Linear Programming: Advantages, Disadvantages and Strategies

wholeness-dimensional computer programing Advantages, Disadvantages and StrategiesI elongate programIn a decision-making embroilment, ride formula is important beca affair it represents the essence of business decision worry. The term formulation is apply to mean value the process of converting the verbal description and numerical data into numeral expressions which represents the relevant relationship among decision factors, impersonals and restrictions on the use of resourcefulnesss. atomic bod 53-dimensional Programming (LP) is a particular type of proficiency use for stinting eachocation of sc sparke or limited resources, such as labour, material, machine, time, store space, capital, animation, 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 argon not in unlimited in availability during the intend period. The cri terion of optimality oecumenicly is either consummation, return on investment funds, lucre, monetary value, 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 troubles. But now, it is being used extensively in all controlal areas of management, hospitals, airlines, agriculture, military appendages, oil refining, education, energy planning, pollution control, transportation planning and scheduling, research and development, etc. Even though these applications are diverse, all I.P examples consist of certain common properties and assumptions. Before applying bi one-dimensional programming to a real-life decision line of work, the decision-maker moldiness be aware of all these properties and assumptions.The word analogue refers to linear relationship among variables in a model. Thus, a given swop in one variable will unendingly cause a resulting proportional change in another variable. For example, stunt woman the investment on a certain project will only double the rate of the return. The word programming refers to modelling and solving a puzzle mathematically that involves the stinting storage allocation of limited resources by choosing a particular course of action or strategy among desegregateed choice strategies to achieve the desired bearing.STRUCTURE OF elongate PROGRAMMINGGeneral anatomical structure of LP ModelThe general structure of LP model consists of three components.Decision variables (activities) We get to evaluate various options (courses of action) for arriving at the optimal value of intention function. Obviously, if in that respect 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 be certain activities usually denoted by x1, x2xn. The value of these activities represent s the extent to which each of these is make outed. For example, in a product-mix manufacturing, the management may use LP to decide how legion(predicate) 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 damage of consumption of limited resources, require simultaneous stems. All decision variables are continuous, controllable and non-negative. That is, x10, x20, .xn0.The objective function The objective function of each L.P problem is a mathematical representation of the objective in terms of a mensural meter such as profit, cost, revenue, distance, etc. In its general form, it is represented asOptimise (Maximise or Minimise) Z = c1x1 + c2X2. cnxnWhere 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(prenominal) 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 uniformly certain limitations (or constraints) on the use of resources, e.g. labour, machine, primitive material, space, money, etc. that limit the stop to which objective bottom of the inning 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 piece of ass be expressed as linear mathematical functions.APPLICATION AREAS OF LINEAR PROGRAMMING running(a) programming is the most widely used technique of d ecision-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 ApplicationsThese applications fall into categories of farm economics and farm management. The former deals with awkward 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 output signal. Efficient deed patterns tooshie be condition by a linear programming model under regional get resources and national demand constraints. elongated programming can be utilise in agricultural planning, e.g. allocation of limited resources such as acreage, labour, body of water supply and working capital, etc. in a way so as to maximise net revenue.Military ApplicationsMilitary applications include the problem of selecting an air weapon system against enemy so as to go them pi nned down and at the same time minimising the numerate of aviation gas pedal used. A variation of the transportation problem that maximises the sum of money tonnage of bombs dropped on a set of targets and the problem of community defence against disaster, the solution of which yields the reduce of defence units that should be used in a given oncoming in order to provide the required level of protection at the lowest doable cost.Production troubleProduct mix A company can produce several different products, each of which requires the use of limited fruit 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 get along 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 init ial number of units in inventory, production capacity, constraints on production, workforce and all relevant cost factors. The objective is to downplay chalk up operation costs.Assembly-line balancing This problem is samely to scrape when an item can be made by assembling different components. The process of assembling requires whatsoever 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 shape 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 utmost constraints on certain product constituents.Trim detriment 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.Finan cial ManagementPortfolio woof This deals with the selection of specific investment activity among several other activities. The objective is to uncovering the allocation which maximises the total expected return or minimises risk under certain limitations. winnings planning This deal with the maximisation of the profit margin from investment in plant facilities and equipment, cash in hand and inventory.Marketing ManagementMedia selection one-dimensional programming technique stand bys 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 gross salesman problem The problem of salesman is to find the shortest route from a given city, visiting each of the specified cities and hence returning to the original point of departure, provided no city shall be visited double during the tour. Such type of problems can be solved with the help of the special assignment technique.Physical distribution Linear programming determines the most economic and efficient panache of locating manufacturing plants and distribution centres for physical distribution.Personnel ManagementStaffing 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 PROGRAMMINGFollowing are certain advantages of lin ear programmingLinear 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 be surveys 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 key. 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 butt on demand while other remains idle for some of the time.Linear programming also helps in re-evaluation of a basic plan for ever-changing conditions. If conditions change when the plan is partly carried out, they can be persistent so as to adjust the remainder of the plan for best results.LIMITATIONS OF LINEAR PROGRAMMINGThere should be an objective which should be clearly recognizable 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 finishing should also be identifiable and measurable quantitatively. They must b e 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 solutio n 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 organisationOnly one single objective is dealt with while in real life situations, problems come with multi-objectives.II SITUATION ANALYSISPhang furniture system Inc. (Fursys) manufactures two models of stools, faecal matter which is basic model and a better model called sturdy.SUPPLIESMaximum of 350 pounds bendable 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 VariablesThe production units are in terms of number on daily basis. Therefore the decision variables areLet, X1 = No. of mickles production dailyX2 = No. of insolents production dailyObjective FunctionThe 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 shaping + one set of leg= ($1. 5*1) + $0.75(1)= $2.25 realize made by selling = $12.75 $2.25 = $10.5Cost 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 = $15ConstraintsPlasticPotty requires one pound of plastic and Hardy requires 1.5 pound plastic. So the total plastic used daily is(1)X1 + (1.5)X2This plastic supply cant exceed the limit of 350 pounds daily, so constraint is(1)X1 + (1.5)X2