequence-to-sequence tasks. In these networks, attention aligns encoder and decoder states and is often used for ...visualizing network behavior. However, the mechanisms used by networks to generate appropriate attention matrices are still mysterious. Moreover, how these mechanisms vary depending on the particular architecture used for the encoder and decoder (recurrent, feed-forward, etc.) are also not well understood. In this work, we investigate how encoder-decoder networks solve different sequence-to-sequence tasks. We introduce a way of decomposing hidden states over a sequence into temporal (independent of input) and input-driven (independent of sequence position) components. This reveals how attention matrices are formed: depending on the task requirements, networks rely more heavily on either the temporal or input-driven components. These findings hold across both recurrent and feed-forward architectures despite their differences in forming the temporal components. Overall, our results provide new insight into the inner workings of attention-based encoder-decoder networks.
It has been argued that conventional discounted cash flow (DCF) techniques, which are commonly used for investment justification, are inadequate and may even be inappropriate for the justification of ...advanced manufacturing systems whose strategic value comes from such attributes as flexibility. The problem lies in the proper estimation of the value of flexibility in financial or cash flow terms, so that the DCF techniques, which are otherwise conceptually sound, become relevant. This involves an assessment of the value of the flexibility of the manufacturing system in dealing with the uncertainties in its operating environment. We propose a simulation-optimization methodology for this assessment in cash flow terms and use it in a DCF framework. We use simulation to generate the environmental parameters in each period of an appropriate evaluation horizon. We develop a mathematical programming model to determine the distribution of the possible net revenues of the system in each period by capturing the combined effect of the different types of flexibilities that the manufacturing system may possess. We illustrate the application of our methodology using numerical examples and discuss how it can be used to assess the value of flexibility in cash flow terms. We show that our approach facilitates the justification of capital investment in advanced manufacturing systems which tend to get undervalued under the traditional DCF approaches. It would also help managers address such important questions as “how much incremental investment should we be willing to make now for the additional flexibility features?” and “does the expected present value of the future benefits of added flexibility justify the incremental capital investment now?” In essence, our paper addresses the question as to appropriate techniques or approaches for justifying proposed strategic investment decisions.
Despite the widespread application of recurrent neural networks (RNNs) across a variety of tasks, a unified understanding of how RNNs solve these tasks remains elusive. In particular, it is unclear ...what dynamical patterns arise in trained RNNs, and how those patterns depend on the training dataset or task. This work addresses these questions in the context of a specific natural language processing task: text classification. Using tools from dynamical systems analysis, we study recurrent networks trained on a battery of both natural and synthetic text classification tasks. We find the dynamics of these trained RNNs to be both interpretable and low-dimensional. Specifically, across architectures and datasets, RNNs accumulate evidence for each class as they process the text, using a low-dimensional attractor manifold as the underlying mechanism. Moreover, the dimensionality and geometry of the attractor manifold are determined by the structure of the training dataset; in particular, we describe how simple word-count statistics computed on the training dataset can be used to predict these properties. Our observations span multiple architectures and datasets, reflecting a common mechanism RNNs employ to perform text classification. To the degree that integration of evidence towards a decision is a common computational primitive, this work lays the foundation for using dynamical systems techniques to study the inner workings of RNNs.
A central challenge in developing versatile machine learning systems is catastrophic forgetting: a model trained on tasks in sequence will suffer significant performance drops on earlier tasks. ...Despite the ubiquity of catastrophic forgetting, there is limited understanding of the underlying process and its causes. In this paper, we address this important knowledge gap, investigating how forgetting affects representations in neural network models. Through representational analysis techniques, we find that deeper layers are disproportionately the source of forgetting. Supporting this, a study of methods to mitigate forgetting illustrates that they act to stabilize deeper layers. These insights enable the development of an analytic argument and empirical picture relating the degree of forgetting to representational similarity between tasks. Consistent with this picture, we observe maximal forgetting occurs for task sequences with intermediate similarity. We perform empirical studies on the standard split CIFAR-10 setup and also introduce a novel CIFAR-100 based task approximating realistic input distribution shift.
Ternary quantum processors offer significant computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level ...systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard Randomized Benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find a single-qutrit gate infidelity as low as \(2.38 \times 10^{-3}\). Through interleaved RB, we find that this qutrit gate error is largely limited by the native (qubit-like) gate fidelity, and employ simultaneous RB to fully characterize cross-talk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of \(0.82\). Our results demonstrate a RB-based tool to characterize the obtain overall performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.
Despite the far reaching implications of the advanced manufacturing technologies (AMT) for the maintenance and enhancement of a firm's competitive position, the financial justification of investments ...in AMT has not been easy. Recent research in manufacturing strategy, financial theory, management accounting and organization decision making suggests that the AMT-justification process should involve (i) a strategic analysis to ascertain the strategic fit and the competitive advantage of AMT, (ii) an economic analysis to ascertain the financial viability of AMT and (iii) an understanding of the dynamics of organizational decision making to overcome the barriers to the adoption of AMT. Focusing on the economic analysis we present a concise review of the state of the art and propose a four-level justification framework for investment in AMT. At Level 1 of this framework, we analyze the easily quantifiable benefits and costs using the traditional discounted cash flow (DCF) models. We examine the limitations of the traditional DCF analysis and discuss some refinements suggested in the literature. At Level 2, we develop and illustrate with a numerical example, a stochastic mathematical programming model to quantify the strategic benefits such as flexibility and quality. At Level 3, we quantify the benefits of the time series linkages between the project currently being justified and a related future project using a learning curve model. Finally, at Level 4 we focus on a qualitative assessment of the benefits which were not included in the evaluation at the first three levels.
A computationally efficient decomposition technique for large-scale linear programs with an underlying linked staircase structure is presented in this paper. The technique utilizes a ...solution-cascading approach with subproblem solutions. On a set of test problems, drawn from a variety of applications, the procedure has resulted in a reduction in computation time averaging about 68% of the undecomposed time. Similar tests on groups of randomly generated problems resulted in time savings as high as 95%. Three features of the approach make it particularly attractive. First, it is a meta-algorithm. That is, it can be embedded within any appropriate LP solver, implying even better time savings with more efficient solvers. Second, the procedure should become relatively less expensive as the problem size increases. Third, the procedure easily lends itself to parallel processing.
