Linear 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.
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.
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.
The 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.
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.