Optimization of bakery production by using branch and bound approach

Abstract

Mommy Ai Kitchen is one the businesses specializing in the bakery business, producing cupcakes, birthday cakes, brownies, and donuts. However, it does not optimally determine each bakery’s production quantity, so it offers fewer profits and becomes a problem. This research aims to find the optimal production quantity so that this business maximizes profits. The method used was integer programming using the branch and bound approach, which counts the decision variable value using the simplex method. This research was based on the number of raw materials on hand wheat flour, sugar, eggs, modal, and the profits of each bakery. Based on the analysis of the branch and bound approach, it was known that the maximum profit value was IDR 253,200, with eight alternative options for the bakeries that were produced. One of them was Mommy Ai Kitchen, which could produce three cupcakes, five birthday cakes, one brownie, and nine donuts to get that maximum profit. Meanwhile, Mommy Ai Kitchen’s estimation could produce one cupcake, one brownie, and six donuts using available materials with a profit of IDR 78,800. As a result, the profit difference before and after integer programming was IDR 174,400.