# Profit Optimization of Soap Industry by using Benders’ Decomposition Method

## Authors

• Sanjida Aktar Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

## Keywords:

Benders’ Decomposition Method, Soap Industry, Linear Program, Profit Optimization

## Abstract

In this paper, a large-scale linear programming problem including several parameters such as labor cost, raw material cost, machine and other cost have been formulated. Then the formulated problem has been solved by using Benders’ Decomposition Method. The formulated large model is divided into master and small sub problem. In order to validate and calibrate the model, real data from a soap industry named Mega Sornali Soap and Cosmetics Industry have been collected. Soap industry is one of the most feasible business options owing to the straightforward manufacturing process involved starting a soap and detergent manufacturing business in Bangladesh. These models are solved by using AMPL. To find out the significant parameters of the model, the sensitivity analysis of different cost parameters such as labor cost, raw material cost and machine cost have been be considered. From the sensitivity analysis, the decision makers of the factory would able to find out the ranges of cost coefficients and all the resources. As a result, the company could able to see how any change can affect the profit or loss of the factory. From the numerical results, the most profitable product of the company is found to be Sornali Soap and Mega Extra Powder. On the contrary, Mega SornaliSobiMarka Soap and Mega Washing Powder are not more profitable. Further, raw material cost is the most significant sensitive cost. If the raw material cost can be decreased the profit could also beincreased. Finally, the result of the optimal solution has been represented in tabular and graphs.

GANITJ. Bangladesh Math. Soc.41.2 (2021) 5-17

Abstract
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2022-02-08

## How to Cite

Aktar, S. ., & Uddin, M. F. . (2022). Profit Optimization of Soap Industry by using Benders’ Decomposition Method. GANIT: Journal of Bangladesh Mathematical Society, 41(2), 5–17. https://doi.org/10.3329/ganit.v41i2.55026

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