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Operations research
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Replacement and maintenance Replacement problems involve items that degenerate with use or with the passage of time and those that fail after a certain amount of use or time. Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships, and home appliances). Nondeteriorating items tend to be small and relatively inexpensive (e.g., light bulbs, vacuum tubes, ink cartridges). The longer a deteriorating item is operated the more maintenance it requires to maintain efficiency. Furthermore, the longer such an item is kept the less is its resale value and the more likely it is to be made obsolete by new equipment. If the item is replaced frequently, however, investment costs increase. Thus the problem is to determine when to replace such items and how much maintenance (particularly preventive) to perform so that the sum of the operating, maintenance, and investment costs is minimized.
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George Dantzig
In the case of nondeteriorating items the problem involves determining whether to replace them as a
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Systems engineering
group or to replace individuals as they fail. Though group replacement is wasteful, labour cost of
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Industrial engineering
replacements is greater when done singly; for example, the light bulbs in a large subway system may
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Engineering
be replaced in groups to save labour. Replacement problems that involve minimizing the costs of
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Management science
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Social science
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Manufacturing
The “items” involved in replacement problems may be people. If so, maintenance can be interpreted
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Humanities
as training or improvements in salary, status, or fringe benefits. Failure can be interpreted as
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Research and development
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Logistics
items, failures, and the replacement labour are solvable either by numerical analysis or simulation.
departure, and investment as recruiting, hiring, and initial training costs. There are many additional complexities in such cases; for example, the effect of one person’s resigning or being promoted on the behaviour of others. Such controllable aspects of the environment as location of work and working hours can have a considerable effect on productivity and failure rates. In problems of this type, the inputs of the behavioral sciences are particularly useful.
Queuing A queue is a waiting line, and queuing involves dealing with items or people in sequence. Thus, a queuing problem consists either of determining what facilities to provide or scheduling the use of them. The cost of providing service and the waiting time of users are minimized. Examples of such problems include determining the number of checkout counters to provide at a supermarket, runways at an airport, parking spaces at a shopping centre, or tellers in a bank. Many maintenance problems can be treated as queuing problems; items requiring repair are like users of a service. Some inventory problems may also be formulated as queuing problems in which orders are like users and stocks are like service facilities.
Job shop sequencing In queuing problems, the order in which users waiting for service are served is always specified. Selection of that order so as to minimize some function of the time to perform all the tasks is a sequencing problem. The performance measure may account for total elapsed time, total tardiness in meeting deadlines or due dates, and the cost of in-process inventories. The most common context for sequencing problems is a batch, or job shop, production facility that processes many different products with many combinations of machines. In this context account may have to be taken of such factors as overlapping service (that is, if a customer consists of a number of items to be taken through several steps of a process, the first items completing the initial step may
SIMILAR TOPICS
start on the second step before the last one finishes the first), transportation time between service
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Total Quality Management
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Logistics
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Human resources management
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Managerial economics
A simplified job shop sequencing problem, with two jobs and four machines, is shown in the figure. At
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Flowchart
the top of the figure is the operations sequence of the two jobs. Job A must go first to machine 1, then
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Production management
to 2, then to 3, and finally to 4, and the order of processing on the four machines cannot be changed.
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Research and development
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Critical path analysis
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facilities, correction of service breakdowns, facility breakdowns, and material shortages. Russell L. Ackoff
The processing time for the job is one hour at each machine, for a total of four hours of machining time. In this example, the job can only be on one machine at a time, as if the job consisted of a single product being processed through four machine tools.
FEATURED ON BRITANNICA Job shop sequencing problem with two solutions. DEMYSTIFIED / GEOGRAPHY
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Job B must follow a different sequence. It also starts on machine 1, but then it goes to machine 4, then to 2, and finally back to machine 4. Each machining operation on Job B also requires one hour.
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Underneath the charts showing the required sequence of operations, two alternative schedules are shown for the two jobs. (In a bar chart, time is shown on the horizontal line, and the bars or blocks
DEMYSTIFIED / GEOGRAPHY
represent the time that each operation is scheduled on each of the four machines.) The first schedule assumes that Job A is run first. Once Job A is laid out on the schedule, Job B’s operations are placed on the chart as far to the left as possible, without violating the sequence constraints. In this case, the
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chart shows that both jobs (eight hours of work) can be completed in five hours. This is made possible by running both jobs at the same time (on separate machines) during the second, third, and fourth
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hours. The second schedule assumes that Job B is run first. This schedule requires a total of six hours, one more than the previous schedule. If the total elapsed time for completion of the two jobs is an important criterion, the first schedule would be superior to the second. Although this problem is easily solved, solutions to actual job shop sequencing problems require the use of sophisticated models and the calculating power of computers. It is not unusual for job shops to have 5,000 customer orders in process at any given time, with each order requiring 50 or 60 distinct processing or machine operations. The number of combinations of feasible sequences is astronomical in such problems, and they provide many problems in modeling and systems development for operations researchers and industrial engineers. William K. Holstein
Manufacturing progress function Because of the enormous complexity of a typical mass production line and the almost infinite number of changes that can be made and alternatives that can be pursued, a body of quantitative theory of mass production manufacturing systems has not yet been developed. The volume of available
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observational data is, however, growing, and qualitative facts are emerging that may eventually serve as a basis for quantitative theory. An example is the “manufacturing progress function.” This was first
HISTORY QUIZ
recognized in the airframe industry. Early manufacturers of aircraft observed that as they produced
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increasing numbers of a given model of airplane, their manufacturing costs decreased in a predictable fashion, declining steeply at first, then continuing to decline at a lower rate. When an actual cost graph
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is drawn on double logarithmic paper plotting the logarithm of the cost per unit as a function of the
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logarithm of the total number of units produced results in data points that almost form a straight line. Over the years similar relationships have been found for many products manufactured by mass
HISTORY QUIZ
production techniques. The slope of the straight line varies from product to product. For a given class
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of products and a given type of production technology, however, the slope appears remarkably
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constant.
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Manufacturing progress functions can be of great value to the manufacturer, serving as a useful tool in estimating future costs. Furthermore, the failure of costs to follow a well-established progress function may be a sign that more attention should be given to the operation in order to bring its cost performance in line with expectation. Though manufacturing progress functions are sometimes called “learning curves,” they reflect much more than the improved training of the manufacturing operators. Improved operator skill is important in the start-up of production, but the major portion of the long-term cost improvement is contributed by improvements in product design, machinery, and the overall engineering planning of the production sequence. Morris Tanenbaum William K. Holstein
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LEARN MORE in these related Britannica articles: 20th-century international relations: Science and technology in wartime Known as “operational research,” this application of science to practical problems was a major step in the process by which military men in the 20th century lost primacy in their profession to
industrial engineering: The evolving nature of industrial engineering …industrial engineering but also from operations research, management science, computer science, and information systems. In the 1970s and 1980s industrial engineering became a more quantitative and computer-based profession, and operations research techniques were adopted as the core of most industrial engineering academic curricula in both the United States and Europe.… George Dantzig …helped develop the field of operations research (essentially, the application of computers to optimization problems). From 1960 to 1966 he served as chairman of the Operations Research Center at Berkeley, and from 1966 until his retirement in 1997 he was a professor of operations research and computer science at Stanford… Alvin E. Roth All his degrees were in operations research, a field of engineering that applies scientific principles to the solution of administrative problems. Roth applied the science to business and economics, which he taught at the University of Illinois (1974–82), the University of Pittsburgh (1982–98), Harvard University (1998–2012), and Stanford (2012– ).…
management science Originally a synonym for operations research, the term management science (often used in the plural) now designates a distinct field. Whereas operations research affords analytical data, statistics, and methods to increase the efficiency of management systems, management science applies these tools in such fields as data mining, engineering, economic…
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MORE ABOUT Operations research 5 REFERENCES FOUND IN BRITANNICA ARTICLES
Assorted References role in World War II (In 20th-century international relations: Science and technology in wartime)
relationship to industrial engineering (In industrial engineering: The evolving nature of industrial engineering)
management science (In management science)
work of Dantzig (In George Dantzig)
Roth (In Alvin E. Roth)
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