Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant

Abstract

In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.