# Inventory-Production Theory

## A Linear Policy Approach

Book

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

1. Front Matter
Pages I-VI
2. Christoph A. Schneeweiß
Pages 1-3
3. Christoph A. Schneeweiß
Pages 4-6
4. Christoph A. Schneeweiß
Pages 7-35
5. Christoph A. Schneeweiß
Pages 36-62
6. Christoph A. Schneeweiß
Pages 63-77
7. Christoph A. Schneeweiß
Pages 78-94
8. Christoph A. Schneeweiß
Pages 95-109
9. Christoph A. Schneeweiß
Pages 110-113
10. Back Matter
Pages 114-118

### Introduction

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.

### Keywords

Lagerhaltung Lineare Optimierung Produktionsplanung distribution optimization

#### Authors and affiliations

1. 1.Fachbereich Wirtschaftswissenschaften Fachrichtung Operations ResearchFreie Universität BerlinBerlinDeutschland

### Bibliographic information

• Book Title Inventory-Production Theory
• Book Subtitle A Linear Policy Approach
• Authors C.A. Schneeweiss
• Series Title Lecture Notes in Economics and Mathematical Systems
• DOI https://doi.org/10.1007/978-3-642-95311-8
• Copyright Information Springer-Verlag Berlin Heidelberg 1977
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Softcover ISBN 978-3-540-08443-3
• eBook ISBN 978-3-642-95311-8
• Series ISSN 0075-8442
• Edition Number 1
• Number of Pages VI, 118
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
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