Presentation of Management Science

KEEN ORBIT

PRESENTED BY GROUP-

Name of group members

Md. Abdul Motaleb Roll- 1126

Md. Omar FaruqRoll- 1120

Md. Jahirul IslamRoll- 1128

Suhail Mahmud ShakilRoll- 1121

Shanjida AfrozRoll- 1119

Mehedi Hasan Roll-1114

What is Management Science?

Management science (MS), is an interdisciplinary branch of applied mathematics, engineering and sciences that uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and algorithms to improve an organization's ability to enact rational and meaningful management decisions. The discipline is typically concerned with maximizing profit, assembly line performance, crop yield, bandwidth, etc. or minimizing expenses, loss, risk, etc.

OverviewManagement science is concerned with a number of different areas of study including developing and applying models and concepts that may prove useful in helping to illuminate management issues and solve problems. Management science research can be done on three levels:

A fundamental level that lies in three mathematical disciplines: probability, optimization, and dynamic systems theory,

A modeling level that builds models, gathers data, and analyzes them mathematically, and

An application level, just as any other engineering discipline that has strong aspirations to make a practical impact in the real world.

ApplicationsApplications of management science are abundant in industry such as airlines, manufacturing companies, service organizations, military branches, and in government. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes:  scheduling airlines, both planes and crew, deciding the appropriate place to place new facilities such as a

warehouse or factory, managing the flow of water from reservoirs, identifying possible future development paths for parts of the

telecommunications industry, establishing the information needs and appropriate systems to

supply them within the health service, and identifying and understanding the strategies adopted by

companies for their information systems.

Linear programming Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labor, and then determining the "best" production levels for maximal profits under those conditions. In "real life", linear programming is part of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources. These "real life" systems can have dozens or hundreds of variables, or more. In algebra, though, you'll only work with the simple (and graph able) two-variable linear case. Applications of Linear Programming

Linear programming is used to solve problems in many aspects of business administration including:

 product mix planning

distribution networkstruck routing

staff schedulingfinancial portfolios

corporate restructuring

Linear programming in Business

Businesses use linear programming methods to determine the best ways to increase profits and decrease operational costs. Linear programming methods enable businesses to identify the solutions they want for their operational problems, define the issues that may alter the desired outcome and figure out an answer that delivers the results they seek. Although the phrase "linear programming" came into use well before the widespread use of computers, software packages are available that replicate the linear programming processes.

Linear programming in Business

Production PlanningLinear programming methods are often

helpful at solving problems related to production. A company that produces multiple types of products can use linear programming methods to calculate how much of each product to produce to maximize its profits. For instance, a custom furniture shop that makes chairs and tables can calculate how many of each item they must sell to maximize their profits by looking at the numbers of each item previously sold and their prices.

Linear programming in Business

Marketing Mix• A key aspect of marketing strategy is

the "marketing mix." The marketing mix determines how much of a company's marketing budget will go toward various advertising and marketing channels. A linear programming simulation can measure which blend of marketing avenues deliver the most qualified leads at the lowest cost. For example, the custom furniture store can use a linear programming method to examine how many leads come from TV commercials, newspaper display ads and online marketing efforts. The solution will also compare the relative prices of each medium to find the most economical mix.

Linear programming in Business

Product Distribution• Manufacturers and distributors can

use linear programming methods to solve distribution problems. These mathematical exercises can help manufacturers determine the most cost-effective way to ship products from the factory to the warehouse. Warehouse managers can also use similar models to calculate the most economical way to transport the products from the warehouse to the retail outlets. These models can also ensure that warehouses maintain an optimal amount of each product in stock as demand fluctuates.

Personnel Assignments

Human resources planners can use linear programming methods to determine when to hire more workers, which skill sets the company needs and how much they can offer in compensation. These methods can also be used to anticipate times of increased demand for available workers. For example, a department store can use linear programming methods to calculate how many new hires they will make for the busy holiday shopping season, as well as which departments will see higher traffic and require more staff.

Charactaristics

Linear programming is a branch of mathematics and statistics that allows researchers to determine solutions to problems of optimization. Linear programming problems are distinctive in that they are clearly defined in terms of an objective function, constraints and linearity. The characteristics of linear programming make it an extremely useful field that has found use in applied fields ranging from logistics to industrial planning.

Charactaristics

• OptimizationAll linear programming problems are problems of optimization. This means that the true purpose behind solving a linear programming problem is to either maximize or minimize some value. Thus, linear programming problems are often found in economics, business, advertising and many other fields that value efficiency and resource conservation. Examples of items that can be optimized are profit, resource acquisition, free time and utility.

Charactaristics

• LinearityAs the name hints, linear programming problems all have the trait of being linear. However, this trait of linearity can be misleading, as linearity only refers to variables being to the first power (and therefore excluding power functions, square roots and other non-linear functions). Linearity does not, however, mean that the functions of a linear programming problem are only of one variable. In short, linearity in linear programming problems allows the variables to relate to each other as coordinates on a line, excluding other shapes and curves.

Charactaristics

• Objective Function

All linear programming problems have a function called the "objective function." The objective function is written in terms of the variables that can be changed at will (e.g., time spent on a job, units produced and so on). The objective function is the one that the solver of a linear programming problem wishes to maximize or minimize. The result of a linear programming problem will be given in terms of the objective function. The objective function is written with the capital letter "Z" in most linear programming problems.

Charactaristics

• Constraints

All linear programming problems have constraints on the variables inside the objective function. These constraints take the form of inequalities (e.g., "b < 3" where b may represent the units of books written by an author per month). These inequalities define how the objective function can be maximized or minimized, as together they determine the "domain" in which an organization can make decisions about resources.

Limitation and advantageLinear programming is a mathematical technique that helps businesses solve some problems they face. It helps them deal with constrained optimization situations in which they have to make the best of their resources, such as labor, given certain constraints. For instance, one constraint for a business is the number of workers it can hire. Another could relate to the amount of raw material it has available.

Example Consider a bicycle manufacturer that manufactures mountain bikes and street bikes, each of which generates a different profit level. The manufacturer would like to know how many bikes of each category to produce so as to maximize profits, given that the business can sell its entire output. Two different teams produce the mountain bikes and the street bikes by hand, each with production constraints in terms of how many bikes it can produce per day. The bikes also have to go through a machine finishing process that has a limited processing capacity. The business could use the linear programming technique to solve this sort of problem.

Limitation Assumption of Linearity

The linear programming approach is based on an assumption that the world is linear. In the real world, this is not always the case. There are certain ways of mixing the inputs that a linear programming approach doesn't permit. For instance, the bicycle manufacturer might find that if it orders materials for the two types of bicycles from the same supplier, it could cut costs. This effect can't be incorporated into a linear programming model. Linear models also don't account for factors such as increased production efficiency as the level of production rises.

Fractional ValuesThe linear programming model assumes that inputs and outputs can be fractional. This is not always the case in the real world. For instance, if a business is trying to find out how many people it should have on staff during peak business hours, this can't be a fraction. Similarly, if a taxi business is trying to decide how many cars it should buy, this can't be a fraction, either. If even one variable involved has to be in integer form, linear programming is not a suitable technique.

Advantages

Even though linear programming has a number of disadvantages, it's a versatile technique that can be used to represent a number of real-world situations. Businesses use the technique to solve problems that involve multiple variables and constraints. The use of computers has made this technique easier to apply.

Conclusion

Linear programming is one of the widely used modeling techniques. Linear programming problems consist of an objective function (also know as cost function) which has to be minimized or maximized subject to a certain number of constraints. The objective function consists of a certain number of variables. The constraints are linear inequalities of the variables used in the objective function. This technique is closely related to linear algebra and uses inequalities in the problem statement rather than equalities.

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