Linear Programming In Optimization And Mathematical Programming

In real world situations,we use optimization techniques to obtain optimal solu
tions. Resources are scarce and we seek to utilize them, maximizing the proï¬ts
obtained while minimizing the time and cost associated with them. Linear pro
gramming is one of many optimization techniques. It is the simplest technique
as it enables solving complex optimization problems by making few simpliï¬ed as
sumptions. In this research paper,we will focus on a transportation problem,and
an assignment problem which are linear programming problems. Diï¬€erent situ
ations give rise to the assignment problem, where we must discover an optimal
way to allocate n resources to m facilities. We will use the Hungarian method
in solving the assignment problem. Computations for both linear programming
problems will be done in a statistical software known as R, using the packages
lpSolve and lpSolveAPI. In the case of the transportation problem, we seek to
minimize the costs associated in transporting petroleum from reï¬neries A,B and
C to four petrol stations 1,2,3 and 4. For the assignment problem, we allocate
4 persons;A,B,C and D to diï¬€erent tasks 1,2,3 and 4 such that the total cost is
minimized.