Linear programming projects portray real-life challenges and problem-solving through mathematical techniques. Methods of linear programming apply to a wide range of industrial contexts and problem scenarios. Modern-day businesses utilize LP models to plan the manufacturing process, schedule personnel, maximize office space, ensure timely delivery of goods, optimize shelf space, etc.
Linear programming is inherent in most statistics and machine learning models. Naturally, this special case of programming has emerged as a favorite among the teaching and learning communities of data science. But what is the reason behind taking a practical approach to understanding this topic?
The Need for Linear Programming Projects
A purely theoretical course can prove counterproductive in creating engaged learners. While students must know about the technicalities, it is equally essential to explore how the textbook knowledge applies in the real world. Recent reports have pointed out how overemphasis on straitjacket teaching methods is making pupils lose interest in Mathematics and Science.
Therefore, rather than learning the theories word for word, students must invest time working on real-life programming projects. Practically attempting multiple linear programming projects, they can also build their very own linear programming class 12 project pdf, which can definitely add to their portfolio in the future.
Here, we should note that these subjects focus on building logical thinking and reasoning capabilities, and hence, they contribute to the overall curriculum. So, how can we incorporate innovative tools in the classroom to improve the situation?
Activity-based learning offers a reliable solution for enhancing student engagement. When students take up group exercises or independent projects to solve actual issues, they can see academic concepts come to life. This assists them with knowledge retention and encourages them to discover new courses of action.
When educators use examples, they also introduce novices to the basics of management and decision-making. A standard realistic scenario of linear programming would include mentions of things like money, time, people, and space. The aim would be to employ the resources so that the organization can achieve minimum costs and maximum efficiency and profit. Familiarity with these fundamentals is vital in almost every career, be it engineering, the social sciences, or artistic pursuits.
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What is Linear Programming?
Linear programming is a simplification problem that seeks to replace a complicated mathematical expression. A typical case is based on three main factors.
Firstly, the simplification relationships should follow a straight line. Hence, the term linear. Secondly, all the values need to be subject to constraints, which may be in numerical or in terms or properties. And lastly, the solution has to optimize (i.e., maximize or minimize, depending on the problem) the quantity of a given variable.
Now that we have broken down LPP to its basic components, let us look at the terminology we use to formulate a problem.
- Decision variables: These variables determine the output and express the ultimate solution. For instance, the number of units of different cars manufactured by an automobile company (represented as x units of Car A and y units of Car B).
- Objective function: It lays down what you want to achieve in a specific problem. For example, increasing profit, reducing lead time, etc. You would generally encounter the use of Z for the total profit function.
- Constraints: These are limitations or restrictions posed on the decision variables, such as the production capacity of machines, availability of inputs, etc.
- Non-negativity: As a rule, LPP decision variables take non-negative values, meaning that they are always greater than or equal to 0.
LPP techniques are relevant for data scientists and programmers as well. You can get a significant headstart as a beginner if you know about different operations research procedures like the simplex method, graphical method, R, and OpenSolver. Overall, your task would involve reducing complexity and developing solutions capable of working under most conditions. Here are some topics to stimulate your creativity.
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How to Start Learning Linear Programming?
Once you have understood what linear programming is through linear programming class 12 project pdf and other practice methods, you will be able to tell the difference that it is not oddly similar to any programming language like Python or Java, rather it is a technique of mathematics to solve a kind of problem. The method is to find the derivatives or transform a matrix to solve the problem.
It calls a program and not a programming language because it is just an algorithm that helps solve problems, be it optimization, time management or space allocation. There are a hand full of day-to-day circumstances where linear programming can be implemented to make the results more efficient.
In order to learn linear programming from scratch, one must have a sound understanding of three major components of the algorithm: variables, constraints and goals.
Once one is done knowing what they are, one can move on to learning one of the basic linear programming methods, the simplex method. It is a mainstream method of minimizing a linear function that has several variables and constraints to a less complex one.
After getting a grasp on the simplex method, one can move on to the dual simplex algorithm. The major difference between the simplex and dual simplex method is that in the simplex method, one has to start with a non-optimal yet feasible solution, while in the dual simplex method, one starts working with a solo optimal infeasible solution.
Once done with both, it is time to practice. Solvers in Python and R or any available programming language can be beneficial for practising while working with linear programming project pdf is another way to strengtne your skills.
Another best way of practising will be going through the NCERT’s Class 12 Linear Programming chapter. The chapter holds an in-depth discussion on linear programming, its types, and various problems and their solutions.
Linear Programming Project Ideas
Below are some great beginner-friendly linear programming project ideas that one can add to their linear programming project pdf.
1. Profit optimization for business plan
Every business needs financial resources to get things started and sustain over time. Moreover, investors and credit providers usually ask for detailed analyses of profitability. And LPP can be immensely helpful in clearly explaining the viability of a business. This is a great optimization project example.
Let us suppose that you want to make a professional B-plan. First and foremost, you will have to define your problem using different variables, constraints, and the objective function. Then, you will solve the LPP using a suitable method, say a graph. Finally, you will evaluate your results and present your solution to the interested parties.
If you are a tutor, you can offer additional guidance and support by communicating the following details:
- Constraints (production capacity, the proportion of input requirement, cost of products, etc.)
- Calculation worksheets
- Coding examples
Class projects on business plans enable immersive experiences as students get the opportunity to apply their imagination and come up with original business names and logos.
2. Project on supply chain management
This problem relates to warehousing and the transfer of manufactured products. Here, you would need to minimize the cost of transporting goods with respect to the resources (motor vehicles and workforce) available in the storage facility and at every depot.
You can take up a project to showcase the feasibility of linear programming in improving supply chain modeling. Consider an industrial case that determines the best transportation schedule within the given limits and establishes an integrated supply chain.
You can employ sensitivity analysis to demonstrate how small changes in the model data can change the optimal solution. Furthermore, your project can add to the existing body of research while highlighting the major issues in supply chain modeling.
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3. On-time delivery example
For delivery services companies (FedEx, Blue Dart, and such), identifying the shortest route to ship packages to their respective destinations forms a core task. This sort of distance optimization saves fuel and time and helps these logistics firms in improving customer experience.
Linear programming can help choose the specific path if a delivery person has to take six packages in a day from the warehouse (located at point X) to six different destinations (cities, namely L, M, N, O, P, and Q). You will need an objective function and linear inequalities subject to certain constraints.
The process of selecting this track can be termed as Operations Research. To solve the LP, you can use the simplex algorithm in a LINGO or LINDO package, depending on your convenience. And in this way, you will have a delivery model. Further, you can get creative and set the algorithm on an Excel worksheet.
4. Applications on diet-based or nutritional problems
Several linear programming project ideas incorporate optimization problems into diet plans. Such applications can be related to any of the following purposes:
- Food aid
- National food programs
- Individual-specific dietary guidelines
As for the constraints, your study can include limits based on nutrition, cost, ecological aspects, or acceptability. You could design an integrated framework covering the domains of nutritional quality, economic feasibility, and environmental sustainability. A linear programming model is an ideal tool for this project as it allows you to satisfy multiple restrictions at once.
If you are just starting with LP modeling, you can try your hand at a chart with only two constraints (per gram nutrient content and unit costs). Your solution should minimize the cost of the diet and list the optimum quantity of different food items you can have in a day. The plan can be such that you eat at least 300 calories with 75 grams of protein, 65 grams of fat, and 300 grams of carbohydrates.
Read more: Linear Algebra for Machine Learning: Critical Concepts, Why Learn Before ML
5. Linear programming projects on automobile production
Take the example of a company that has a product mix of four types of cars – for example, luxury, sedan, minivan, and compact vehicle. The manufacturing facilities have a limit on the total annual production capacity. Additionally, the company has to comply with fuel consumption standards under various energy policies and national laws.
The details about the profit margins, market share, and fuel efficiency are available for all the models. Now, imagine a scenario where the top management wants to maximize the profits under these restrictions. It would be tricky to depict a strategy without simplifying the problem.
You can attempt a similar linear programming project based on the secondary data of any automaker. With this study, you can go a step further to analyze the implications of government policies on profitability. It is a unique way of looking at production planning problems that generally revolve around ERP data.
6. Allocation of space in a University
A study conducted by researchers at Landmark University, Nigeria, applied the optimization principle to allocate classroom space. Based on the data obtained from lecture halls and the committees of examination timetable management, the project sought to maximize the usage of the available classroom space. The result was a framework that reduced overcrowding and utilized the existing seating capacity in the best possible way.
7. Linear programming in a restaurant setup
In a restaurant-based project, you can work with the following decision variables:
- Number of meals per day (say 250 meals, including 100 vegetarian and 150 non-vegetarian meals)
- Different menu items (for example, cream soup, veg pasta, chicken curry, etc.)
If the management wants to maximize the profit given the constraints on the menu like monetary budget and number of meals, we would require a simplification model. The number of food ingredients and the increase /decrease in meals are linearly related. Therefore, basic algebra applies to meal production in the restaurant kitchen, one of the most critical aspects of running a restaurant business. Cost and time would be some other limitations in such a problem.
You can use the above example to simulate a tangible eatery and create a plan for earning optimal profit. Alternatively, you can design a tool using the LP and graph approach to minimize the total kitchen preparation time for orders in a realistic setting.
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8. Marketing applications
Marketing managers have a fixed budget to execute campaigns. Maximum reach, frequency, and exposure quality are a few factors that tell us whether an initiative turned out successful. The availability of media real estate, corporate policy, and contractual requirements can pose restrictions. With these demands, linear programming projects can help them in selecting the right advertising media mix. Nowadays, the options go beyond traditional mass media like newspapers and television. And with the advancements in the digital marketing ecosystem, the need for optimization measures has increased manifold.
There is a similar example of a choice-mix tool from the financial industry. You can duplicate an investment portfolio creation tool using stock market data from secondary sources. This project would aim to maximize the return, given the budgetary limit and stock/bond prices.
Also Read: Machine Learning Project Ideas
9. Construction management application
You can develop a decision-making tool that optimizes the selection of the best competitive tender for construction works from a real case study. Project managers in the civil engineering branch can use the linear programming model to control the project cost and time of completion. LP concepts are widely used by construction engineers and managers to back several management objectives and to generate results with minimal computational effort and cost.
Read more: Business Analytics: Tools, Applications & Benefits
10. Energy industry applications
These applications use linear programming for power system design, spanning conventional electrical systems and renewables like photovoltaics. The effort is to keep costs within a reasonable limit to sustain profits and optimize load matching. In the modern grid and energy industry, LP models help provide a valuable way of matching the load in the shortest distance between electricity generation and its over-time demand.
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These conclude some of the best optimization project examples to help you comprehend and practice linear programming effectively.
What Next After Learning Linear Programming?
Knowing linear programming alone might not be that helpful. Therefore, one must continue their journey of learning once they have mastered this subject.
There is no argument that AI and Machine learning are the future and fortunately, those who are good at mathematics, especially topics like linear programming, calculus, probability, vectors etc, automatically get an added advantage.
One who has just finished learning linear programming can definitely learn programming languages later if not simultaneously. It will help them cover all the grounds required for starting their machine learning journey.
Once done with the basics of programming languages like Python, Java and C languages, one can start familiarizing themselves with the famous machine learning tools such as Numpy, Pandas, Matplotlib etc. These are some of Python’s widely used visualization libraries which help an individual to analyze and manipulate data.
The best platform to practice machine learning would be Kaggle, which is an online community platform for data scientists and machine learning connoisseurs. The platform is filled with practice tasks that will eliminate the burden of coming up with one’s own project idea, therefore, leaving ample room to focus on enhancing the skillsets.
With this, we have covered 10 examples of linear programming projects to help you practice and rewire your technical skills. Use these topics as guide maps for your projects and begin the process of hands-on learning!
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Why is linear programming important?
Linear programming is a mathematical method to determine the optimal solution to a complex problem. As a problem can be thought of as a maximization of a linear combination of variables subject to a set of linear inequalities, it can be solved by linear programming. In linear programming, a combination of variables is used to maximize or minimize a linear objective function. Most problems seen in the real world have multiple objectives and constraints, so it is typical to use this method to find the optimum decision. Linear programming is used in economics, engineering and other fields. More precisely the area of application of linear programming includes transportation, location of facilities, finance, production and inventory control.
What are the limitations of linear programming?
Linear programming is a powerful tool; however, it can't do everything. It is only as good as the data that is input. If the data is bad, the results will be bad. The best way to get good results of linear programming is to make sure that your data is set up properly and is accurate. Also, linear programming can only handle 'solved' problems. You can't use linear programming to determine the best course of action for a problem that hasn't been solved yet. For example, linear programming can't help you find the best way to get from your house to your job. It can help you determine the best way to get to your job after you have figured out how to get to your house.
What is the assumption of linear programming?
Linear programming is a mathematical programming technique for the optimization of an objective function, subject to a linear inequality or linear equality constraint. In practice, linear programming is considered the simplest possible method for optimization. It is a mathematical procedure for optimizing a linear function in a finite interval. Many classical problems in applied mathematics can be solved by linear programming.