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 Balance Number
Unlock Audio Lesson
Today we will learn about the balance number, which is the optimal number of trucks for one loader to maximize productivity and control costs. Can anyone tell me what you think affects this balance number?
Maybe the speed of the trucks and loader cycles?
That's correct! The truck cycle time and the loader cycle time are crucial. Our calculation shows that with a truck cycle time of 39.5 seconds and a loader cycle time of 5.5 seconds, the balance number is about 7.18 trucks, which we can round to either 7 or 8. Remember, you can use 'T/L= Balance Number' as an acronym.
Why do we have to round it? Shouldn’t we just use the exact number?
Good question! Rounding helps us decide between practical truck numbers. It also allows the loader some downtime for efficiency. So, what's our balance number?
It’s 7, right?
Exactly! Knowing this is key when discussing productivity and avoiding increased costs from having too many trucks waiting.
Productivity Scenarios
Unlock Audio Lesson
Now let's discuss how productivity changes with different truck numbers. If we have 5 trucks, what would be the productivity?
Isn't it 5 times the truck productivity?
Correct! If the individual truck productivity is 12.53 cubic meters per hour, then 5 trucks give us 62.65 cubic meters per hour. What happens if we increase to 6 trucks?
That would be 75.18 cubic meters per hour.
Exactly! But what happens at the balance number of 7?
We reach maximum efficiency at 87.71 cubic meters.
Correct! But beyond that, if we move to 8 trucks or more, at what level does productivity cap?
At 90 cubic meters per hour, due to the loader's limitations.
That's right! Remember: as trucks increase beyond the balance number, the loader controls productivity.
Calculating Unit Costs
Unlock Audio Lesson
Let’s move on to calculating unit costs. For 5 trucks with a cost of 1650 per truck and 2700 for one loader, how do we find total cost?
We multiply the truck cost by the number of trucks and add the loader cost.
Exactly! So, for 5 trucks, what’s our total cost?
I think it's 10950 rupees.
Well done! How would we calculate unit cost for that scenario?
We would divide the total cost by productivity.
Correct! For 5 trucks with productivity at 62.65, what’s the unit cost?
It's 174.78 rupees per cubic meter.
Perfect! This calculation shows how costs vary. What happens as we approach or exceed our balance number?
Costs rise without an increase in productivity—it’s inefficient.
Exactly! Always evaluate the balance number to optimize production costs.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In this section, the relationship between the number of trucks and the loader's productivity is explored. The 'balance number' is defined, showing how both too few or too many trucks can lead to increased production costs, and an in-depth analysis of different scenarios clarifies the economics of truck-loader combinations.
Detailed
Graphical Representation of Unit Production Cost
In this section, we delve into the concepts surrounding the balance number of trucks needed for effective loader operation. The balance number is the ideal number of trucks that allows for optimal productivity without unnecessary costs. It is calculated by dividing the truck cycle time (39.5 seconds) by the loader cycle time (5.5 seconds), leading to a balance number of approximately 7.18 trucks, which may be rounded to either 7 or 8.
Key Concepts
As the number of trucks increases beyond the balance number, the loader becomes the productivity constraint. Here, productivity is initially governed by the truck cycle time when the number of trucks is below or equal to the balance number but shifts to being controlled by the loader once this number is surpassed. The productivity levels for different scenarios (5 to 9 trucks) are calculated, highlighting the diminishing returns when exceeding the balance number.
Economic Analysis
Additionally, this section discusses how to calculate total unit costs for various truck-loader combinations. The costs associated with running trucks and loaders are outlined, and the unit production costs are calculated for different configurations. The analysis shows that while productivity increases with the number of trucks, costs can rise significantly beyond the balance number due to idle trucks waiting for the loader. It culminates in a conclusion stressing the economic preference for choosing a truck count equal to or less than the balance number. This understanding is crucial for managing operational efficiency and costs in production settings.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Estimating the Balance Number of Trucks
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now let us find the balance number of trucks needed for one loader. So, that depends upon your truck cycle time divided by load of cycle time. So, you have estimated the truck cycle time earlier, so estimated it is 39.5. The truck cycle time is 39.5 and the loader cycle time is 5.5, we have calculated the loader cycle time as 5.5. So, this gives me the balance number of 7.18.
Detailed Explanation
To determine how many trucks are needed for one loader, we use the truck cycle time and loader cycle time. The truck cycle time is the total time it takes for a truck to complete its cycle, while the loader cycle time is how long it takes to load the truck. By dividing the truck cycle time (39.5) by the loader cycle time (5.5), we arrive at a balance number of approximately 7.18 trucks. This means if we have fewer than 7 trucks, the trucks would not work efficiently because they can't keep up with the loader's capacity.
Examples & Analogies
Imagine you have a friend who is a server at a restaurant, and she can serve a maximum of 5 tables at a time. If you have only 3 tables set up, the restaurant isn't operating at full efficiency because your friend could potentially handle more. However, if you set up 8 tables, your friend becomes overwhelmed and can't serve customers effectively because she would be running back and forth without enough time to attend to each table properly.
Impact of Truck Numbers on Productivity
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, just to give you a better explanation I am just working out what will be the economics when I go for different number of trucks. Say if I go for 5 number of trucks 6, 7, 8 and 9, how the productivity will vary, how the unit production cost will vary?
Detailed Explanation
In this chunk, we explore how the number of trucks influences both productivity and unit production costs. If we were to analyze scenarios where we have 5, 6, 7, 8, or 9 trucks, we would notice a trend: as we increase the number of trucks, initially, productivity increases. However, once we hit the balance number (in this case, around 7 trucks), adding more trucks won't necessarily lead to increased productivity beyond what a single loader can handle.
Examples & Analogies
Suppose you're a delivery driver with a truck capable of making 10 deliveries per hour. If you only have 3 packages, you won't make as many deliveries as possible because you're not maximizing your capacity. But as you add more packages, your deliveries increase. Once you hit the limit of your truck, adding more packages (like adding more trucks in our scenario) will not help you make more deliveries; it just creates extra waiting time.
Calculating Unit Production Costs
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, how to calculate the total unit cost for the truck loader combination I need the input data, so the input data is given to you what is the cost associated with the loader and the truck. The hourly cost data is already given to you as rupees 2700 per hour for the loader and rupees 1650 per hour for the truck.
Detailed Explanation
To calculate the total unit production cost, we need to consider the costs associated with both the loader and the trucks. The cost for the loader is rupees 2700 per hour, and the cost for each truck is rupees 1650 per hour. For any given number of trucks, we multiply the hourly truck cost by the number of trucks and then add the loader's hourly cost to find the total cost. This total cost can then be divided by the productivity to find the unit cost.
Examples & Analogies
Think of running a small cafe. You need to factor in your hourly expenses like the rent for the cafe and the costs of ingredients. Let's say your rental cost is fixed, but as you serve more customers (like adding more trucks), your ingredient costs (similar to truck costs) rise. Just like in our calculations, you would determine how much each coffee costs you to make by dividing your total costs by the number of coffees sold.
Understanding Productivity and Unit Cost Relationships
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
One important thing you have to note here is when the number of trucks is 5 though the total cost is less in this case, but the productivity is also less, that is why you can see that the unit cost is high.
Detailed Explanation
This point highlights a key relationship between the number of trucks, total costs, and unit cost. While the total costs might be lower with fewer trucks (like 5), the productivity also decreases, meaning that each truck is not fully utilized. The unit cost reflects this inefficiency: with lower productivity, the cost per unit becomes higher because you're spreading the costs over fewer delivered cubic meters of material. Therefore, there's a balance to find.
Examples & Analogies
Imagine a factory. If the factory operates with fewer machines, it may spend less on utility costs, but the slower production speed means they can’t meet demand. You might think you’re saving money, but in the end, customers might turn to competitors, costing even more in lost sales. So, sometimes having more machines (or trucks, in our example) is worth the extra cost because they help produce more products, reducing the cost per product.
Graphical Interpretation of Costs
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Graphically you can see this, so when the number of trucks or less your unit production cost is less when the number of trucks is 5, when the number of trucks is less the unit production cost is higher than the optimum value.
Detailed Explanation
This visual representation helps students understand the relationship between the number of trucks and the unit production cost. Initially, as the number of trucks increases, the unit cost decreases due to better productivity. However, once we reach the balance number, the unit production cost hits an optimum level. Beyond this point, additional trucks lead to higher costs without real productivity gains. This illustrates the concept of 'diminishing returns' and the importance of choosing the right number of trucks for maximum efficiency.
Examples & Analogies
Consider a team of students working on a project. At a certain point, adding more team members helps get work done faster and improves quality. But if the team continues to grow, coordinating becomes difficult and efficiency drops. In essence, there is an optimal team size at which performance peaks; going beyond this leads to chaos and slower productivity.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
As the number of trucks increases beyond the balance number, the loader becomes the productivity constraint. Here, productivity is initially governed by the truck cycle time when the number of trucks is below or equal to the balance number but shifts to being controlled by the loader once this number is surpassed. The productivity levels for different scenarios (5 to 9 trucks) are calculated, highlighting the diminishing returns when exceeding the balance number.
-
Economic Analysis
-
Additionally, this section discusses how to calculate total unit costs for various truck-loader combinations. The costs associated with running trucks and loaders are outlined, and the unit production costs are calculated for different configurations. The analysis shows that while productivity increases with the number of trucks, costs can rise significantly beyond the balance number due to idle trucks waiting for the loader. It culminates in a conclusion stressing the economic preference for choosing a truck count equal to or less than the balance number. This understanding is crucial for managing operational efficiency and costs in production settings.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Example 1: When using 5 trucks, the total productivity is 62.65 cubic meters per hour. This shows a scenario where productivity doesn’t meet optimum levels.
-
Example 2: At 7 trucks, productivity peaks at 87.71 cubic meters, showcasing the balance number effect.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
Seven for balance is good to see, too many trucks just won't let it be.
📖 Fascinating Stories
-
Imagine a loader as a chef, cooking for diners. If too many waiters (trucks) come but can’t serve more food, diners (productivity) will remain hungry. Thus a balance ensures everyone is fed efficiently.
🧠 Other Memory Gems
-
To recall cycle times: 'T L - T to L, make sure to balance well.'
🎯 Super Acronyms
BUST (Balance = Under/Over/Same Trucks) helps remember the effects of varying truck counts.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Balance Number
Definition:
The optimal number of trucks matched with a loader to achieve maximum productivity without unnecessary cost.
-
Term: Truck Cycle Time
Definition:
The total time taken for a truck to complete a cycle of loading, transporting, and unloading.
-
Term: Loader Cycle Time
Definition:
The amount of time taken for a loader to load a truck.
-
Term: Unit Production Cost
Definition:
The cost incurred to produce a unit of output.