A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal sequential stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear or linear programming parts, i determining optimal probability distributions, ii approximating the optimal distributions as closely as possible by decision rules of prescribed form.

Chance-Constrained Programming

List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

Lectures on Stochastic Programming: Modeling and Theory

An accelerating increase in linear programming applications to industrial problems has made it virtually impossible to keep abreast of them, not only because of their number and diversity but also because of the conditions under which many are carried out. Industrial and governmental secrecy is often present. Other conditions also bar access to ascertainment and assessment of the pattern of applications. Lack of a tradition for publication is one. Failure to ascertain the general significance of particular findings is another, as is discouragement arising from the fact that similar applications have previously been published by others. Immediate remedies are not available for these difficulties. Presumably conventions such as this will help, over a period of time, by encouraging informal contacts between interested persons.

A talk on “industrial applications of linear programming” must be altered to suit these circumstances. In place of a survey or evaluation of industrial studies, two broad issues which are relevant to all such applications will be discussed. These are, 1 use of linear programming models as guides to data collection and 2 analysis and prognosis of fruitful areas of additional research, especially those which appear to have been opened by industrial applications.

Management Models and Industrial Applications of Linear Programming

The objective of this paper is to review the state-of-the-art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are presented.

Reservoir Management and Operations Models: A State‐of‐the‐Art Review

http://cepac.cheme.cmu.edu/pasilectures/sahinidis/NVSpaperthree.pdf

Optimization under uncertainty: state-of-the-art and opportunities

Scheduling heating oil production is an important management problem. It is also a complex one. Weather and demand uncertainties, allocation of production between different refineries, joint-and by-product relations, storage limitations, maintenance of minimal supplies and many other factors need to be considered.

This paper is concerned with one of an integrated series of operations research studies directed toward improvement in such scheduling methods. Emphasis is on essentials of the mathematical model. Institutional features and other phases of the OR studies are brought in only as required.

G. H. Symonds

Papers

Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil