Implementation of the Branch and Bound Method on Optimization of the Number of Roti Production at Doel Cake Bakery

Oct 13, 2025 by wbrum.org 86 views

Implementation of the Branch and Bound Method on Optimization of the Number of Roti Production at Doel Cake Bakery

Introduction

The Doel Cake bakery, located in the city of Binjai, faces challenges in optimizing the amount of their bread production. This shop produces four types of bread with variations of flavors, namely chocolate, coconut, blueberry, and black beans. To solve this problem, the research team applied the Branch and Bound method, a technique that was first introduced by A.H. Land and A.G. DOIG in 1960. This method is designed to find optimal solutions in linear programming, especially when the decision variable must be an integer.

The Branch and Bound Method: A Technique for Optimization

The Branch and Bound method works by limiting the optimum settlement that might produce fractions. This technique makes the upper and lower branches for each decision variable that is in a fraction, so that it allows the desired results to always be round. In the context of the Doel Cake bakery, the problem of optimizing the amount of production is modeled as a linear program, and a decision regarding the amount of production of each type of bread is represented by integers through the integer program.

Modeling the Problem as a Linear Program

After the model is determined, the first step taken is to calculate the value of the decision variable using the simplex method. This is a crucial step because the results of the simplex method will be used as a starting point for the branch and bound method. This process allows researchers to explore further on possible branches of solutions.

The Simplex Method: A Crucial Step in the Branch and Bound Process

The simplex method is a powerful algorithm for solving linear programming problems. It works by iteratively improving the solution until an optimal solution is reached. In the context of the Doel Cake bakery, the simplex method is used to calculate the value of the decision variable, which represents the amount of production of each type of bread.

The Results of the Application of the Branch and Bound Method

The results of the application of this method are very significant. After going through the right steps in the Branch and Bound process, the Doel Cake bakery can identify and obtain a sales profit difference of 8.27% or equivalent to Rp. 2,630,775.00 compared to the estimated previous profit. This figure shows the positive impact of the application of systematic mathematical methods in making operational decisions in small industries such as bakeries.

Additional Analysis and Explanation

The implementation of the Branch and Bound method not only gives more accurate results in terms of calculating the amount of production, but also provides insight into the importance of optimization in business. In the context of the bread industry, where profit margin can be very thin, every increase in production efficiency contributes directly to profitability. Therefore, this method can be a valuable tool for business owners to achieve optimal results.

The Importance of Optimization in Business

The calculation process involving the simplex method as a first step enables business people to understand the strengths and weaknesses of each production strategy. Through this method, they can more easily determine which type of bread should be produced more and which should be minimized, based on market analysis and consumer demand.

Conclusion

The application of the Branch and Bound method at the Doel Cake bakery not only solves the problem of optimization, but also increases the understanding of shop owners regarding better business strategies. This can be a model that can be adopted by other business actors in similar industries, especially those who want to increase the competitiveness and sustainability of their business.

Recommendations

By utilizing appropriate technology and analytical methods, small entrepreneurs are expected to find new ways to innovate and grow in increasingly competitive markets. Optimization in the amount of bread production is one of the important steps in achieving that goal.

Future Research Directions

Future research can focus on applying the Branch and Bound method to other industries, such as the food industry, to see if similar results can be achieved. Additionally, research can be conducted to explore the use of other optimization techniques, such as genetic algorithms or simulated annealing, to see if they can be used to solve similar problems.

Limitations of the Study

This study has several limitations. Firstly, the study only focuses on the Doel Cake bakery and does not generalize the results to other bakeries. Secondly, the study assumes that the demand for each type of bread is constant, which may not be the case in reality. Finally, the study does not consider the impact of external factors, such as changes in market trends or consumer preferences, on the production of bread.

Conclusion

In conclusion, the implementation of the Branch and Bound method at the Doel Cake bakery has shown significant results in terms of optimizing the amount of bread production. The method has provided a valuable tool for business owners to achieve optimal results and has increased the understanding of shop owners regarding better business strategies.
Q&A: Implementation of the Branch and Bound Method on Optimization of the Number of Roti Production at Doel Cake Bakery

Q: What is the Branch and Bound method and how does it work?

A: The Branch and Bound method is a technique used to solve linear programming problems, particularly when the decision variable must be an integer. It works by limiting the optimum settlement that might produce fractions, making the upper and lower branches for each decision variable that is in a fraction, so that it allows the desired results to always be round.

Q: What is the significance of the Branch and Bound method in the context of the Doel Cake bakery?

A: The Branch and Bound method is significant in the context of the Doel Cake bakery because it helps to optimize the amount of bread production, which is a crucial aspect of the business. By using this method, the bakery can identify and obtain a sales profit difference of 8.27% or equivalent to Rp. 2,630,775.00 compared to the estimated previous profit.

Q: How does the Branch and Bound method help business owners achieve optimal results?

A: The Branch and Bound method helps business owners achieve optimal results by providing a systematic approach to solving linear programming problems. It allows business owners to explore further on possible branches of solutions, which can lead to more accurate results and better decision-making.

Q: What are the benefits of using the Branch and Bound method in business?

A: The benefits of using the Branch and Bound method in business include:

More accurate results in terms of calculating the amount of production
Increased understanding of the importance of optimization in business
Ability to determine which type of bread should be produced more and which should be minimized, based on market analysis and consumer demand
Increased competitiveness and sustainability of the business

Q: Can the Branch and Bound method be applied to other industries?

A: Yes, the Branch and Bound method can be applied to other industries, such as the food industry. However, it is essential to consider the specific characteristics of each industry and adjust the method accordingly.

Q: What are the limitations of the study?

A: The limitations of the study include:

The study only focuses on the Doel Cake bakery and does not generalize the results to other bakeries
The study assumes that the demand for each type of bread is constant, which may not be the case in reality
The study does not consider the impact of external factors, such as changes in market trends or consumer preferences, on the production of bread

Q: What are the future research directions?

A: Future research directions include:

Applying the Branch and Bound method to other industries, such as the food industry
Exploring the use of other optimization techniques, such as genetic algorithms or simulated annealing, to solve similar problems
Considering the impact of external factors, such as changes in market trends or consumer preferences, on the production of bread

Q: What are the recommendations for business owners?

A: The recommendations for business owners include:

Utilizing appropriate technology and analytical methods to find new ways to innovate and grow in increasingly competitive markets
Applying the Branch and Bound method to optimize the amount of production and increase competitiveness and sustainability of the business
Considering the importance of optimization in business and using systematic approaches to solve linear programming problems.