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Inventory-Production Theory

A Linear Policy Approach

  • Book
  • © 1977

Overview

Authors:
  1. Christoph A. Schneeweiß

    1. Fachbereich Wirtschaftswissenschaften Fachrichtung Operations Research, Freie Universität Berlin, Berlin, Deutschland

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 151)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Christoph A. Schneeweiß
    Pages 1-3

  3. The General Model

    • Christoph A. Schneeweiß
    Pages 4-6

  4. The Linear-Quadratic Model

    • Christoph A. Schneeweiß
    Pages 7-35

  5. The Linear Non-Quadratic Model

    • Christoph A. Schneeweiß
    Pages 36-62

  6. Comparison with Optimal Dynamic Programming Solutions

    • Christoph A. Schneeweiß
    Pages 63-77

  7. Comparison with Deterministic Approximations

    • Christoph A. Schneeweiß
    Pages 78-94

  8. Comparison with AHM-Inventory Models

    • Christoph A. Schneeweiß
    Pages 95-109

  9. Summary and Concluding Remarks

    • Christoph A. Schneeweiß
    Pages 110-113

  10. Back Matter

    Pages 114-118
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Keywords

About this book

The term inventory-production theory is not well defined. It com­ prises e. g. such models like cash balance models, production smoothing models and pure inventory models. We shall here mainly be concerned with stochastic dynamic problems and shall give exact definitions in the next section. Most of our work will concentrate on cash balance models. However, production smoothing situations and pure inventory problems will also be investigated. Since we are faced in principle with dynamic stochastic situa­ tions a dynamic programming approach would be appropriate. This approach, however, due to computational restraints, is limited to only but the simplest models. Therefore, in practice, one ruduces stochastics just in taking forecasts of demand and then treating the problem as a deterministic optimization problem. In addition one often introduces certain safety stocks to safeguard the system from possible forecasting errors. In general, this proce­ dure is suboptimal. However, there exists one particular situa­ tion when a separation in a forecasting procedure and a subse­ quent optimization of the remaining deterministic model is not suboptimal. This is known as the linear-quadratic model, i. e. a model having linear system equations and a quadratic cost crite­ rion. For this type of model H. A. Simon ~3J and later H. Theil [25J have shown that the above separation property holds. In fact, Simon's and Theil's results are nothing else but what has later and more generally become known to control engineers as Kalman's famous separation principle.

Authors and Affiliations

  • Fachbereich Wirtschaftswissenschaften Fachrichtung Operations Research, Freie Universität Berlin, Berlin, Deutschland

    Christoph A. Schneeweiß

Bibliographic Information

  • Book Title: Inventory-Production Theory

  • Book Subtitle: A Linear Policy Approach

  • Authors: Christoph A. Schneeweiß

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-95311-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1977

  • Softcover ISBN: 978-3-540-08443-3Published: 01 September 1977

  • eBook ISBN: 978-3-642-95311-8Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: VI, 118

  • Topics: Operations Management, Operations Research/Decision Theory

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