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Über dieses Buch

Interactive Operations Research with Maple: Methods and Models has two ob­ jectives: to provide an accelerated introduction to the computer algebra system Maple and, more importantly, to demonstrate Maple's usefulness in modeling and solving a wide range of operations research (OR) problems. This book is written in a format that makes it suitable for a one-semester course in operations research, management science, or quantitative methods. A nwnber of students in the departments of operations research, management science, oper­ ations management, industrial and systems engineering, applied mathematics and advanced MBA students who are specializing in quantitative methods or opera­ tions management will find this text useful. Experienced researchers and practi­ tioners of operations research who wish to acquire a quick overview of how Maple can be useful in solving OR problems will find this an excellent reference. Maple's mathematical knowledge base now includes calculus, linear algebra, ordinary and partial differential equations, nwnber theory, logic, graph theory, combinatorics, statistics and transform methods. Although Maple's main strength lies in its ability to perform symbolic manipulations, it also has a substantial knowledge of a large nwnber of nwnerical methods and can plot many different types of attractive-looking two-dimensional and three-dimensional graphs. After almost two decades of continuous improvement of its mathematical capabilities, Maple can now boast a user base of more than 300,000 academics, researchers and students in different areas of mathematics, science and engineering.

Inhaltsverzeichnis

Frontmatter

1. Introduction to Operations Research

Abstract
The activity called operations research (OR) was developed during World War II when leading British scientists were consulted to improve military strategy against the enemy. A team of physicists, mathematicians, statisticians, engineers and sometimes even psychologists and chemists conducted research on military operations under the leadership of R M. S. Blacken.1 These scientists worked on important military problems such as the deployment of radar, management of bombing and antisubmarine operations and military logistics. Many of these problems were solved by applying the scientific method and using mathematical techniques such as algebra, calculus and probability theory.2
Mahmut Parlar

2. A Quick Tour of Maple

Abstract
Maple is a mathematical problem-solving environment that combines symbolic, numerical and graphical methods used in different areas of mathematics. This chapter provides an introduction to Maple and presents those aspects of it that can be useful in operations research applications.
Mahmut Parlar

3. Maple and Mathematical Foundations of Operations Research

Abstract
Although there have been some isolated cases1 of successful applications of operations research that did not involve any mathematics, operations research modeling generally requires a good understanding of basic university-level mathematics such as algebra, calculus, linear algebra, differential equations, transform methods and probability theory.
Mahmut Parlar

4. Linear Programming

Abstract
Linear programming (LP) is a flexible and powerful optimization technique that is used to determine the nonnegative values of n decision variables xj, which satisfy m linear constraints
$$\begin{array}{*{20}{c}} {\sum\limits_{j = 1}^n {{a_{ij}}{x_j}\{ \leqslant , = \geqslant \} {b_i},} }&{i = 1,2, \ldots ,m} \end{array}$$
and maximize (or minimize) a linear objective function
$$z = \sum\limits_{j = 1}^n {{c_j}{x_j}}$$
where the parameters a ij , b i; and c j are given constants.
Mahmut Parlar

5. Nonlinear Programming

Abstract
As we discussed in Chapter 4, in linear programming (LP) applications, our purpose is to optimize (i.e., maximize or minimize) a linear objective function subject to linear constraints. Although a large number of practical decision problems can be accurately modeled as linear programs, it should be emphasized that in some cases using LP to formulate an inherently nonlinear decision problem (i.e., forcing the world to fit the model) may not provide an accurate representation of reality. In many OR problems due to economies/diseconomies of scale (e.g., quantity discounts), interaction among decision variables (e.g., variance of a portfolio) or transformations that result in nonlinearities (e.g., a linear stochastic programming formulation transformed into an equivalent nonlinear deterministic one), an LP formulation becomes impossible to use. In these cases, we would need to utilize the techniques of nonlinear programming (NLP) that can deal with both nonlinear objective functions and nonlinear constraints.
Mahmut Parlar

6. Dynamic Programming

Abstract
Dynamic programming (DP) is a simple yet powerful approach for solving certain types of sequential optimization problems. Most real-life decision problems are sequential (dynamic) in nature since a decision made now usually affects future outcomes and payoffs. An important aspect of optimal sequential decisions is the desire to balance present costs with the future costs. A decision made now that minimizes the current cost only without taking into account the future costs may not necessarily be the optimal decision for the complete multiperiod problem. For example, in an inventory control problem it may be optimal to order more than the current period’s demand and incur high inventory carrying costs now in order to lower the costs of potential shortages that may arise in the future. Thus, in sequential problems it may be optimal to have some “short-term pain” for the prospect of “long-term gain.”
Mahmut Parlar

7. Stochastic Processes

Abstract
Operations research models can be categorized broadly as detenninistic and probabilistic. When the variable of interest—e.g., the number of customers in a service system or the number of units in inventory—randomly evolves in time, a probabilistic model provides a more accurate representation of the system under study.
Mahmut Parlar

8. Inventory Models

Abstract
According to recent estimates the total value of inventories in the United States is in excess of $1 trillion [135, p. 184]. Almost 80% of this investment in inventories is in manufacturing, wholesale and retail sectors. Many of the mathematical models that we will discuss in this chapter have proved very useful in managing inventories and their applications have resulted in substantial savings for the companies employing them.
Mahmut Parlar

9. Queueing Systems

Abstract
The English poet Milton once wrote, “They also serve who only stand and wait,” [178, Sonnet 19] but he never elaborated on the average number of people who would wait and the average time spent waiting for service. Of course, as a poet he had no interest in such technicalities and even if he did, the mathematical tools available to him and his contemporaries in the 17th century would not have been of much help in analyzing the queueing processes arising in his day.l
Mahmut Parlar

10. Simulation

Abstract
Simulation1 is a computer-based probabilistic modeling tool that is used to imitate the behavior of an existing or a proposed system. If an existing system such as a bank branch is experiencing long queues and long customer waiting times, the manager of the branch may use simulation to examine different alternatives for improving service without actually making any physical changes in the system.
Mahmut Parlar

Backmatter

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