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Linear Programming

Writer: RICHA RAMBHIARICHA RAMBHIA
Dec 30, 20223 min read

Linear programming is a mathematical technique which would determine the best way to use the available resources where managers use this process in order to make decisions about the various resources like money, time, materials, and machinery. (“Linear Programming”). The linear programming has widely been used in the field of economics, business, telecommunication, and manufacturing where the linear programming is defined as the problem of maximizing or minimizing a linear function which is subjected to linear constraints.


The components of the linear programming include decision variables, constraints, data, and objective functions where the characteristics are the linearity, finiteness, non-negativity, and decision variables.

Linear programming is highly used in business and industry in the production planning, transportation and routing and various other types of scheduling. For example, the airlines flights are scheduled using the linear programming taking both the scheduling aircraft and staff into consideration. The reason why linear programming is important and beneficial to such businesses is because they are helpful in solving the problems which are related to the production, like for example, in order to calculate how much of each product is produced in order to maximize profits, companies and businesses use the linear programming which produces multiple types of products. Whereas if we consider the production management field, linear programming is applied in order to determine the optimal allocation of such resources as materials and machines. LP is such fields and businesses is beneficial and important as it helps to determine the optimal product which is a mix of the firm to maximize its revenue and it is also used for product smoothing and assembly line balancing.


Considering the structure of the LP model, it consists of three components, decision variables, objective function, and the constraints. The objective function of the LP problem is a representation of the mathematical model of the objective in terms of the measurable quantity like the profit, cost, revenue, distance, etc. With respect to the constraints, there are limitations on the use of the resources that would limit the degree to which the objective can be achieved. Thus, the solution of the LP model must satisfy these constraints as this is the technique for choosing the best alternative from a set of feasible alternatives.


The impact that the linear programming has on the various areas and businesses is that it helps in attaining the optimal use of productive resources indicating how a decision-maker can employ his productive factors by selecting and distributing the resources. LP techniques and models improves the quality of decisions where the decision making approach for the user becomes objective and less subjective. The models and techniques provide solutions as they must be taken into account and thus necessary modifications is needed for the decision making process.


For example, to find out the number of men and machines that would be needed in order to perform a particular job where a non-integer programming is used to ensure integer value to the decision variables. Since, the linear programming model does not take the effect of time and uncertainty into consideration, thus the model should be defined in a way that whatever changes would occur that would be due to internal as well as external factors which can be incorporated into.


Slack variables in the linear programming problem are that it applies to less than or equal constraints and if a constraint is binding, then the corresponding slack variable value would be equal to zero. Thus, if we consider an optimization problem, a slack variable is a variable which is added to an inequality constraint to transform it into an equality. (“What are slack variables in linear programming?”).


If we consider other variables, then the slack variables cannot take on the negative values because the simplex algorithm requires them to be positive or zero. A decision variable on the other hand is a quantity which controls the decision maker like for example, in the optimization model for the labor scheduling, the number of nurses to employ during morning shift could be a decision variable.



References:

Linear Programming. (n.d.). BYJU’S, from https://byjus.com/maths/linear-programming/


What is the role of linear programming in the business management? (n.d.). Asking the Lot, from https://askingthelot.com/what-is-the-role-of-linear-programming-in-the-business-management/



What are slack variables in linear programming? (2020, March 26). Tree Hozz, from https://treehozz.com/what-are-slack-variables-in-linear-programming


 
 
 

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