Use of Linear programming in decision making

What is Linear Programming?

Linear programming is a way of achieving the best outcome, such as minimum cost or maximum profit, using a mathematical model represented by linear relationships.

Example of Linear Programming

A businessman remains undecided on the type of transportation to use. Given the volume of the goods he wants to transport, he has two options: air transport and sea freight. However, the businessman has constraints in terms of the amount he can spend on transporting the goods (C) and time of delivery of the goods (T). Let’s suppose the cost of transporting 1kg of the goods through air transport   requires C1 of cost and T1 days in time, while the cost of transporting through sea freight requires C2 in cost and T2 days in time. Let S1 be the selling price of 1kg of the goods if delivered by air, and S2 be the selling price of the goods if delivered by sea. If we denote the quantity of the goods delivered by air and by sea by x1 and x2, respectively, then profit can be maximized by choosing optimal values for x1 and x2.

Types of Linear Programming Problems

There are lots of problems that can be solved using linear programming. Below, are some of the common problems:

• Manufacturing problem: This is mostly encountered byproduction companies, this type of problem involves solving for making the maximum profit or minimum cost given various constraints like labor, output units, and machine runtime
• Diet problem: The main objective of this problem is to optimize for adequate nutrition considering the requirements of the body and the costs involved.
• Transportation problem: This type of problem includes finding the right transportation solutions given the constraints of cost and time.
• Resource allocation problem: This problem is concerned with managing the efficiency of a project. The main objective is to complete the maximum number of tasks, given the constraints of man-hours and the resources available.

Components of Linear Programming

1. Decision Variables

These are the unknown quantities in an optimization problem that need to be solved. For example, in the case of a businessman that wants to decide the mode of transportation for his goods, given various constraints, the quantity of goods he is delivering  becomes the decision variable.

2. Constraints

Constraints are the limitations one needs to consider while solving a given problem. For example, constraints can be regarding resources such as time, cost, and so on.

3. Objective Functions

Objective functions are the real-valued functions that need to be optimized for either minimum or maximum output given a set of constraints.

4. Non-Negativity Restriction

The decision variables should always take non-negative values, i.e., they should be greater than or equal to 0.

Advantages of using Linear Programming

The following are some of the key advantages of using linear programming:

• Attaining optimum use of scarce resources.
• It is a more objective way of arriving at decisions.
• It ensures due attention is given to bottlenecks before the problems occur.
• Easy adaptation to changes in circumstances. #EMBA28