Linear Programming: Advantages, Disadvantages and Strategies

Linear Programming: Advantages, Disadvantages and Strategies I LINEAR PROGRAMMING In a decision-making embroilment, model formulation is important because it represents the essence of business decision problem. The term formulation is used to mean the process of converting the verbal description and numerical data into mathematical expressions which represents the relevant relationship among decision factors, objectives and restrictions on the use of resources. Linear Programming (LP) is a particular type of technique used for economic allocation of scarce or limited resources, such as labour, material, machine, time, warehouse space, capital, energy, etc. to several competing activities, such as products, services, jobs, new equipment, projects, etc. on the basis of a given criterion of optimally. The phrase scarce resources mean resources that are not in unlimited in availability during the planning period. The criterion of optimality generally is either performance, return on investment, profit, cost, utility, time, distance, etc. George B Dantzing while working with US Air Force during World War II, developed this technique, primarily for solving military logistics problems. But now, it is being used extensively in all functional areas of management, hospitals, airlines, agriculture, military operations, oil refining, education, energy planning, pollution control, transportation planning and scheduling, research and development, etc. Even though these applications are diverse, all I.P models consist of certain common properties and assumptions. Before applying linear programming to a real-life decision problem, the decision-maker must be aware of all these properties and assumptions. The word linear refers to linear relationship among variables in a model. Thus, a given change in one variable will always cause a resulting proportional change in another variable. For example, doubling the investment on a certain project will exactly double the rate of the return. The word programming refers to modelling and solving a problem mathematically that involves the economic allocation of limited resources by choosing a particular course of action or strategy among various alternative strategies to achieve the desired objective. STRUCTURE OF LINEAR PROGRAMMING General Structure of LP Model The general structure of LP model consists of three components. Decision variables (activities): We need to evaluate various alternatives (courses of action) for arriving at the optimal value of objective function. Obviously, if there are no alternatives to select from, we would not need LP. The evaluation of various alternatives is guided by the nature of objective function and availability of resources. For this, we pursue certain activities usually denoted by x1, x2xn. The value of these activities represents the extent to which each of these is performed. For example, in a product-mix manufacturing, the management may use LP to decide how many units of each of the product to manufacture by using its limited resources such as personnel, machinery, money, material, etc. These activities are also known as decision variables because they arc under the decision makers control. These decision variables, usually interrelated in terms of consumption of limited resources, require simultaneous solutions. All decision variables are continuous, controllable and non-negative. That is, x1>0, x2>0, .xn>0. The objective function: The objective function of each L.P problem is a mathematical representation of the objective in terms of a measurable quantity such as profit, cost, revenue, distance, etc. In its general form, it is represented as: Optimise (Maximise or Minimise) Z = c1x1 + c2X2. cnxn Where Z is the measure-of-performance variable, which is a function of x1, x2 , xn. Quantities c1, c2cn are parameters that represent the contribution of a unit of the respective variable x1, x2, xn to the measure-of-performance Z. The optimal value of the given objective function is obtained by the graphical method or simplex method. The constraints: There are always certain limitations (or constraints) on the use of resources, e.g. labour, machine, raw material, space, money, etc. that limit the degree to which objective can be achieved. Such constraints must be expressed as linear equalities or inequalities in terms of decision variables. The solution of an L.P model must satisfy these constraints. The linear programming method is a technique for choosing the best alternative from a set of feasible alternatives, in situations in which the objective function as well as the constraints can be expressed as linear mathematical functions. APPLICATION AREAS OF LINEAR PROGRAMMING Linear programming is the most widely used technique of decision-making in business and Industry and in various other fields. In this section, we will discuss a few of the broad application areas of linear programming. Agricultural Applications These applications fall into categories of farm economics and farm management. The former deals with agricultural economy of a nation or region, while the latter is concerned with the problems of the individual farm. The study of farm economics deals with inter-regional competition and optimum allocation of crop production. Efficient production patterns can be specified by a linear programming model under regional land resources and national demand constraints. Linear programming can be applied in agricultural planning, e.g. allocation of limited resources such as acreage, labour, water supply and working capital, etc. in a way so as to maximise net revenue. Military Applications Military applications include the problem of selecting an air weapon system against enemy so as to keep them pinned down and at the same time minimising the amount of aviation gasoline used. A variation of the transportation problem that maximises the total tonnage of bombs dropped on a set of targets and the problem of community defence against disaster, the solution of which yields the number of defence units that should be used in a given attack in order to provide the required level of protection at the lowest possible cost. Production Management Product mix: A company can produce several different products, each of which requires the use of limited production resources. In such cases, it is essential to determine the quantity of each product to be produced knowing its marginal contribution and amount of available resource used by it. The objective is to maximise the total contribution, subject to all constraints. Production planning: This deals with the determination of minimum cost production plan over planning period of an item with a fluctuating demand, considering the initial number of units in inventory, production capacity, constraints on production, manpower and all relevant cost factors. The objective is to minimise total operation costs. Assembly-line balancing: This problem is likely to arise when an item can be made by assembling different components. The process of assembling requires some specified sequence(s). The objective is to minimise the total elapse time. Blending problems: These problems arise when a product can be made from a variety of available raw materials, each of which has a particular composition and price. The objective here is to determine the minimum cost blend, subject to availability of the raw materials, and minimum and maximum constraints on certain product constituents. Trim loss When an item is made to a standard size (e.g. glass, paper sheet), the problem that arises is to determine which combination of requirements should be produced from standard materials in order to minimise the trim loss. Financial Management Portfolio selection: This deals with the selection of specific investment activity among several other activities. The objective is to find the allocation which maximises the total expected return or minimises risk under certain limitations. Profit planning: This deal with the maximisation of the profit margin from investment in plant facilities and equipment, cash in hand and inventory. Marketing Management Media selection: Linear programming technique helps in determining the advertising media mix so as to maximise the effective exposure, subject to limitation of budget, specified exposure rates to different market segments, specified minimum and maximum number of advertisements in various media. (if) Travelling salesman problem The problem of salesman is to find the shortest route from a given city, visiting each of the specified cities and then returning to the original point of departure, provided no city shall be visited twice during the tour. Such type of problems can be solved with the help of the modified assignment technique. Physical distribution: Linear programming determines the most economic and efficient manner of locating manufacturing plants and distribution centres for physical distribution. Personnel Management Staffing problem: Linear programming is used to allocate optimum manpower to a particular job so as to minimise the total overtime cost or total manpower. Determination of equitable salaries: Linear programming technique has been used in determining equitable salaries and sales incentives. Job evaluation and selection: Selection of suitable person for a specified job and evaluation of job in organisations has been done with the help of linear programming technique. Other applications of linear programming lie in the area of administration, education, fleet utilisation, awarding contracts, hospital administration and capital budgeting. ADVANTAGES OF LINEAR PROGRAMMING Following are certain advantages of linear programming: Linear programming helps in attaining the optimum use of productive resources. It also indicates how a decision-maker can employ his productive factors effectively by selecting and distributing (allocating) these resources. Linear programming techniques improve the quality of decisions. The decision-making approach of the user of this technique becomes more objective and less subjective. Linear programming techniques provide possible and practical solutions since there might be other constraints operating outside the problem which must be taken into account. Just because we can produce so many units docs not mean that they can be sold. Thus, necessary modification of its mathematical solution is required for the sake of convenience to the decision-maker. Highlighting of bottlenecks in the production processes is the most significant advantage of this technique. For example, when a bottleneck occurs, some machines cannot meet demand while other remains idle for some of the time. Linear programming also helps in re-evaluation of a basic plan for changing conditions. If conditions change when the plan is partly carried out, they can be determined so as to adjust the remainder of the plan for best results. LIMITATIONS OF LINEAR PROGRAMMING There should be an objective which should be clearly identifiable and measurable in quantitative terms. It could be, for example, maximisation of sales, of profit, minimisation of cost, and so on, which is not possible in real life. The activities to be included should be distinctly identifiable and measurable in quantitative terms, for instance, the products included in a production planning problem and all the activities cant be measured in quantitative terms for example if labour is sick, which will decrease his performance which cant be measured. The resources of the system which arc to be allocated for the attainment of the goal should also be identifiable and measurable quantitatively. They must be in limited supply. The technique would involve allocation of these resources in a manner that would trade off the returns on the investment of the resources for the attainment of the objective. The relationships representing the objective as also the resource limitation considerations, represented by the objective function and the constraint equations or inequalities, respectively must be linear in nature, which is not possible. There should be a series of feasible alternative courses of action available to the decision makers, which are determined by the resource constraints. When these stated conditions are satisfied in a given situation, the problem can be expressed in algebraic form, called the Linear Programming Problem (LPP) and then solved for optimal decision. While solving an LP model, there is no guarantee that we will get integer valued solutions. For example, in finding out how many men and machines would be required lo perform a particular job, a non-integer valued solution will be meaningless. Rounding off the solution to the nearest integer will not yield an optimal solution. In such cases, integer programming is used to ensure integer value to the decision variables. Linear programming model does not take into consideration the effect of time and uncertainty. Thus, the LP model should be defined in such a way that any change due to internal as well as external factors can be incorporated. Sometimes large-scale problems can be solved with linear programming techniques even when assistance of computer is available. For it, the main problem can be fragmented into several small problems and solving each one separately. Parameters appearing in the model are assumed to be constant but in real-life situations, they are frequently neither known nor constant. Parameters like human behaviour, weather conditions, stress of employees, demotivated employee cant be taken into account which can adversely effect any organisation Only one single objective is dealt with while in real life situations, problems come with multi-objectives. II SITUATION ANALYSIS Phang furniture system Inc. (Fursys) manufactures two models of stools, Potty which is basic model and a better model called Hardy. SUPPLIES Maximum of 350 pounds plastic per day at the rate of $1.5 per pound by Keow supplies Up to 30 boxes of legs per day at the rate of $7.5 per box. Each box has 10 sets of legs by Yuen supplies Using linear programming the optimal production should be determined for maximum profit. Decision Variables The production units are in terms of number on daily basis. Therefore the decision variables are: Let, X1 = No. of Pottys production daily X2 = No. of Hardys production daily Objective Function The objective in the problem is to attain maximum profit. We have selling price for Potty and Hardy as $12.75 and $18. We need to calculate the unit profit gained by selling Potty and Hardy. Cost of production for 1 Potty = one pound plastic + one set of leg = ($1.5*1) + $0.75(1) = $2.25 Profit made by selling = $12.75 $2.25 = $10.5 Cost of production for 1 Hardy = 1.5 pound of plastic + one set of leg = ($1.5*1.5) + ($0.75*1) = $3 Unit profit made by selling Hardy = $18 $3 = $15 Constraints Plastic Potty requires one pound of plastic and Hardy requires 1.5 pound plastic. So the total plastic used daily is: (1)X1 + (1.5)X2 This plastic supply cant exceed the limit of 350 pounds daily, so constraint is (1)X1 + (1.5)X2

A response to the great Gatsby Essay

â€Å"The Great Gatsby† by F. Scott Fitzgerald is a widely considered masterpiece of American literature. Set in Long island, 1922, The Great Gatsby portrays a time in which massive war-born wealth and cheap liquor give birth to the great American party period, where booze and bobbed hair reign supreme in newly rich New York. This sets the scene for the tragic love story between † The golden girl†, Daisy Buchanan and war hero, James Gatz (Gatsby). The Great Gatsby is an interesting novel due to the ideas it presents that our society can still relate to today. Media manipulation, money before love and fame because of nothing more than wealth, are all ideas presented in the novel and they are all ideas that our society is notorious for today. Daisy and Gatsby were pre-war lovers that become separated by the war and the overbearing difference in social class, Gatsby was poor and believed he was unworthy of Daisy, determined to make something of himself Gatsby leaves. Daisy is madly in love with Gatsby, but marries Tom Buchanan, the richest man in east egg, straight after she gets a letter from Gatsby, asking her to wait until he becomes a rich man so they can be wed. Scott Fitzgerald uses this situation to portray a major ideology in the novel and of the time; that enough money can buy love. This is still relevant today as we constantly see Hollywood’s rich and famous will marry not out of love, but out of the desire for publicity and money. Gatsby, now a rich man who hosts extravagant parties every weekend but barely reveals his identity, is likely the most talked about person in New York, yet almost no one knows anything real about him. Throughout the novel our bank of information surrounding Gatsby grows, as we know nothing of him at the beginning, wild rumors spread around by the city folk New York are the only prior knowledge we have of Gatsby. â€Å"Well, they say he’s a nephew or a cousin of the Keiser Wilhelm’s, that’s where all the money comes from† This quote from minor character Catherine, shows how little most people know about Gatsby, and how willing and excited they are to spread false rumor. Fitzgerald deliberately presents Gatsby as a man of mystery and intrigue to show us how known, yet unknown he is. This is effective in creating uncertainty in the reader about Gatsby’s character, as we start to feel as if no information received about Gatsby, even from Gatsby’s own mouth, can  be trusted. It’s the same case today with the media’s tendency to manipulate and exaggerate, combined with possibly edited and misleading sources of information such as photographs and video, separating the real from the fake becomes almost impossible. The Great Gatsby is unique in the sense that it was not written as Gatsby’s own experience, but the experience of character who’s role in the plot is more to observe than to intervene. Nick Carraway is Daisy’s cousin and was a solider of the Great war who, after the conflict, joins the bond business and later moves to West Egg becoming Gatsby’s Neighbor. Nick becomes the bridge between Gatsby and Daisy, having connections to them both, yet not interfering with their lives in the sense a character like Tom does. We read the entire novel out of his experience and this allows us to view a completely separate perspective to that of the true main characters, and unlike a third person writing style, we are also given the opinions, biases and thoughts of the man who is â€Å"Within, and without.† The purpose of using this writing style is to show us insight in to the lives of all main characters, while still delivering a story in a first person perspective. This technique is effective in making the reader feel connected to the text and in reading of Nick’s experiences putting you in the situation whist still showing Gatsby’s and Daisy’s life as opposed to a restrictive first person perspective following only one. The Great Gatsby was a definitive novel at the time of its publication, and is just as relevant today. Gatsby was in the end, a celebrity only due to his large wealth and even larger parties, but when misunderstanding holds him to blame for a horrific car accident, people lose interest in the man they once found fascinating. Gatsby is very relatable to a modern day celebrity: he was famous because of wealth, had his relationship ended because of money, was subject to public rumor, scandal, and in the end forgotten, and replaced by the next rich man to host a big party. When Gatsby dies at the end of the novel, the only one to attend his funeral is our narrator, Nick Carraway. Fitzgerald does this to show that, Gatsby; a man with hundreds of acquaintances and thousands of followers, had in fact only one true friend, only one person who knew anything at all about him and  still cared after his death. Celebrities, the Gatsbys of today, may think they have hundreds of friends, even millions amongst fans, but hardly any truly know them, and those who do, like Daisy, usually care more about wealth and status than friendship.

Moral values

It would be gross injustice to categorize all children and youths as lacking in manners and morals, but the general trend would certainly suggest there has been a major decline among many of them. Family values have changed dramatically in the past few decades, producing a crop of undisciplined teenagers and children who lack morals and manners as a result of poor training. Good manners were once the norm with young people very much aware the older generation.Saying â€Å"please† and â€Å"thank ou†, giving up a seat on the bus and holding open doors were all considered normal mannerly behavior. Times have changed and we now live in a predominantly me-first society which is reflected in many young people. If good manners are taught at an early age, they will generally continue to be part of the personality of the young child all the way into adulthood. The lack of good manners observed in society in general is no doubt a reflection of the situation found within the home .Without parental xample and training the area of manners, it is likely the children will sadly lack in displaying them. The same can be said of the lack of morals we find in many of today's youth. A large proportion of children have grown up with little or no respect for authority, for property, for family or even themselves. Living a life of immorality is considered normal behavior today and has produced a bumper crop of young people with venereal disease, unwanted pregnancies and a feeling of emptiness in their ives.Lacking in moral stability, we find young people involved in crime, violence and drug abuse. The so-called freedom they have has actually brought them into slavery to an amoral lifestyle. There is a contrast though in many children and teenagers who are moral and do have good manners, proving that it is still possible to develop these delightful characteristics. It is a real pleasure to come across young people who are mannerly and who have the courage to lead a moral life, not†¦ Moral values It would be gross injustice to categorize all children and youths as lacking in manners and morals, but the general trend would certainly suggest there has been a major decline among many of them. Family values have changed dramatically in the past few decades, producing a crop of undisciplined teenagers and children who lack morals and manners as a result of poor training. Good manners were once the norm with young people very much aware the older generation.Saying â€Å"please† and â€Å"thank ou†, giving up a seat on the bus and holding open doors were all considered normal mannerly behavior. Times have changed and we now live in a predominantly me-first society which is reflected in many young people. If good manners are taught at an early age, they will generally continue to be part of the personality of the young child all the way into adulthood. The lack of good manners observed in society in general is no doubt a reflection of the situation found within the home .Without parental xample and training the area of manners, it is likely the children will sadly lack in displaying them. The same can be said of the lack of morals we find in many of today's youth. A large proportion of children have grown up with little or no respect for authority, for property, for family or even themselves. Living a life of immorality is considered normal behavior today and has produced a bumper crop of young people with venereal disease, unwanted pregnancies and a feeling of emptiness in their ives.Lacking in moral stability, we find young people involved in crime, violence and drug abuse. The so-called freedom they have has actually brought them into slavery to an amoral lifestyle. There is a contrast though in many children and teenagers who are moral and do have good manners, proving that it is still possible to develop these delightful characteristics. It is a real pleasure to come across young people who are mannerly and who have the courage to lead a moral life, not†¦

The First Form Of Education - 1411 Words

What was the first form of education in China? I have traced the first form of education in China back to the Shang Dynasty (16-1405 BCE). Education was necessary to achieve desired positions in the civil service (the administrative system of the government who ran the daily affairs in China) which were the key to wealth. By establishing an educational system for the young of the elite, the positions in the civil service became a cycle of the designated offspring being the most educated and the educated being the most elite people in China. Most schools were divided into political entities to gain social influence. The main focuses in the education of young Chinaman were the teachings of Confucian. The curriculum was based on the philosophy of Confucianism. Confucianism is a form of Humanism (a devotion of the humanities) with the main focus on educating people in the beliefs, values and practices that govern life within the family and between family and state. The teachings of Confu cianism were taught from four books and the five classics. The four books are Chinese classic texts that illustrated the core value and belief systems of Confucianism. The five classics were key text of Confucianism; these were sacred books of traditional Chinese beliefs. Book one of the four books was the Analects of Confucius (the saying of ideas recognized only by the Chinese), Book two was Mencius, Mencius was a fourth-century BCE (before the common/current/Christian era) Chinese philosopherShow MoreRelatedPlato Education Reform Essay1574 Words   |  7 Pagesthat â€Å"education is the craft concerned with..turning around and with how the soul can most easily and effectively be made to do it† (Plato 190). In this paper, I will propose Plato’s reform for the American education system through analyzing his account of education, the nature and different kinds of education using the allegory of the cave, its correlation to kallipolis, the nature of the soul, and his metaphysical theory of forms. I shall argue that Plato would propose the American education systemRead MoreThe First Secondary School For Four Years After The End Of World War II894 Words   |  4 PagesNations mandate, Britain occupied Tanganyika and Zanzibar, at the same time adding subsidies to the education system previously under German control. By the contrast, the people in Tanganyika did not appreciate the colonial education, they instead, viewed it as an interruption to their agriculture routine as it intended to profit the colonial regime instead of people (Ingham, 2013). In the meantime, education fashioned aristocracies and servers, where indigenous people saved as servants to the colonialRead MorePedagogy Of The Oppressed By Paulo Freire1215 Words   |  5 PagesHow do we sum up what education is? Is it just the practice of memorization, or is it something we obtain through experience? Paulo Freire does a good job analyzing education in chapter 2 of â€Å"Pedagogy of the Oppressed†. He reveals that there are two main types of education (banking education and problem-posing education) and shows how they contradict each other. By first giving a description of how both styles work, by showing how each one mirrors society, and then by showing the contradictionsRead MoreThe Colonial Rule Of Under The United Nations ( Un ) Mandate880 Words   |  4 Pagesmandate, Britain occupied Tanganyika and Zanzibar, at the same time adding subsidies to the education system previously under German control. In contrast, the people in Tanganyika did not appreciate the colonial education; they instead, viewed it as an interruption of their agricultural routines, as it favored the colonial regime’s benefit, instead of the indigenous people (Ingham, 2013). In the meantime, education fashioned aristocracies and servers, where indigenous became servants to the colonial rulersRead MoreEssay about Business Education726 Words   |  3 Pages Argumentative Draft Formal Education Is the Key to Success nbsp;nbsp;nbsp;nbsp;nbsp;The advancement of technology in the last decade has increased the demand for Americans to seek higher and formal education. No longer do we live in the age of manual labor, family owned amp; operated conveniences, but rather a computerized age. Thirty-years ago job seekers could find stable and secure work that would ensure stability and a prosperous future. Those white collar jobs could be obtainedRead More Dance In Public School Curricular Essay1490 Words   |  6 Pages DANCE IN PUBLIC SCHOOL CURRICULA nbsp;nbsp;nbsp;nbsp;nbsp;Dancing is a form of art that allows many children to express themselves through body motion while developing many skills. Children throughout the world have been dancing since the day they began walking. When a child to take their first steps and puts together the simplest combination of movements, that would be considered as dancing. Music also plays a major role in the development of children understanding dance, because it is canRead MoreEvolution Of Education : How Much Has Education1545 Words   |  7 PagesEvolution of Education How much has education developed in the past 3,000 years? From the earliest civilizations, to Greece and Rome, to present day education has been around, and evolving. Education started off very basic, learning everyday tasks, all the way to military strategy. Then it blossomed into writing, rhetoric, science, debate, and as if it wasn’t complex enough it developed from there. However, what time period had the most rigorous education, answers to the question may vary, but logicRead MoreThe Education Of Distance Education929 Words   |  4 Pageslike online learning or distance education, thoughts of digitized content, and images of different types of technological media frequently come to mind. However, traditionally it has been revealed that distance education is actually not a new phenomenon at all. Historically speaking one could actually uncover that distance education was practiced in the United States in the form of correspondence schools as early as the eighteenth century. In fact, one of the first educational programs to provideRead MoreAmerican Higher Education Of The Deaf And Dumb At Columbia University1413 Words   |  6 Pagesestablishment of the division for the deaf and dumb at Columbia University in 1864. American Higher education has been influenced and responsive to changes in federal civil rights protections for students with disabilities while facing both internal and external pressures on how to deal with persons with disabilities. The establishment of students with disabilities in an American higher education context found its start with the admission of students with sensory disabilities, primarily deaf andRead MoreAnalytical Essay Michelle Obama1034 Words   |  5 Pagesï » ¿Delprà ¸ve 2, opgave B Analytical essay of †Remarks by the First Lady at Education Event with DC High School Sophomores† The speech was held by the First Lady, Michelle Obama, at the DC High School as an educational event for the sophomores. The overriding subject of the speech is education which is an area Michelle Obama and her husband, Barack Obama, has spent a lot of time and resources on. After the introduction of the speech she speaks of a goal that her husband has set for America. She tells