No matter how reasonable you are in arguing your position, others may disagree or hold other positions. Widely debated topics such as animal rights or gun control can be difficult to write on if you have no personal connection to them.
Better topics include those that interest you right now, are focused, and have some personal connection to your life. Identify issues that interest you. Pick a few of the roles you list, and identify the issues that interest or concern you. Try wording each issue as a question starting with should: Should college cost less than it does? Should student achievement be measured by standardized tests?
What would be better than standardized tests for measuring student achievement? This strategy will help you think about the issue and find a clear focus for your essay. Choose one issue to write about. Generating ideas and text. Most essays that successfully argue a position share certain features that make them interesting and persuasive.
Consider what interests you about the topic and what more you may need to learn in order to write about it. It may help to do some preliminary research; start with one general source of information a news magazine or Wikipedia, for example to find out the main questions raised about your issue and to get some ideas about how you might argue it. There are various ways to qualify your thesis: in certain circumstances, under certain conditions, with these limitations, and so on.
You need to convince your readers that your thesis is plausible. Start by stating your position and then answering the question why? This analysis can continue indefinitely as the underlying reasons grow more and more general and abstract. Identify other positions. Think about positions that differ from yours and about the reasons that might be given for those positions. To refute other positions, state them as clearly and as fairly as you can, and then show why you believe they are wrong. Perhaps the reasoning is faulty or the supporting evidence is inadequate.
Acknowledge their merits, if any, but emphasize their shortcomings. Ways of organizing an argument. Alternatively, you might discuss each reason and any counterargument to it together. And be sure to consider the order in which you discuss your reasons. Usually, what comes last makes the strongest impression on readers, and what comes in the middle makes the weakest impression.
End with Give the a call to second action, a reason, with support. To read an example argument essay, go to digital. This chapter describes the key elements of an essay that analyzes a text and provides tips for writing one. Your readers may not know the text you are analyzing, so you need to include it or tell them about it before you can analyze it. Attention to the context. All texts are part of ongoing conversations, controversies, or debates, so to understand a text, you need to understand its larger context.
To analyze the lyrics of a new hip-hop song, you might need to introduce other artists that the lyrics refer to or explain how the lyrics relate to aspects of hip-hop culture. A clear interpretation or judgment. When you interpret something, you explain what you think it means. In an analysis of a cologne advertisement, you might explain how the ad encourages consumers to objectify themselves. Reasonable support for your conclusions. You might support your interpretation by quoting passages from a written text or referring to images in a visual text.
Most of the time, you will be assigned a text or a type of text to analyze: the work of a political philosopher in a political science class, a speech in a history or communications course, a painting or sculpture in an art class, and so on. You might also analyze three or four texts by examining elements common to all.
In analyzing a text, your goal is to understand what it says, how it works, and what it means. To do so, you may find it helpful to follow a certain sequence for your analysis: read, respond, summarize, analyze, and draw conclusions. Read to see what the text says. Start by reading carefully, noting the main ideas, key words and phrases, and anything that seems noteworthy or questionable.
Do you find the text difficult? Do you agree with what the writer says? Decide what you want to analyze. Think about what you find most interesting about the text and why. Does the language interest you?
You might begin your analysis by exploring what attracted your notice. Think about the larger context. All texts are part of larger conversations, and academic texts include documentation partly to weave in voices from the conversation. Does he or she respond to something others have said? Is there any terminology that suggests that he or she is allied with a particular intellectual school or academic discipline?
Words like false consciousness or hegemony, for instance, would suggest that the text was written by a Marxist scholar. Consider what you know about the writer or artist. The credentials, other work, reputation, stance, and beliefs of the person who created the text are all useful windows into understanding it.
Write a sentence or two summarizing what you know about the creator and how that information affects your understanding of the text. Visual texts might be made up of images, lines, angles, color, light and shadow, and sometimes words. Look for patterns in the way these elements are used. Write a sentence or two describing the patterns you discover and how they contribute to what the text says.
Analyze the argument. What is the main point the writer is trying to make? Are the reasons plausible and sufficient? Are the arguments appropriately qualified? How credible and current are they? After considering these questions, write a sentence or two summarizing the argument and your reactions to it.
Come up with a thesis. Do you want to show that the text has a certain meaning? Your analysis might be structured in at least two ways. You might discuss patterns or themes that run through the text. Alternatively, you might analyze each text or section of text separately.
State your thesis. To read an example rhetorical analysis, go to digital. Newspapers report on local and world events; textbooks give information about biology, history, writing; websites provide information about products jcrew. Very often this kind of writing calls for research: you need to know your subject in order to report on it.
This chapter describes the key elements found in most reports and offers tips for writing one. Accurate, well-researched information. Reports usually require some research. The kind of research depends on the topic. Library research may be necessary for some topics—for a report on migrant laborers during the Great Depression, for example. Most current topics, however, require internet research. For a report on local farming, for example, you might interview some local farmers.
Various writing strategies. For example, a report on the benefits of exercise might require that you classify types of exercise, analyze the effects of each type, and compare the benefits of each. For a report on the financial crisis for a general audience, for example, you might need to define terms such as mortgage-backed security and predatory lending. Appropriate design. Numerical data, for instance, can be easier to understand in a table than in a paragraph. A photograph can help readers see a subject, such as an image of someone texting while driving in a report on car accidents.
If you get to choose your topic, consider what interests you and what you wish you knew more about. They may be academic in nature or reflect your personal interests, or both. Even if an assignment seems to offer little flexibility, you will need to decide how to research the topic and how to develop your report to appeal to your audience. And sometimes even narrow topics can be shaped to fit your own interests.
Start with sources that can give you a general sense of the subject, such as a Wikipedia entry or an interview with an expert. Your goal at this point is to find topics to report on and then to focus on one that you will be able to cover. Come up with a tentative thesis. Once you narrow your topic, write out a statement saying what you plan to report on or explain. Think about what kinds of information will be most informative for your audience, and be sure to consult multiple sources and perspectives.
Revisit and finalize your thesis in light of your research findings. Ways of organizing a report [Reports on topics that are unfamiliar to readers] Begin Explain by with an anecdote, quote, or other means of interesting comparing, Provide background, and state your thesis.
Describe classifying, your topic, analyzing defining causes or any key effects, terms. Conclude by restating your thesis or referring to your beginning. Conclude by topic; provide any necessary background information; state your Narrate the second event or procedure. Narrate the third event or procedure.
Repeat as necessary. Conclude by restating your Repeat as necessary. To read an example report, go to digital. Parents read their children bedtime stories as an evening ritual. Preachers base their sermons on religious stories to teach lessons about moral behavior. Grandparents tell how things used to be, sometimes telling the same stories year after year. College applicants write about significant moments in their lives.
Writing students are often called on to compose narratives to explore their personal experiences. This chapter describes the key elements of personal narratives and provides tips for writing one.
Most narratives set up some sort of situation that needs to be resolved. That need for resolution makes readers want to keep reading. Vivid detail. Details can bring a narrative to life by giving readers vivid mental images of the sights, sounds, smells, tastes, and textures of the world in which your story takes place.
To give readers a picture of your childhood home in the country, you might describe the gnarled apple trees in your backyard and the sound of crickets chirping on a spring night. You may reveal its significance in various ways, but try not to state it too directly, as if it were a kind of moral of the story. Describe the setting. List the places where your story unfolds. Think about the key people. Narratives include people whose actions play an important role in the story.
Try narrating the action using active and specific verbs pondered, shouted, laughed to capture what happened. Consider the significance. You need to make clear why the event you are writing about matters. How did it change or otherwise affect you? What aspects of your life now can you trace to that event?
How might your life have been different if this event had not happened? Ways of organizing a personal narrative. Tell about what happened.
Say how Say the conflict something was about the resolved. Fill in details: setting, people, specific actions. Make clear how the situation was resolved. Say something about the significance. To read an example narrative, go to digital. In both cases, you go below the surface to deepen your understanding of how the texts work and what they mean.
This chapter describes the key elements expected in most literary analyses and provides tips for writing one. Your thesis, then, should be arguable. You might argue, for example, that the dialogue between two female characters in a short story reflects current stereotypes about gender roles.
Careful attention to the language of the text. Attention to patterns or themes. Literary analyses are usually built on evidence of meaningful patterns or themes within a text or among several texts. When you write a literary analysis, you show one way the text may be understood, using evidence from the text and, sometimes, relevant contextual evidence to support what you think the text means. MLA style. Start by considering whether your assignment specifies a particular kind of analysis or critical approach.
Look for words that say what to do: analyze, compare, interpret, and so on. Choose a method for analyzing the text. Trace the development and expression of themes, characters, and language through the work. How do they help to create particular meaning, tone, or effects? Explore the way the text affects you as you read through it.
Read closely, noticing how the elements of the text shape your responses, both intellectual and emotional. How has the author evoked your response? Read the work more than once. When you first experience a piece of literature, you usually focus on the story, the plot, the overall meaning. Compose a strong thesis. Your goal is not to pass judgment but to suggest one way of seeing the text. Do a close reading. Find specific, brief passages that support your interpretation; then analyze those passages in terms of their language, their context, and your reaction to them as a reader.
Why does the writer choose this language, these words? What is their effect? If something is repeated, what significance does the pattern have? Support your argument with evidence. The parts of the text you examine in your close reading become the evidence you use to support your interpretation. Paying attention to matters of style.
Literary analyses have certain conventions for using pronouns and verbs. Describe the historical context of the setting in the past tense. Document your sources. To read an example literary analysis, go to digital. Lovers propose marriage; students propose that colleges provide healthier food options in campus cafeterias. These are all examples of proposals, ideas put forward that offer solutions to some problem. All proposals are arguments: when you propose something, you are trying to persuade others to consider—and hopefully to accept—your solution to the problem.
This chapter describes the key elements of a proposal and provides tips for writing one. Some problems are self-evident and relatively simple, and you would not need much persuasive power to make people act.
While some might not see a problem with colleges discarding too much paper, for example, most are likely to agree that recycling is a good thing. Other issues are more controversial: some people see them as problems while others do not.
For example, some believe that motorcycle riders who do not wear helmets risk serious injury and also raise the cost of health care for all of us, but others think that wearing a helmet—or not—should be a personal choice; you would have to present arguments to convince your readers that not wearing a helmet is indeed a problem needing a solution. A solution to the problem.
Once you have defined the problem, you need to describe the solution you are suggesting and to explain it in enough detail for readers to understand what you are proposing. Sometimes you might suggest several possible solutions, analyze their merits, and then say which one you think will most likely solve the problem. You need to provide evidence to convince readers that your solution is feasible—and that it will, in fact, solve the problem.
A response to questions readers may have. You need to consider any questions readers may have about your proposal—and to show how its advantages outweigh any disadvantages. A proposal for recycling paper, for example, would need to address questions about the costs of recycling bins and separate trash pickups.
A call to action. The goal of a proposal is to persuade readers to accept your proposed solution—and perhaps to take some kind of action. You may want to conclude your proposal by noting the outcomes likely to result from following your recommendations. An appropriate tone. Readers will always react better to a reasonable, respectful presentation than to anger or self-righteousness. Choose a problem that can be solved. Large, complex problems such as poverty, hunger, or terrorism usually require large, complex solutions.
Most of the time, focusing on a smaller problem or a limited aspect of a large problem will yield a more manageable proposal. Rather than tackling the problem of world poverty, for example, think about the problem faced by people in your community who have lost jobs and need help until they find employment. Most successful proposals share certain features that make them persuasive. Explore several possible solutions to the problem.
Decide on the most desirable solution s. One solution may be head and shoulders above others, but be open to rejecting all the possible solutions on your list and starting over if you need to, or to combining two or more potential solutions in order to come up with an acceptable fix. Think about why your solution is the best one. What has to be done to enact it?
What will it cost? What makes you think it can be done? Why will it work better than others? Ways of organizing a proposal. You can organize a proposal in various ways, but you should always begin by establishing that there is a problem. You may then identify several possible solutions before recommending one of them or a combination of several. Sometimes, however, you might discuss only a single solution. Identify possible Propose a Call for action, solutions and solution and or reiterate consider their pros give reasons your proposed and cons one by one.
Anticipate and answer questions. To read an example proposal, go to digital. Such essays are our attempt to think something through by writing about it and to share our thinking with others. A reflective essay has a dual purpose: to ponder something you find interesting or puzzling and to share your thoughts with an audience.
Whatever your subject, your goal is to explore it in a way that will interest others. One way to do that is to start by considering your own experience and then moving on to think about more universal experiences that your readers may share. For example, you might write about your dog, and in doing so you could raise questions and offer insights about the ways that people and animals interact.
Some kind of structure. A reflective essay can be organized in many ways, but it needs to have a clear structure. Whether you move from detail to detail or focus your reflection on one central question or insight about your subject, all your ideas need to relate, one way or another. The challenge is to keep your readers interested as you explore your topic and to leave them satisfied that the journey was interesting and thought-provoking. Every now and then someone will cheer her on.
Details such as these will help your readers understand and care about your subject. A questioning, speculative tone. So your tone will often be tentative and open, demonstrating a willingness to entertain, try out, accept, and reject various ideas as your essay progresses from beginning to end, maybe even asking questions for which you can provide no direct answers.
Choose a subject you want to explore. Make a list of things that you think about, wonder about, find puzzling or annoying. Explore your subject in detail. Reflections often include descriptive details that provide a base for the speculations to come.
Back away. Ask yourself why your subject matters: why is it important or intriguing or otherwise significant? Your goal is to think on screen or paper about your subject, to see where it leads you.
Think about how to keep readers with you. Reflections must be carefully crafted so that readers can follow your train of thought. Ways of organizing a reflective essay. Reflections may be organized in many ways because they mimic the way we think, sometimes associating one idea with another in ways that make sense but do not necessarily follow the kinds of logical progression found in academic arguments or reports.
Here are two ways you might organize a reflection. To read an example reflective essay, go to digital. You may be assigned to create annotated bibliographies to weigh the potential usefulness of sources and to document your search efforts.
This chapter describes the key elements of an annotated bibliography and provides tips for writing two kinds of annotations: descriptive and evaluative. Doherty, Thomas. Unwin Hyman, A historical discussion of the identification of teenagers as a targeted film market. Foster, Harold M. An evaluation of the potential of using teen films such as Sixteen Candles and The Karate Kid to instruct adolescents on the difference between film as communication and film as exploitation.
They are often helpful in assessing how useful a source will be for your own writing. Gore, A. An inconvenient truth: The planetary emergency of global warming and what we can do about it. New York, NY: Rodale. It centers on how the atmosphere is very thin and how greenhouse gases such as carbon dioxide are making it thicker. The thicker atmosphere traps more infrared radiation, causing warming of the Earth. He includes several examples of problems caused by global warming.
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Submit your data to receive a complimentary benchmark report and gain informal CPD. BCIS content papers. Description Type Tooling Dept. Time hr. Description Shape, drill, Automatic. SA1 Enclose Dennison None. Plunger housing O-ring SA-1 A Plunger retainer Lock nut A Pipe plug A Packaging materials A The operation process chart can be complemented with transportations, stor- ages, and delays including distances and times when the information is available.
Such a chart is referred to as a flow process chart by some and a process chart by others [4]. Assembly charts and operation process charts may be viewed as analog models of the assembly process and the overall production process, respectively. As noted previously, circles and squares represent time, and horizontal connections represent sequential steps in the assembly of the product. Notice in the assembly chart that components have been identified with a four-digit code starting with 1, 2, 3, and 4.
Furthermore, subassemblies SA and as- semblies A have been identified with letters and numbers. The same identification approach has been used in the operation process chart. Additionally, fabrication op- erations have been represented with a four-digit code starting with 0. A second viewpoint, based on graph and network theory, is to interpret the charts as network representations, or more accurately, tree representations of a pro- duction process.
Company Prepared by. Air Flow Regulator Product Date. Plunger Plunger Plunger retainer Seat ring Plunger housing housing Shape, drill, Shape, Mill, Shape, Cut to tap inside drill, shape, drill, length length thread. Drill 8 Deburr holes.
Deburr and Drill 4 holes, blowout tap, ream, inspect countersink. Drill, tap, roll ream. O-ring, Lock nut A2 Pipe plug A3 Packaging A4. The precedence diagram is a directed network and is often used in project planning. A precedence diagram for the air flow regulator is given in Figure 2. The precedence diagram shows part numbers on the arcs and denotes operations and inspections by circles and squares, respectively. A procurement operation, , is used in Figure 2.
The following convention is used in the construction of the precedence dia- gram as illustrated in Figure 2.
Purchased parts and materials that do not require modifications are placed on the top and bottom part of the diagram so that they can be inserted in the center part of the diagram when needed packaging materials, pipe plug, lock nut, spring, and O-rings. Fabrication and assembly operations are placed in the center part of the diagram.
The precedence diagram representation of the operations and inspections in- volved in a process can be of significant benefit to the facilities planner. Packaging No additional constraints are implicitly imposed; no assumptions are made concerning which parts move to which parts; no material handling or layout decisions are implicit in the way the precedence diagram is constructed.
The same claims cannot be made for the assembly chart and operation process chart. Just as there are al- ternative disassembly sequences that can be used, there are also alternative assembly sequences.
The assembly chart and the operation process chart depict a single sequence. The particular sequence used can have a major impact on space and handling system requirements. Notice operations , , , , , , and are not shown in series in Figure 2.
Hence, there exists some latitude in how the product is assembled. On the other hand, the operations process chart does not provide a mecha- nism for showing the possibility of alternative processing sequences.
In order to further demonstrate our concerns regarding the misuse of the op- eration process chart in layout planning, consider the processes involved in manu- facturing an axle for an over-the-road tractor. Using the advice typically provided in texts that describe the construction of operation process charts, the axle itself should be shown at the extreme right side of the chart.
Subassemblies, components, and purchased parts would be shown sequentially feeding into the axle until a fin- ished assembly was produced.
By observing the operation process chart, one might be tempted to develop an assembly line for the axle assuming sufficient quantities are to be produced. The axle would be moved along the assembly line, and subassemblies, compo- nents, and purchased parts would be attached to it.
Using such an approach, space and handling equipment requirements for the line would be based on the largest component part in the assembly. Alternatively, and especially for low-volume production, there may be benefits to leaving the axle in a stationary position after the last operation.
A large axle would require heavy duty lifting and moving equipment occupying a large space and would require high energy consumption. Moving subassemblies and parts to the axle would need less significant material handling and space requirements, al- though there would likely be more total movements.
Because of the limitations of the assembly chart and the operation process chart, we recommend a precedence diagram be constructed first. Based on the precedence diagram, alternative assembly charts and operation process charts should then be constructed. Another methodology that has made an impact on product and process design is group technology.
Group technology GT refers to grouping parts into families and then making design decisions based on family characteristics.
Groupings are typically based on part shapes, part sizes, material types, and processing requirements. In cases where there are thousands of individual parts, the number of families might be less than Group technology is an aggregation process that has been found to be use- ful in achieving standardized part numbers and standard specifications of purchased parts, for example, fasteners and standardized process selection [6, 9, 11, 12, 16 ].
The importance of the process design or process plan in developing the facil- ities plan cannot be overemphasized. Furthermore, it is necessary that the process planner understand the impact of process design decisions on the facilities plan. Our experience indicates that process planning decisions are frequently made with- out such an understanding. As an example, it is often the case that alternatives exist in both the selection of the processes to be used and their sequence of usage.
The final choice should be based on interaction between schedule design and facilities planning. The resulting standardization of process selection has yielded considerable labor savings and reductions in produc- tion lead times. At the same time, standardization in process selection might create disadvantages for schedule and facility design. If such a situation occurs, a mecha- nism should exist to allow exceptions. Many of the degrees of freedom available to the facilities planner can be affected by process selection decisions.
Production quantity decisions are referred to as lot size decisions; determining when to produce is referred to as production scheduling. In addition to how much and when to produce, it is important to know how long pro- duction will continue. Such a determination is obtained from market forecasts. Schedule design decisions impact machine selection, number of machines, number of shifts, number of employees, space requirements, storage equipment, material handling equipment, personnel requirements, storage policies, unit load design, building size, and so on.
Consequently, schedule planners need to interface continuously with marketing and sales personnel and with the largest customers to provide the best information possible to facilities design planners. To plan a facility, information is needed concerning production volumes, trends, and the predictability of future demands for the products to be produced. The less specificity provided regarding product, process, and schedule designs, the more general purpose will be the facility plan.
The more specific the inputs from product, process, and schedule designs, the greater the likelihood of optimizing the facility and meeting the needs of manufacturing. Lastly, consider a facility that pro- duces 10, television sets per month for the next 10 years versus one that produces 10, television sets per month for three months and is unable to predict what product or volume will be produced thereafter; they too should differ. As a minimum, the market information given in Table 2.
Prefer- ably, information regarding the dynamic value of demands to be placed on the fa- cility is desired. Ideally, information of the type shown in Table 2.
Packaging 2. Susceptibility to product changes 3. Susceptibility to changes in marketing strategies Where are the consumers located? Facilities location 2. Method of shipping 3. Warehousing systems design Why will the consumer purchase the product? Seasonability 2. Variability in sales 3. Packaging Where will the consumer purchase the product? Unit load sizes 2. Order processing 3. Packaging What percentage of the market does the product 1.
Future trends attract and who is the competition 2. Growth potential 3. Need for flexibility What is the trend in product changes? Space allocations 2. Materials handling methods 3. Need for flexibility.
If such information is available, a facilities plan can be developed for each demand state, and a facility designed with sufficient flexibility to meet the yearly fluctuations in product mix. By developing facilities plans annually and not- ing the alterations to the plan, a facilities master plan can be established. Dynamic layouts can be designed to accommodate varying product demands [14]. In many cases, however, information of the type given in Table 2.
Therefore, facilities typically are planned using deterministic data. The assumptions of deterministic data and known demands must be dealt with when evaluating alter- native facilities plans. In addition to the volume, trend, and predictability of future demands for var- ious products, the qualitative information listed in Table 2. Ad- ditionally, the facilities planner should solicit input from marketing as to why market trends are occurring.
Such information may provide valuable insight to the facilities planner. Surprisingly, his observations apply to several aspects of facilities planning. Such a situation is depicted by the volume-variety chart, or Pareto chart, given in Figure 2. By knowing this at the outset, development of the facilities plan may be significantly simplified. This volume-variety information is very important in determining the layout type to use. Schedule design determines the number of each equipment type required to meet the production schedule.
Specification of process requirements typically occurs in three phases. The first phase determines the quantity of components that must be produced, including allowances for defective items, in order to meet the market estimate.
The second phase determines the machine requirements for each operation, and the third phase combines the operation requirements to obtain overall machine requirements. We define an item to be defective when the final attributes after processing do not meet the control limits specified by quality control standards.
A review of Figure 2. The concept is general in the sense that the component used in an as- sembly may be a purchased component, and the defective percentage gives the estimate of the percent of rejects from an arriving lot. It is always better to achieve zero defects for many reasons, including the elimination of wasteful activities related to handling defective items. Some parts might be scrapped while others may be reworked.
Fewer defects usually result from more automated processing, looser part tolerance, the use of certified suppliers, quality at the source, prevention techniques, and use of higher-grade materials. All of these factors point to fundamental economic trade-offs. The required inputs to manufacturing and assembly operations can be deter- mined as follows. Let dk represent the percentage of defective items produced on the kth operation, Ok the desired output without defects, and Ik the production in- put.
Example 2. The market estimate is the output required from step 3. As a general principle, it is desirable to design processes with zero defects. Should this not be possible, there should be fewer defects at processes that are near the end of the manufacturing steps. The reason is that the cost of the item increases as more operations are performed on it.
The graphical representation for operations with rework is shown in Figure 2. Given that rework is performed based on the assumption above, calculate the number of units required for processing at the first op- eration. We assume that the components are outsourced and the final assembly is performed locally. The final products are two assemblies requiring three components. As- sembly 1 requires four units of component 1 and three units of component 2.
Assembly 2 requires two units of component 2 and one unit of component 3. See Figure 2. The calculations required are also shown in Figure 2. The calculations performed using Equations 2. However, when pro- ducing small batches, the use of average values is less appropriate. If conditions are such that the foundry has only one chance to produce the number of castings required, then the probability of a casting being good should be considered when determining the batch size to be produced.
In determining how many castings to produce, the following questions come to mind: 1. How much does it cost to produce a good casting? How much for a bad casting? How much revenue is generated from a good casting? How much from a bad casting? What is the probability distribution for the number of good castings resulting from a production lot? If answers are available for these questions, then a determination can be made re- garding the number of castings to schedule in order to, say, maximize the expected profit or achieve a desired confidence level of not producing fewer good castings than are needed.
Determining the number of additional units to allow when sched- uling low-volume production where rejects randomly occur is called the reject al- lowance problem [17].
If it is desired to maximize expected profit, the value of Q that maximizes Equation 2. For most cost and revenue formulations, Equation 2. The necessary and sufficient conditions for the optimal production quantity Q when X is binomially distributed is given in [17]. An order for 20 custom-designed castings has been received. Based on historical records, the probability dis- tributions given in Table 2. How many castings should be scheduled.
What is the probability of losing money at this production level? The profits resulting from various combinations of Q and x are shown in Table 2. The vector prod- ucts of columns from Tables 2.
From Table 2. We use the term machine fractions. The machine fraction for an operation is determined by dividing the total time re- quired to perform the operation by the time available to complete the operation. The total time required to perform an operation is the product of the standard time for the operation and the number of times the operation is to be performed.
For ex- ample, if it takes 0. Whether or not 1. Are the parts actually being made to the 0. Is the machine available when needed during the two-hour period? Are the standard time, the number of parts, and the time the machine takes known with certainty and fixed over time?
The first question may be handled by dividing the standard time by the histor- ical efficiency of performing the operation. The reliability factor is the percentage of time the machine is actually producing.
The third question dealing with the uncertainty and time-varying nature of machine fraction variables can be an important factor in determining machine re- quirements. If considerable uncertainty and variation exist over time, it may be useful to consider using probability distributions instead of point estimates for the parameters and utilizing a stochastic machine fraction model. Typically, such mod- els are not utilized, and the approach taken is to use a deterministic model and plan the facility to provide sufficient flexibility to handle changes in machine frac- tion variables.
In Equation 2. During an eight-hour shift, units are to be produced. How many milling machines are required? Such a determination is not necessarily straight- forward. Even if only one operation is to be performed on a particular equipment type, overtime and subcontracting must be considered. If more than one operation is to be run on a particular equipment type, several alternatives must be considered. No drill press operator, overtime, or subcontracting is available for any operation on the ABC drill press.
It may be seen that a minimum of four and a maximum of six machines are required. How many should be purchased? The answer is either four, five, or six. With no further information, a specific recommendation cannot be made.
Clustering considerations may require the application of group technology methods to determine the commonality of parts and make decisions of how the ma- chines are assigned to departments. A job shop type of layout will result in fewer machines, while dedicated production lines will require values that are closer to the upper bounds as listed in the last column in Table 2. Clustering analysis is covered in Chapter 3, and determination of layout configurations is discussed in Chapter 6.
It is assumed that a deter- mination of the number of people to be employed in the facility already has been made. Typically, such decisions are not a part of the facilities planning process.
However, the combination of product, process, and schedule design decisions sig- nificantly influences the number of employees involved in producing the product. In this section, we consider how decisions regarding the assignment of machines to operators can affect the number of employees. Specifically, we consider a situation involving the assignment of operators to semiautomatic production equipment. For purposes of this discussion, it is assumed the machines are identical.
In contrast to the reject allowance problem, it is assumed that the times required to load and un- load each machine are constant, the automatic machining time is constant, and the time required for the operator to travel between machines, prepare parts for ma- chining, and inspect and pack parts is constant.
To illustrate the situation under consideration, see Figure 2. The chart is called a human- machine chart or a multiple activity chart, since it shows the activities of one or more people and one or more machines. Such charts can be used to analyze multi- ple activity relationships when nonidentical machines are being tended by one or more operators. As shown, the analysis begins with each machine empty and the operator standing in front of Machine 1 M The oper- ator loads M-1, walks to M-2, loads M-2, walks to M-3, loads M-3, walks to M-1, unloads M-1, loads M-1, inspects and packs the part removed from M-1, travels to M-2, and so forth.
As shown in Figure 2. In other words, if nothing interrupts the activities of the operator and the three machines, the 9-minute cycle will repeat indefinitely. Under conditions similar to those depicted by Figure 2. T-3 3 L-3 Loaded 4 Machining. Transient State 12 min T Hence, an ideal assignment is. Since a fractional number of machines cannot be assigned to an operator, consider what will happen if some integer number of machines, m, is assigned. The repeating cycle will be the larger of the two, and the difference in the two will be idle time.
If we wish to determine the cost per unit produced by an m machine assignment, the following notation will be helpful:. Finished product Raw material Figure 2. Reprinted with permission from [18]. Assuming each machine produces one unit during a repeating cycle, the cost per unit pro- duced during a repeating cycle can be determined as follows:.
Hence, from Equation 2. Therefore, H equals 0. The problems at the end of the chapter explore various aspects of the machine assignment problem, such as assigning machines to operators if, say, a total of 11 machines are required to meet the daily production schedule or there is uncertainty re- garding the value of Cm. Some typical business objectives include breakthroughs in production cost, on-time deliv- ery, quality, and lead time.
Some tools frequently used by quality practitioners e. The seven management and planning tools have gained acceptance as a methodology for improving planning and implementa- tion efforts [5]. In the mids a committee of engineers and scientists in Japan refined and tested the tools as an aid for process improvement, as proposed by the Deming cycle. In , Dr. Deming proposed a model for continuous process improvement that involves four steps: planning and goal setting, doing or execution, checking or analysis, and performing corrective actions Plan—Do—Check—Act.
The seven management and planning tools are the affinity diagram, the inter- relationship digraph, the tree diagram, the matrix diagram, the contingency diagram, the activity network diagram, and the prioritization matrix.
Each is described below and illustrated with examples related to facilities design. Suppose we are interested in generating ideas for reducing manufacturing lead time. Each group then receives a heading. An affinity diagram for reducing manufacturing lead time is presented in Figure 2. The headings selected were facilities design, equipment issues, quality, setup time, and scheduling. The term digraph is employed because the graph uses directed arcs.
Suppose we want to study the relationship. Issues in reducing manufacturing lead time. Facilities design Equipment issues Quality Setup time Scheduling. Form 1. Operator cer- 1. Provide 1. Provide doc- 1.
Provide visi- product fam- tification training on umentation bility to daily ilies program how to use on setup product se- process doc- procedures quence 2.
Assign fami- 2. Sit techni- umentation lies to cells cians closer 2. Locate fix- 2. Do not au- to produc- 2. Implement tures and thorize prod- 3. Monitor with feed- needed parts breakdowns back 3. Provide are not avail- 4. Keep receiv- to predict fu- training so ing and ship- able ture oc- 3. Develop operators ping close to curences mistake- can partici- 3. Negotiate production proof pate frequent and 4. Recruit devices smaller lots enough tech- 4.
Provide in- to customers nicians per 4. Develop ca- formation on shift pabilities for daily se- monitoring quence key machine parameters Figure 2. Form product 2. Assign families 3.
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