Linear Programming In Optimization And Mathematical Programming

Optimization is part of our daily lives. We have scarce resources and limited time and we strive to make the most of them. From using time productively to solving distribution problems for an industry, we use optimization. An optimization problem can also be seen when sharing a chocolate between siblings. Linear programming is one of many optimization techniques. It is the simplest technique as it enables you solve complex optimization problems by making few simplified assumptions. We will focus on the assignment problem, a special case of linear programming. Different situations give rise to the assignment problem, where we must discover an optimal way to allocate n resources to m facilities. In this research paper we will use the Hungarian method in r-software using packages lpSolve and lpSolveAPI to allocate 4 service engineers Akinyi, Ben, Carlos and David based at various locations to 4 customers M, N, O and P in a way that the total distance covered is minimal.