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JA6. Learning Journal 6

Answer the following questions in your Learning Journal

1. Describe what you did. You need to describe what you did and how you did it

This was the 6th week of this course; it was all about linear programming. I started by reading the materials assigned in the learning guide, then I did the discussion assignment which was about using the simplex method to solve a linear programming problem.

2. Describe your reactions to what you did

I was excited to learn more about one more programming or algorithm pattern. The name linear programming was repeated many times in the past (in some podcasts or blogs), and this is my first time to learn about it. I found the simplex method to be an interesting algorithm to solve linear programming problems. I found it hard to understand the pivot operations and tableau, but I accepted it as explained by Dr. David Taipala in the video lectures (UoPeople, n.d.).

3. Describe any feedback you received or any specific interactions you had. Discuss how they were helpful

The discussion assignment asked to analyze the profits of a textile manufacturer who produces pants and jackets. I represented the problem in a table format that summarizes the objective function and constraints. I also explained the pivot operations and tableau in the simplex method to solve the problem. The feedback on my discussion assignment was particularly positive. I represented the problem in a clear and concise manner that was easy to understand.

4. Describe your feelings and attitudes

I feel that the discussion assignment seemed particularly practical as it presented a real life issue which connects the theory to the real world. However, I think that manually applying the simplex method is not the greatest idea; I think that student should implement the simples method using a programming language to understand it better.

5. Describe what you learned

We previously learned about various patterns of algorithms including greedy algorithms, dynamic programming, and randomized and divide-and-concur algorithms. This week we have added linear programming and reductions to our knowledge (UoPeople, n.d.).

Greedy algorithms build up a solution piece by piece, always choosing the next piece that offers the most immediate benefit. In randomized algorithms we make decisions that are as rational as possible and leave some factors up to the chance. Divide and conquer breaks large problems into subsequently smaller problems until those small problems can be easily solved and then combined together to get a solution for the larger problem.

Dynamic programming is an optimization technique that is applicable to problems that can be divided into overlapping subproblems. The results of the repeated subproblems are stored and reused rather than recomputed. The sub-problems are ordered from the easiest to solve to the hardest.

Linear programming involves choosing a course of action that will maximize or minimize a linear objective function, subject to a set of linear constraints. The Simplex Method is a popular algorithm for solving linear programming problems; it is an algorithm that implements LP solutions (Shaffer, 2011).

The simplex algorithm is an iterative method for solving linear programming problems. It starts with an initial feasible solution and iteratively moves to adjacent feasible solutions that improve the objective function value until an optimal solution is reached. The algorithm uses pivot operations to move between adjacent solutions and maintains a tableau to keep track of the current solution and the objective function value. The simplex algorithm is widely used in practice due to its efficiency and effectiveness in solving linear programming problems (UoPeople, n.d.).

6. What surprised me or caused me to wonder?

The definition of linear programming was a surprise to me; from the name it seemed to be like parallelizing algorithms so they run faster in linear time. However, it was about solving optimization problems using linear equations and inequalities. I found the simplex method to be smart, and I wonder how did they come up with it in the first place.

7. What happened that felt particularly challenging? Why was it challenging to me?

Manually running the simplex method was particularly challenging. It involves a lot of manual calculation and copying table values which is prune to errors. Dr. David Taipala in the video lectures (UoPeople, n.d.) explained the simplex method in a clear and concise manner, but I found some parts of it to be unclear, like when we divide the ratios to find the pivot row and column, we don’t save the ratios in the tableau, we just use them to find the pivot and only the pivot ration is saved while the rest of the column value returned to the original values.

8. What skills and knowledge do I recognize that I am gaining?

I am gaining a better understanding of linear programming and the simplex method. As mentioned, I found the simplex method to be smart but it is important to implement it using a programming language to understand it better.

9. What am I realizing about myself as a learner?

I am realizing that I need a systemic method to verify what I am working on. For example, the simplex method involves a lot of manual calculations and copying table values which is prune to errors. I don’t have a systematic way to verify my work, so I need a function that I supply the objective function and constraints, and then it gives me back the solution to compare with my manual solution.

10. In what ways am I able to apply the ideas and concepts gained to my own experience?

There are many optimization problems in the real world that can be solved using linear programming. For example, a company can use linear programming to optimize its production process, a transportation company can use it to optimize its routes, and a financial company can use it to optimize its investment portfolio. I think that learning the simplex method will help me to solve these problems in the future.

References