It appears that the impact of OR will continue to grow. For example, according to the U.S. Bureau of Labor Statistics, OR currently is one of the fastest-growing career areas for U.S. college graduates. To give you a better notion of the wide applicability of OR, we list some actual award winning applications in Table 1.1. Note the diversity of organizations and applications in the first two columns. The curious reader can find a complete article describing each application in the January-February issue of Interfaces for the year cited in the third column of the table. The fourth column lists the chapters in this book that describe the kinds of OR techniques that were used in the application. (Note that many of the applications combine a variety of techniques.) The last column indicates that these applications typically resulted in annual savings in the millions (or even tens of millions) of dollars. Furthermore, additional benefits not recorded in the table (e.g., improved service to customers and better managerial control) sometimes were considered to be even more important than these financial benefits. (You will have an opportunity to investigate these less tangible benefits further in Probs. 1.3-1 (/*wocoen bukune ning 7th eds) and 1.3-2.) Although most routine OR studies provide considerably more modest benefits than these award-winning applications, the figures in the rightmost column of Table 1.1 do accurately reflect the dramatic impact that large, well-designed OR studies occasionally can have. We will briefly describe some of these applications in the next chapter, and then we present two in greater detail as case studies in Sec. 3.5
Label: masbeg impact
The research part of the name means that operations research uses an approach that resembles the way research is conducted in established scientific fields. To a considerable extent, the scientific method is used to investigate the problem of concern. (In fact, the term management science sometimes is used as a synonym for operations research.) In particular, the process begins by carefully observing and formulating the problem, including gathering all relevant data. The next step is to construct a scientific (typically mathematical) model that attempts to abstract the essence of the real problem. It is then hypothesized that this model is a sufficiently precise representation of the essential features of the situation that the conclusions (solutions) obtained from the model are also valid for the real problem. Next, suitable experiments are conducted to test this hypothesis, modify it as needed, and eventually verify some form of the hypothesis. (This step is frequently referred to as model validation.) Thus, in a certain sense, operations research involves creative scientific research into the fundamental properties of operations. However, there is more to it than this. Specifically, OR is also concerned with the practical management of the organization. Therefore, to be successful, OR must also provide positive, understandable conclusions to the decision maker(s) when they are needed. Still another characteristic of OR is its broad viewpoint. As implied in the preceding section, OR adopts an organizational point of view. Thus, it attempts to resolve the conflicts of interest among the components of the organization in a way that is best for the organization as a whole. This does not imply that the study of each problem must give explicit consideration to all aspects of the organization; rather, the objectives being sought must be consistent with those of the overall organization.
An additional characteristic is that OR frequently attempts to find a best solution (referred to as an optimal solution) for the problem under consideration. (We say a best instead of the best solution because there may be multiple solutions tied as best.) Rather than simply improving the status quo, the goal is to identify a best possible course of action. Although it must be interpreted carefully in terms of the practical needs of management, this "search for optimality" is an important theme in OR. All these characteristics lead quite naturally to still another one. It is evident that no single individual should be expected to be an expert on all the many aspects of OR work or the problems typically considered; this would require a group of individuals having diverse backgrounds and skills. Therefore, when a full-fledged OR study of a new problem is undertaken, it is usually necessary to use a team approach. Such an OR team typically needs to include individuals who collectively are highly trained in mathematics, statistics and probability theory, economics, business administration, computer science, engineering and the physical sciences, the behavioral sciences, and the special techniques of OR. The team also needs to have the necessary experience and variety of skills to give appropriate consideration to the many ramifications of the problem throughout the organization.
Label: tribute to pak Pratik
The bulk of this blog from the Hamdy’s book is devoted to the mathematical methods of operations research (OR). This is quite appropriate because these quantitative techniques form the main part of what is known about OR. However, it does not imply that practical OR studies are primarily mathematical exercises. As a matter of fact, the mathematical analysis often represents only a relatively small part of the total effort required. The purpose of this chapter is to place
things into better perspective by describing all the major phases of a typical OR study. One way of summarizing the usual (overlapping) phases of an OR study is the following:
1. Define the problem of interest and gather relevant data.
2. Formulate a mathematical model to represent the problem.
3. Develop a computer-based procedure for deriving solutions to the problem from the
model.
4. Test the model and refine it as needed.
5. Prepare for the ongoing application of the model as prescribed by management.
6. Implement.
Each of these phases will be discussed in turn in the following sections. Most of the award-winning OR studies introduced in Table 1.1 provide excellent ex- amples of how to execute these phases well. We will intersperse snippets from these ex- amples throughout the chapter, with references to invite your further reading.
DEFINING THE PROBLEM AND GATHERING DATA
In contrast to textblog examples, most practical problems encountered by OR teams are initially described to them in a vague, imprecise way. Therefore, the first order of busi- ness is to study the relevant system and develop a well-defined statement of the problem to be considered. This includes determining such things as the appropriate objectives, constraints on what can be done, interrelationships between the area to be studied and other areas of the organization, possible alternative courses of action, time limits for making a decision, and so on. This process of problem definition is a crucial one because it greatly affects how relevant the conclusions of the study will be. It is difficult to extract a "right" answer from the "wrong" problem! The first thing to recognize is that an OR team is normally working in an advisory capacity. The team members are not just given a problem and told to solve it however they see fit. Instead, they are advising management (often one key decision maker). The team performs a detailed technical analysis of the problem and then presents recommendations to management. Frequently, the report to management will identify a number of alternatives that are particularly attractive under different assumptions or over a different range of values of some policy parameter that can be evaluated only by management (e.g., the trade off between cost and benefits). Management evaluates the study and its recommendations,
takes into account a variety of intangible factors, and makes the final decision based on its best judgment. Consequently, it is vital for the OR team to get on the same wavelength as management, including identifying the "right" problem from management's viewpoint, and to build the support of management for the course that the study is taking. Ascertaining the appropriate objectives is a very important aspect of problem definition. To do this, it is necessary first to identify the member (or members) of management who actually will be making the decisions concerning the system under study and then to probe into this individual's thinking regarding the pertinent objectives. (Involving the decision maker from the outset also is essential to build her or his support for the imple-
mentation of the study.) By its nature, OR is concerned with the welfare of the entire organization rather than
that of only certain of its components. An OR study seeks solutions that are optimal for the overall organization rather than suboptimal solutions that are best for only one component. Therefore, the objectives that are formulated ideally should be those of the entire organization. However, this is not always convenient. Many problems primarily concern only a portion of the organization, so the analysis would become unwieldy if the stated objectives were too general and if explicit consideration were given to all side effects on the rest of the organization. Instead, the objectives used in the study should be as specific as they can be while still encompassing the main goals of the decision maker and maintain ing a reasonable degree of consistency with the higher-level objectives of the organization. For profit-making organizations, one possible approach to ircumventing the problem of suboptimization is to use long-run profit maximization (considering the time value of money) as the sole objective. The adjective long-run indicates that this objective provides the flexibility to consider activities that do not translate into profits immediately (e.g., research and development projects) but need to do so eventually in order to be worthwhile. This approach has considerable merit. This objective is specific enough to be used conveniently, and yet it seems to be broad enough to encompass the basic goal of profit making organizations. In fact, some people believe that all other legitimate objectives can be translated into this one.
However, in actual practice, many profit-making organizations do not use this approach. A number of studies of U.S. corporations have found that management tends to adopt the goal of satisfactory profits, combined with other objectives, instead of focusing on long-run profit maximization. Typically, some of these other objectives might be to maintain stable profits, increase (or maintain) one's share of the market, provide for product diversification, maintain stable prices, improve worker morale, maintain family control of the business, and increase company prestige. Fulfilling these objectives might achieve long-run profit maximization, but the elationship may be sufficiently obscure that it may not be convenient to incorporate them all into this one objective.
ancing the workload tive. Finally, the third objective was incorporated by adopting the long-term goal of minimizing the number of officers needed to meet the first two objectives. Furthermore, there are additional considerations involving social responsibilities that are distinct from the profit motive. The five parties generally affected by a business firm located in a single country are (1) the owners (stockholders, etc.), who desire profits (div-
idends, stock appreciation, and so on); (2) the employees, who desire steady employment at reasonable wages; (3) the customers, who desire a reliable product at a reasonable price; (4) the suppliers, who desire integrity and a reasonable selling price for their goods; and (5) the government and hence the nation, which desire payment of fair taxes and consideration of the national interest. All five parties make essential contributions to the firm, and the firm should not be viewed as the exclusive servant of any one party for the exploitation of others. By the same token, international corporations acquire additional obligations to follow socially responsible practices. Therefore, while granting that manage ment's prime responsibility is to make profits (which ultimately benefits all five parties),
we note that its broader social responsibilities also must be recognized. OR teams typically spend a surprisingly large amount of time gathering relevant data about the problem. Much data usually are needed both to gain an accurate understanding of the problem and to provide the needed input for the mathematical model being formu-
lated in the next phase of study. Frequently, much of the needed data will not be available when the study begins, either because the information never has been kept or because what was kept is outdated or in the wrong form. Therefore, it often is necessary to install a new computer-based management information system to collect the necessary data on an on going basis and in the needed form. The OR team normally needs to enlist the assistance
of various other key individuals in the organization to track down all the vital data. Even with this effort, much of the data may be quite "soft," i.e., rough estimates based only on educated guesses. Typically, an OR team will spend considerable time trying to improve the precision of the data and then will make do with the best that can be obtained.
Examples. An OR study done for the San Francisco Police Department resulted in
the development of a computerized system for optimally scheduling and deploying police
patrol officers. The new system provided annual savings of $11 million, an annual $3 mil-
lion increase in traffic citation revenues, and a 20 percent improvement in response times.
In assessing the appropriate objectives for this study, three fundamental objectives were identified:
1. Maintain a high level of citizen safety.
2. Maintain a high level of officer morale.
3. Minimize the cost of operations.
To satisfy the first objective, the police department and city government jointly established a desired level of protection. The mathematical model then imposed the requirement that this level of protection be achieved. Similarly, the model imposed the requirement of balequitably among officers in order to work toward the second objec sign an effective needle exchange program to combat the spread of the virus that causes AIDS (HIV), and succeeded in reducing the HIV infection rate among program clients by 33 percent. The key part of this study was an innovative data collection program to obtain the needed input for mathematical models of HIV transmission. This program
involved complete tracking of each needle (and syringe), including the identity, location, and date for each person receiving the needle and each person returning the needle during an exchange, as well as testing whether the returned needle was HIV- positive or HIV-negative.
An OR study done for the Citgo Petroleum Corporation optimized both refinery operations and the supply, distribution, and marketing of its products, thereby achieving a profit improvement of approximately $70 million per year. Data collection also played a key role in this study. The OR team held data requirement meetings with top Citgo management to ensure the eventual and continual quality of data. A state-of-the-art management database system was developed and installed on a mainframe computer. In cases where needed data did not exist, LOTUS 1-2-3 screens were created to help operations personnel input the data, and then the data from the personal computers (PCs) were uploaded to the mainframe computer. Before data was inputted to the mathematical model, a preloader program was used to check for data errors and inconsistencies. Initially, the preloader generated a paper log of error messages 1 inch thick! Eventually, the number of error and warning messages (indicating bad or questionable numbers) was reduced to less than 10 for each new run.
Label: masbeg line
Since the advent of the industrial revolution, the world has seen a remarkable growth in
the size and complexity of organizations. The artisans' small shops of an earlier era have
evolved into the billion-dollar corporations of today. An integral part of this revolutionary change has been a tremendous increase in the division of labor and segmentation of management responsibilities in these organizations. The results have been spectacular. However, along with its blessings, this increasing specialization has created new problems, problems that are still occurring in many organizations. One problem is a tendency for the many components of an organization to grow into relatively autonomous empires with their own goals and value systems, thereby losing sight of how their activities and objectives mesh with those of the overall organization. What is best for one component frequently is detrimental to another, so the components may end up working at cross purposes. A related problem is that as the complexity and specialization in an organization increase, it becomes more and more difficult to allocate the available resources to the various activities in a way that is most effective for the organization as a whole. These kinds of problems and the need to find a better way to solve them provided the environment for the emergence of operations research (commonly referred to as OR).
The roots of OR can be traced back many decades, when early attempts were made to use a scientific approach in the management of organizations. However, the beginning of the activity called operations research has generally been attributed to the military services early in World War II. Because of the war effort, there was an urgent need to allocate scarce resources to the various military operations and to the activities within each operation in an effective manner. Therefore, the British and then the U.S. military management called upon a large number of scientists to apply a scientific approach to dealing with this and other strategic and tactical problems. In effect, they were asked to do research on (military) operations. These teams of scientists were the first OR teams. By developing effective methods of using the new tool of radar, these teams were instrumental in winning the Air Battle of Britain. Through their research on how to better manage convoy and antisubmarine operations, they also played a major role in winning the Battle of the North Atlantic. Similar efforts assisted the Island Campaign in the Pacific. When the war ended, the success of OR in the war effort spurred interest in applying OR outside the military as well. As the industrial boom following the war was running its course, the problems caused by the increasing complexity and specialization in organizations were again coming to the forefront. It was becoming apparent to a growing number of people, including business consultants who had served on or with the OR teams during the war, that these were basically the same problems that had been faced by the military but in a different context. By the early 1950s, these individuals had introduced the use of OR to a variety of organizations in business, industry, and government. The rapid spread of OR soon followed.
At least two other factors that played a key role in the rapid growth of OR during this period can be identified. One was the substantial progress that was made early in improving the techniques of OR. After the war, many of the scientists who had participated on OR teams or who had heard about this work were motivated to pursue research relevant to the field; important advancements in the state of the art resulted. A prime example is the simplex method for solving linear programming problems, developed by George Dantzig in 1947. Many of the standard tools of OR, such as linear programming, dynamic programming, queueing theory, and inventory theory, were relatively well developed before the end of the 1950s.
A second factor that gave great impetus to the growth of the field was the onslaught of the computer revolution. A large amount of computation is usually required to deal most effectively with the complex problems typically considered by OR. Doing this by hand would often be out of the question. Therefore, the development of electronic digital computers, with their ability to perform arithmetic calculations thousands or even millions of times faster than a human being can, was a tremendous boon to OR. A further boost came in the 1980s with the development of increasingly powerful personal computers accompanied by good software packages for doing OR. This brought the use of OR within the easy reach of much larger numbers of people. Today, literally millions of individuals have ready access to OR software. Consequently, a whole range of computers from mainframes to laptops now are being routinely used to solve OR problems. (Hamdy A. Taha)
OR mempelajari tentang sejarah, pengertian, system & model OR dan tahap-tahap pengambilan keputusan serta Memecahkan permasalahan teknis dan manajemen dengan menggunakan metode LP, dan kondisi apabila terjadi perubahan pada parameter model dengan analisis sensitivitas. Memecahkan permasalahan transportasi agar biaya yang dikeluarkan minimum dgn menggunakan beberapa metode trasnportasi. Memecahkan permasalahan transportasi agar biaya penugasan yang dikeluarkan minimum (atau keuntungan yang diperoleh maksimum) dgn metode Hungarian, Merumuskan permasalahan LP dengan fungsi tujuan lebih dari satu. Namun Yang paling utama adalah bagaimana meletakkan dasar matematis linear programming
Linear Programming (pemrograman linier) merupakan teknik matematik yang didesain untuk membantu manajer dalam perencanaan dan pengambilan keputusan penggunaan sumber daya ekonomi yang dimiliki oleh suatu perusahaan.
Aplikasi di bidang marketing:
1. pemilihan media periklanan
2. riset pemasaran
3. dan distribusi produk dari gudang perusahaan ke berbagai pasar.
Aplikasi bidang produksi/operasi:
1. kombinasi produk yang akan diproduksi
2. penjadualan proses produksi
3. penjadualan tugas karyawan, dan lain-lain.
Aplikasi bidang keuangan:
1. pemilihan portfolio investasi.
2. financial decision making.
Aplikasi persoalan ekonomi makro: untuk menganalisis pengaruh kebijakan pemerintah dan perubahan pasar pada sektor ekonomi.
Karakteristik Permasalahan Programasi Linier
a. Semua permasalahan PL memiliki tujuan (objective function) untuk memaksimumkan atau meminimumkan sesuatu (kuanti-tas), seperti profit atau biaya.
b. Permasalahan PL memiliki restriksi (konstrain) yang membatasi tingkatan pencapaian tujuan (objective function).
c. Adanya beberapa alternatif tindakan yang bisa dipilih. Sebagai contoh, kalau suatu perusahaan menghasilkan tiga produk ma-ka alternatif solusinya adalah apakah ia akan mengalokasikan semua resources untuk satu produk, membagi rata resources untuk ketiga produk, atau mendistribusikannya dengan cara yang lainnya.
d. Fungsi tujuan dan kendala (konstrain) dalam permasalahan PL diekspresikan dalam bentuk persamaan atau pertidaksamaan linier.
Langkah-langkah Dalam Formulasi LP:
1. Mengidentifikasi dan menotasikan variabel dalam fungsi tujuan dan kendala.
2. Memformulasikan fungsi tujuan.
3. Memformulasikan fungsi kendala.
4. Memasukkan kendala nonnegativitas.
