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2012 | Buch

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Modeling with Stochastic Programming

verfasst von: Alan J. King, Stein W. Wallace

Verlag: Springer New York

Buchreihe : Springer Series in Operations Research

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research at Lancaster University Management School in England.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Uncertainty in Optimization

Abstract

Decisions are rarely made under certainty. There is almost always something relevant about the future that is not known when important decisions are made.

Alan J. King, Stein W. Wallace

Chapter 2. Modeling Feasibility and Dynamics

Abstract

As was illustrated in our News Mix example in Chap. 1, it is not straightforward to pass from a deterministic to a stochastic formulation. We need to rethink the whole model, very often by changing both variables and constraints. Although many reformulations may make sense mathematically, they may in fact be rather peculiar in terms of interpretations. The purpose of this section is to discuss some of these issues, partly in terms of examples. The goal is not to declare some formulations generally superior to others, but rather to help you think carefully about how you rewrite your problems in light of uncertainty.

Alan J. King, Stein W. Wallace

Chapter 3. Modeling the Objective Function

Abstract

The objective function of a mathematical program is what an optimization procedure uses to select better solutions over poorer solutions. For example, if the objective is to maximize profit, then the procedure tries to move in the direction of solutions that increase profit while still remaining feasible. But when the profit depends on a parameter that is uncertain (like prices tomorrow), then the notion of maximizing profit is no longer very simple.

Alan J. King, Stein W. Wallace

Chapter 4. Scenario-Tree Generation: With Michal Kaut

Abstract

So far we have talked about models and structures with respect to uncertainty. But we have not talked about data. We have talked about prices and demand, deterministic or stochastic, we have talked about distributions of random variables. But rarely are these available in the format we need for our algorithm.

Alan J. King, Stein W. Wallace

Chapter 5. Service Network Design: With Arnt-Gunnar Lium and Teodor Gabriel Crainic

Abstract

This chapter represents an investigation following the lines of this book, where the focus is that of a graduate student studying the effects of uncertainty on a specific problem. There is no customer in this problem, and it has not reached the level of sophistication needed for a real application. However, it goes to the heart of this book: What does stochastics do to my problem? What are the implicit options? This chapter is based on the Ph.D. thesis of Arnt-Gunnar Lium of Molde University College. For an overview see [40]. You are going to meet an inherently two-stage problem with, principally, infinitely many stages. However, since in this situation we do not really need the decisions of the inherent second stage, we can approximate, ending up with a two-stage model. In our view, this points to the heart of stochastic programming: inherently two-stage problems with rather complicated stages after the first one.

Alan J. King, Stein W. Wallace

Chapter 6. A Multidimensional Newsboy Problem with Substitution: With Hajnalka Vaagen

Abstract

In this chapter, you will encounter a problem that is inherently two-stage. The first inherent stage is to decide on production levels for a number of substitutable products with correlated demands. This is followed by a second stage where demand is met, partly by giving customers what they want, partly by giving them acceptable substitutes. The chapter is based on [53].

Alan J. King, Stein W. Wallace

Chapter 7. Stochastic Discount Factors

Abstract

In this chapter, we discuss ways to use information from financial markets to calibrate models for discounting future risks. This type of information is important for modeling the impact of future uncertainty on present decisions. In some areas of activity, there exist well developed financial markets with hordes of traders using the tools and information available to them to decide the present value of future events. This chapter describes a methodology to use market information.

Alan J. King, Stein W. Wallace

Chapter 8. Long Lead Time Production: With Aliza Heching

Abstract

We consider a problem faced by a supplier of custom products that have long production lead times. The problem is inherently multistage with a large number of stages. The majority of these products have no salvage value, so the supplier is exposed to significant risk of excess production. Moreover, customer forecasts will likely err on the upside because the option to purchase has value. This chapter describes a counterbalancing mechanism for the supplier to obtain some compensation for part of the inventory risk.

Alan J. King, Stein W. Wallace

Backmatter

Titel: Modeling with Stochastic Programming
verfasst von: Alan J. King
Stein W. Wallace
Copyright-Jahr: 2012
Verlag: Springer New York
Electronic ISBN: 978-0-387-87817-1
Print ISBN: 978-0-387-87816-4
DOI: https://doi.org/10.1007/978-0-387-87817-1

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