Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Understanding the Brute Force Approach
Unlock Audio Lesson
Today, we'll discuss the brute force approach. Can anyone explain what they think this means?
It's trying all possible solutions to find the best one, right?
Exactly. In our photocopy shop example, we would look at every possible order of jobs. This could quickly become overwhelming!
Why is it bad to try all orders?
Good question! The number of possibilities increases exponentially. If we have just 30 jobs, it could take hours to find the optimal sequence.
So, are there better ways to do this?
Yes, we can fix one job and then optimize the remaining jobs. This way, we streamline the process and avoid exhaustively checking every option.
That's interesting! Can we prioritize jobs to make it easier too?
Absolutely! We can prioritize based on shortest jobs or those with imminent deadlines.
To summarize, while the brute force method guarantees an optimal solution, its efficiency drops drastically with more jobs. It's crucial to employ smarter strategies for practical application.
Efficiency through Decomposition
Unlock Audio Lesson
Now let's dive deeper into how we can reduce complexity when scheduling. What do you think happens when we fix one job?
We would have fewer jobs left to consider, right?
Exactly! If we fix one job to complete first, we effectively reduce our problem size from n to n-1.
And then we can optimize the remaining jobs individually?
Spot on! This approach allows us to iteratively optimize.
But how do we know which job to pick first?
That’s where criteria comes into play! We could choose based on shortest time, closest deadline, or other strategies. Do you think these choices impact the results?
Yes, but how do we ensure we're making the optimal choice?
Great point. We must analyze each strategy's effectiveness and compare outcomes to find the best approach for our situation.
In summary, decomposing the problems by fixing jobs allows us to simplify our scheduling task significantly.
Accounting for Variability in the Job Equipment
Unlock Audio Lesson
Next, let's consider our equipment. How might the fact that not all machines perform the same affect our scheduling decisions?
Some will finish the jobs faster or slower based on their age or condition.
Exactly! Newer machines may have different speed capabilities compared to older ones. This variability needs to be factored into our scheduling.
And what about the costs? Does that matter too?
Yes, great insight! Different machines might have different operational costs, affecting our overall profits.
So, we can’t assume all machines are the same?
Correct! Real-world complexities involve maintenance and availability as well. We need to create a balanced strategy catering to all these factors.
To sum up, we must consider machine performance, costs, and maintenance so our scheduling is both efficient and cost-effective.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In this section, we explore the brute force method of solving scheduling problems, specifically in a photocopy shop scenario. While this method guarantees finding an optimal solution, it becomes inefficient for larger problems due to exponential growth in possibilities, leading to the consideration of alternative strategies for better execution.
Detailed
Brute Force Approach
The brute force approach is a methodical and straightforward method of solving problems by considering all possible configurations. In the context of a photocopy shop with numerous urgent project requests from students, we delve into how to schedule jobs effectively. The brute force method would involve testing every possible job order to determine which one yields the best return concerning meeting deadlines and maximizing revenue. However, as the number of requests increases, so do the possible configurations—growing exponentially, which makes this method impractical for even a modest number of jobs (e.g., 30 requests). This leads us to the importance of decomposition and developing efficient strategies. By fixing one job to begin with, we can reduce the complexity by solving the remaining (n-1) jobs optimally. We can also introduce heuristic strategies that prioritize jobs based on specific criteria such as shortest processing time or nearest deadline. This section emphasizes the significance of these strategies while also noting the challenges posed by different machines and the variations in costs and maintenance requirements. Understanding these approaches helps in making more informed decisions that can enhance productivity and revenue for operations like our photocopy shop.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Problem Context
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, suppose we have a photo copy shop, campus Xerox inside the university campus. The deadline for projects is approaching and a bunch of students want their projects copied urgently. So, they all go and submit their reports to the photo copying shop, and say we want so many copies made within such a time. So, now the question for the shop is how best to schedule this job.
Detailed Explanation
In this scenario, a photo copying shop has to deal with multiple students needing urgent copies of their projects. The key challenge is efficiently scheduling the jobs to ensure all students receive their copies on time. The problem is similar to situations where multiple tasks need to be managed under time constraints.
Examples & Analogies
Imagine a pizza delivery restaurant during the Super Bowl. They have multiple orders coming in at once, and they need to decide which pizzas to make and deliver first to ensure all customers get their orders promptly.
Introducing the Brute Force Approach
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
There is always at the background what is called group force approach. You can say now I have to allocate these photo copying jobs to the machines in some order. So, let me try every possible order and choose the one which gives me the best return.
Detailed Explanation
The Brute Force Approach involves checking every possible way to allocate jobs to the machines to find the best schedule. This means testing all combinations of job orders to see which order results in the highest efficiency or least penalties for missed deadlines. However, this method can be highly inefficient as the number of jobs increases exponentially.
Examples & Analogies
Think of a person trying to find the best route for a road trip by considering every possible path between multiple destinations. While this could theoretically yield the fastest route, it would be incredibly time-consuming and impractical for more than just a few locations.
Challenges of the Brute Force Approach
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
The problem with this is that it will take a very large amount of time to do this because number of possibilities is exponential. Even if you have just 30 requests pending, it could take several hours to find an optimized schedule, and that several hours might have gone ahead and done some work, so that you got the jobs done and perhaps not optimally at least got some money for it.
Detailed Explanation
As the number of job requests increases, the number of possible schedules grows exponentially. For example, if there are 30 requests, the shop would have to analyze billions of different orders to find the best one. This often leads to a situation where the shop, instead of waiting for an optimal solution, might choose to proceed with a 'good enough' solution just to keep the business running.
Examples & Analogies
This is like looking for the best restaurant in a city by going through every single review available online. Instead of enjoying a meal quickly, you might spend days analyzing hundreds of reviews, missing out on the experience altogether.
Decomposing the Problem
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, supposing we fix one job to run first. If we fix this job to run first, we are left to the remaining jobs of the remaining jobs are smaller in numbers. So, if there was a way to optimally solve for n minus 1 job, then we can pick each of the first jobs, each of the first jobs to be the first job and for each of them determine how much time it takes efficiently if we can do the remaining n minus 1 and choose the best one.
Detailed Explanation
One way to simplify the problem is to fix one job as the first task, which reduces the complexity by allowing the remaining jobs to be organized. This approach suggests recursively solving the problem by addressing the smaller set of remaining jobs after fixing one. This can lead to an efficient solution rather than trying to evaluate every possible combination directly.
Examples & Analogies
Imagine you're packing for a trip. Instead of choosing the best arrangement for every item in your suitcase at once, you first decide to pack your shoes, and then arrange the other items around them. This strategy simplifies the packing process and helps you organize more efficiently.
Establishing Criteria for Job Selection
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Another option is to just come up with a strategy. Looking at all the jobs which are yet to be done, we find some criteria by which we choose one to do next. Now, we could have different criteria for which we could choose the one to do next which has the least number of pages that you take the shortest time to process, or we could take the one to do next which is closest to its deadline that is one for which we are most likely to miss finishing it in time and having to give a discount.
Detailed Explanation
Apart from using brute force or fixing jobs, the shop can establish rules based on criteria, such as job size (number of pages) or urgency (approaching deadlines). This strategy allows selective prioritization of jobs, enabling quicker decision-making and potentially maintaining better service levels.
Examples & Analogies
Consider a teacher grading assignments. They might decide to grade the shortest ones first to clear them quickly or focus on the longest ones if they're coming up on a deadline. Establishing these criteria can help manage timeframes more effectively.
Factors Complicating the Problem
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
If we assume that the shop has many photo copiers, it is reasonable to assume that some are new and some are old. Therefore, the time that will take to finish a job depends on which machine we put the job on. The other factor is of course that the cost of doing something varies across machines.
Detailed Explanation
The complexity of scheduling also increases with variations in the machines being used. Different machines may have different speeds and costs, affecting how jobs are scheduled. Understanding these factors is essential for optimizing the job allocation to ensure both efficiency and profitability.
Examples & Analogies
This is similar to a delivery service using different types of vehicles. Some vans are newer and quicker, while others are older and slower. Choosing the optimal vehicle for each delivery based on distance and urgency can make a significant difference in overall service quality.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Brute Force Approach: A method involving checking all possibilities to find an optimal solution.
-
Decomposition: Dividing a complex problem into simpler tasks to simplify the solution process.
-
Heuristic Strategy: Using practical, less formal methods to find satisfactory solutions quickly.
-
Machine Variability: The impact of different machine efficiencies and costs on job scheduling.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
In our photocopy shop, if we receive requests for 30 different projects, trying every possible order would look to evaluate 30! (30 factorial) combinations.
-
If a job has to be completed urgently due to a deadline, we might prioritize it even if it wasn't submitted first.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
Brute force leads to stress, try all ways, but guess what? There's smarter to impress!
📖 Fascinating Stories
-
Imagine a baker in a rush, with too many orders they must crush. They tried each recipe, but were in a fuss, until they simplified and found success!
🧠 Other Memory Gems
-
Remember B.D.H: Brute force, Decompose, Heuristic strategies.
🎯 Super Acronyms
P.D.E
- Prioritize
- Decompose
- Execute - a strategy for effective scheduling.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Brute Force Approach
Definition:
A method of solving problems by considering all possible configurations or solutions.
-
Term: Decomposition
Definition:
The process of breaking down a complex problem into simpler parts.
-
Term: Heuristic Strategy
Definition:
A problem-solving method that uses a practical approach to find a satisfactory solution quickly.
-
Term: Time Complexity
Definition:
The computational complexity that describes the amount of time it takes to run an algorithm.