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Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Understanding Truck and Loader Cycle Times
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Today, we are going to discuss a very important aspect of equipment management: the truck and loader cycle times. Can anyone tell me why these cycle times matter?
I think they determine how efficient our operations can be.
Yes! And they help us figure out the number of trucks we need for our loader to function effectively.
Exactly! The truck cycle time is **39.5 seconds**, and the loader cycle time is **5.5 seconds**. Using these, we derive the balance number of trucks needed.
How do we actually calculate that?
The formula is simple: Balance Number = Truck Cycle Time / Loader Cycle Time. Anyone can calculate it?
So, it’s **39.5 / 5.5 = 7.18**!
Great job! That means we round this as needed based on our economic analysis.
To summarize, we determined our balance number of trucks is around **7** to **8**. Let’s remember this balance helps maintain productivity.
Analyzing Productivity with Different Truck Numbers
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Now that we’ve found the balance number, what happens when we have fewer or more trucks?
If we have **5 trucks**, we should calculate the productivity based on individual truck output, right?
Yes! And for **5 trucks**, if each has a productivity of **12.53 cubic meters per hour**, we can find total productivity!
Exactly! So, it’s **5 * 12.53 = 62.65 cubic meters per hour**. And what about **6 trucks**?
That would be **6 * 12.53 = 75.18 cubic meters per hour**.
Right! However, once we reach the balance number of **7**, let’s talk about productivity control.
After we hit that point, if we add more trucks, they just wait for the loader.
Correct! Beyond the balance number the productivity won't increase past **90 cubic meters per hour**.
Let’s highlight again that managing the balance number is crucial for cost effectiveness. Understanding how productivity is influenced by truck numbers is vital!
Economic Implications of Unit Production Costs
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Let’s shift our focus to the economics. How do we calculate the unit production cost?
We need to find total costs and divide by productivity, right?
Exactly! For **5 trucks**, the total cost is calculated as follows...
Should we add the loader’s cost too?
Yes! The cost of the loader is **2700 per hour** and each truck **1650 per hour**. So, for **5 trucks** it will be **5 * 1650 + 2700**.
That makes it **10,950 rupees** total!
Great! Now, calculate the unit cost for **5 trucks** with that productivity.
It's **10,950 / 62.65 = 174.78 rupees per meter cube**.
Right again! Keep doing this for the other truck counts to see how unit cost varies. We have to find the minimum unit production cost.
Remember: as we approach the balanced number our cost efficiency goes up, while surplus trucks can inflate costs without boosting productivity!
Introduction & Overview
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Quick Overview
Standard
This section details the methodology for calculating the ideal balance number of trucks serving a loader, emphasizing the importance of the truck and loader cycle times, estimating job production, and determining unit production costs based on varying numbers of trucks. It highlights the economic impact of selecting the number of trucks and presents practical examples to illustrate the effect on productivity.
Detailed
Detailed Summary
In this section, we explore the Unit Cost Calculation Process, focusing on how to determine the balance number of trucks for a loader. The key concept introduced is that the balance number of trucks per loader is derived from the relationship between the truck cycle time and the loader cycle time. Using the estimated truck cycle time of 39.5 and loader cycle time of 5.5, a balance number of 7.18 trucks is calculated, leading us to consider rounding to either 7 or 8 trucks based on productivity economics.
We examine the varying economies associated with truck numbers ranging from 5 to 9 while recognizing that productivity is governed by the truck cycle time when the number of trucks is less than or equal to the balance number. When the actual number of trucks exceeds this balance, the productivity becomes loader-controlled, indicated by productivity limits of 90 cubic meters per hour.
The section stresses the implications of the loader's capacity on overall productivity, detailing the unit cost calculation through the formula: Unit Cost = Total Cost / Productivity. A comprehensive case study demonstrates this with costs accruing with different truck counts, illustrating how the optimal case arises when the unit production cost is minimized at the balance number. Graphical representations also reinforce these economic insights, highlighting that increasing trucks beyond the balance number could yield diminishing returns in productivity while inflating operational costs.
Audio Book
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Understanding Balance Number of Trucks
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Now let us find the balance number of trucks needed for one loader. So, that depends upon your
the balance number of trucks per loader going to be serve by one loader is equal to 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 calculate the balance number of trucks needed for one loader, you divide the truck cycle time by the loader cycle time. Here, the truck cycle time is given as 39.5 minutes, and the loader cycle time is 5.5 minutes. This calculation gives you the balance number, which helps in determining how many trucks are needed to optimally load the material using one loader. The balance number of trucks is calculated to be approximately 7.18.
Examples & Analogies
Imagine you're running a delivery service with a single van and multiple packages. If your van takes 30 minutes to make a delivery (like truck cycle time) and it takes you 5 minutes to load a package into the van (like loader cycle time), you'd need to find the right amount of packages to keep the van busy but not overloaded. Here, you're figuring out how many deliveries per hour can be efficiently managed with one van.
Productivity Analysis of Trucks
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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? We will work it out and see...
Detailed Explanation
The text discusses examining how productivity and unit production costs change as different numbers of trucks (5 to 9) are considered. It is said that when the number of trucks is less than or equal to the balance number, the productivity is governed by the truck cycle time; however, if exceed the balance number, productivity will be limited by the loader. Calculating how each scenario affects both productivity and costs helps illustrate the economics of equipment usage.
Examples & Analogies
Think of this like a restaurant kitchen. If you have only two cooks (trucks) to prepare meals, each cook must do their part. If you add more cooks than the kitchen can handle or without enough orders, they might end up not working efficiently, just waiting for tasks (like trucks waiting for loaders). The overall productivity is best when the number of cooks matches what the restaurant can effectively serve at once.
Calculating Unit Production Cost
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The unit cost here will be calculated for the different combinations.
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 hour...
Say for first for 5 number of trucks, how will you calculate the total cost? Total cost is nothing but
5 multiped what is the hourly cost of truck 1650 plus there is only one loader 1 multiplied by 2700.
Detailed Explanation
To calculate the unit production cost, first gather the hourly costs of the loader and trucks. For example, if the loader costs 2700 per hour and each truck costs 1650, the total cost can be calculated by multiplying the number of trucks by their hourly cost and adding the cost of one loader. The resulting total cost is then divided by the expected productivity to derive the unit production cost for that configuration.
Examples & Analogies
This is similar to calculating how much it costs to run a car for a trip. If gas (loader) costs $2.70 per gallon and the car (truck) uses $1.65 per mile, you’d want to know how much it costs you for the entire journey based on your mpg (productivity). Understanding these costs helps you decide whether a trip is worth making.
Analyzing How Unit Costs Change with Truck Numbers
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But beyond the balance number, so you can see that number of trucks are more so the truck will be
waiting for the loader unless the loader is available your truck cannot do the job. So, the
productivity here will be controlled by your loader.
Detailed Explanation
When the number of trucks exceeds the balance number, trucks will experience downtime as they must wait for the loader to become available. As a result, the productivity is capped by the loader's capacity. Thus, beyond the balance point, adding more trucks does not contribute to increased productivity but rather incurs additional costs without a return, leading to an inefficient operation.
Examples & Analogies
Imagine an assembly line where workers wait for a machine to provide components. If too many workers are waiting for only one machine, the extra workers might be doing nothing, yet still being paid. The same happens with trucks – if you have more trucks than loaders can handle, you are wasting resources and money.
Optimum Number of Trucks
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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. But as your number of trucks increases you can see that the
productivity increases significantly, that is why your unit cost of production reduces, it is reducing.
Detailed Explanation
The text illustrates how total costs and productivity vary with the number of trucks. Initially, fewer trucks might mean lower total costs but also lower productivity, resulting in higher unit costs. As more trucks are added, productivity increases, leading to lower unit costs. However, once the number of trucks exceeds the balance point, productivity stagnates while costs continue to rise due to increased truck expenses.
Examples & Analogies
Consider a student's study group. If there are too few students, progress is slow (low productivity). As more students join, the work speeds up, and tasks get completed faster (higher productivity, lower individual responsibility). However, if the group gets too large, some students might just sit around, leading to frustration and inefficiency despite having a high number of helpers.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Balance Number: The ideal number of trucks required for a loader to maintain efficient productivity.
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Unit Production Cost: Cost calculation that indicates the expense incurred to produce a unit of output.
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Loader Productivity: The maximum output achievable by the loader and thus limits truck productivity beyond balance.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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For 7 trucks, the productivity equals 87.71 cubic meters per hour, while for 8 trucks it reaches a maximum of 90 cubic meters per hour due to loader limitations.
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The total cost for 5 trucks becomes 10,950 rupees, which contrasts with 12,600 rupees for 6 trucks, showcasing the operation's cost dynamics.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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To find the right balance with ease, count your trucks to avoid unease.
📖 Fascinating Stories
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Imagine a yard with a loader; too many trucks wait in the cold. Balance means fewer trucks and warm loads.
🧠 Other Memory Gems
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Remember 'B. U. T.' - Balance, Unit Cost, Trucks to grasp the hard numbers easily.
🎯 Super Acronyms
P.T.U. = Productivity, Truck numbers, Unit Cost – key elements to enhance efficiencies.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Truck Cycle Time
Definition:
The time taken for a truck to complete one full cycle of loading and unloading.
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Term: Loader Cycle Time
Definition:
The time taken for a loader to load a truck.
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Term: Balance Number
Definition:
The optimal number of trucks that efficiently serve one loader without excess waiting time.
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Term: Productivity
Definition:
The output produced by a system in a given timeframe, measured in cubic meters per hour.
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Term: Unit Production Cost
Definition:
The cost incurred to produce one unit of output, calculated as total cost divided by total productivity.