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Interactive Audio Lesson
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Determining the Balance Number of Trucks
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Today, we're going to learn about the balance number of trucks needed for one loader. Can anyone tell me how we find this balance?
Do we need to consider the cycle times of both the truck and the loader?
Yes! The balance number of trucks per loader is determined by dividing the truck cycle time by the loader cycle time. Given that the truck cycle time is 39.5 seconds and the loader's is 5.5 seconds, can anyone calculate the balance number?
I think it’s 7.18!
Exactly! And when rounding, what do we consider?
We should work out the economics of both rounding up and rounding down.
Correct! It's essential to analyze the economics of both scenarios before making a decision.
To remember this, think of the acronym TRUCK – 'Time, Rounding, Utilization, Cost, Knowledge'.
Productivity and Truck Numbers
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Now let's discuss how productivity changes with different numbers of trucks. If we have 5 trucks, what might our productivity be?
If the individual truck productivity is 12.53 cubic meters per hour, then 5 trucks would yield 62.65 cubic meters per hour.
Exactly! What about at 6 trucks?
That would be 75.18 cubic meters per hour!
Right! And when we reach the balance number of 7 trucks, how much productivity do we expect?
We get 87.71 cubic meters per hour.
But what happens if we increase to 8 or 9 trucks?
The productivity doesn’t increase beyond 90 cubic meters per hour since that's limited by the loader!
Exactly! Remember: beyond the balance number, productivity is loader-controlled. Keep in mind the acronym LIMP – 'Loader Is Maximum Productivity'.
Economic Considerations in Truck Selection
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Next, let's explore costs associated with different truck numbers. Can someone tell me how we'll calculate total costs?
We multiply the number of trucks by the hourly cost of the trucks and add the loader's cost.
That's right! For 5 trucks at 1650 rupees per hour, plus the loader at 2700 rupees, what’s the total?
That comes to 10950 rupees.
Very good! Now, what about the unit cost of production?
We divide the total cost by productivity.
Exactly! Can anyone calculate the unit production cost for 5 trucks?
That would be 174.78 rupees per cubic meter.
Correct! This kind of analysis helps us see that as we increase trucks up to 7, costs decrease, but after that, costs rise without productivity gains. Remember the phrase: 'Costs Go Up, Productivity Stays Down' for our economic insights!
Choosing the Right Number of Trucks
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Finally, how do we decide whether to round down or up to the balance number?
We should analyze the unit costs for both choices before finalizing.
Right! If 7 trucks give us 162.47 rupees per cubic meter and 8 trucks raise it to 176.67, which should we go for?
Definitely 7 trucks to minimize costs!
Exactly! What else might we consider before finalizing our decision?
We should consider the loader’s efficiency and downtime as well!
Good point! By considering all factors, we optimize our operations. Remember to think critically about each component, using the acronym DECIDE – 'Data, Evaluate Costs, Inquire, Decide, Evaluate' to ensure better decisions.
Introduction & Overview
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Quick Overview
Standard
The section explores how to determine the optimal number of trucks needed for a loader by analyzing truck cycle time and loader cycle time. It discusses the relationship between truck numbers and productivity, emphasizing the importance of economics in decision-making regarding equipment combinations.
Detailed
In this section, we delve into the balance of trucks required for a loader, primarily using truck cycle time and loader cycle time to determine efficiency. The balance number of 7.18 trucks is derived from given data, rounding to either 7 or 8 trucks. An examination of different truck numbers—from 5 to 9—shows variations in productivity and cost-efficiency. When the number of trucks exceeds 7, productivity is capped by the loader, while costs increase without gaining further efficiency. The section emphasizes the importance of economics in machine selection, illustrating how total unit cost calculations inform better decision-making in truck-loader scenarios. Critical insights into balancing machine capabilities and operational costs improve overall productivity and cost-effectiveness.
Audio Book
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Determining 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 served 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 determine the 'balance number' of trucks that can efficiently work with one loader, we divide the 'truck cycle time' by the 'loader cycle time'. The truck cycle time is the time it takes for a truck to complete a full cycle of loading, moving, and unloading, while the loader cycle time is the time the loader takes to fill one truck. In this case, we found a balance number of approximately 7.18, which means in practical terms, we can use 7 or 8 trucks depending on our analysis.
Examples & Analogies
Imagine you're running a small delivery service. If each delivery vehicle (truck) takes 39.5 minutes to make a round trip while your delivery helper (loader) takes 5.5 minutes to load packages, then having about 7 delivery vehicles will ensure your operations run smoothly without delays. If you have too few trucks, you won’t meet demand, and having too many will lead to unnecessary waiting for your loader.
Impact of Truck Numbers on Productivity
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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 number of trucks significantly affects overall productivity and costs. By experimenting with various numbers of trucks—5 to 9—we can observe how this change impacts production levels and costs per unit produced. Increasing trucks generally raises productivity until we hit the balance point where the loader's limits restrict further gains. Beyond that point, adding trucks results in longer wait times and increased costs without improving output.
Examples & Analogies
Think of a restaurant kitchen. If Chef needs a certain number of helpers to prepare orders optimally, hiring extra people can initially speed up food preparation. However, past a certain number, the kitchen becomes crowded, hindering workflow, and waiting times for orders increase even with more staff because they cannot work efficiently together.
Calculating Productivity with Varying Truck Numbers
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So, basically how to estimate the job production? So, it is nothing but your single truck productivity multiplied by number of trucks. So, provided the number of trucks are lesser than the balance number. In that case you can calculate by that, because when the trucks are lesser than the balance number or equal to balance number your truck cycle time will govern the productivity.
Detailed Explanation
To find job production, multiply the productivity of a single truck by the number of trucks, as long as the truck count is at or below the balance number. When the truck count exceeds the balance number, the loader cycle time starts to dictate productivity since the loader's speed at which it can fill trucks limits output, making the truck count less critical beyond this point.
Examples & Analogies
Consider a car wash. If you have one hose (loader) and two cars (trucks), you can wash them quickly. However, if you add more cars than the hose can handle at once, the additional cars will wait for their turn, slowing down the overall process, similar to how too many trucks will wait for the loader.
Understanding Productivity Limits Beyond Balance Number
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But when the number of trucks is your balance number say 7, so actual balance number is 7.18. So, when the numbers of trucks are lesser than the balance number say 5 trucks, 5 into productivity of your truck, individual truck productivity is 12.53-meter cube per hour. So, that gives me the value is 62.65-meter cube per hour.
Detailed Explanation
When the truck count is equal to the balance number (in our case, 7 trucks), production is optimized. If the number is less (like 5 trucks), the summed productivity decreases. For example, if each truck can carry 12.53 cubic meters per hour, with 5 trucks, the total productivity drops to 62.65 cubic meters per hour. This demonstrates how having fewer trucks affects overall work output.
Examples & Analogies
Imagine a factory assembly line. If the assembly line can handle a certain number of workers efficiently, but you operate with fewer, the entire production suffers. Assigning work decreases efficiency since not all tasks are covered, similar to running fewer trucks than needed.
Diminishing Returns Beyond the Balance Point
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You cannot go beyond the productivity of the loader beyond the balance number. Though the number of trucks or more you have 8 trucks, you have 9 trucks but the trucks will be simply waiting for the loader only.
Detailed Explanation
Once the truck count exceeds the balance number, productivity levels off because the loader's capability to fill trucks limits output. Additional trucks will just be idle, waiting for the loader to be available. This represents a classic case of diminishing returns where adding more resources yields no additional productivity.
Examples & Analogies
Think of booking seats on a bus. Even if you have the capacity for more passengers, if the bus can only fit a certain number at a time, additional seats will not help since people still need to wait for their turn to board.
Economics of Truck Loader Combinations
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Now let us work out the economics because most of the decisions are based upon the economics. People are more concerned about the unit production cost associated with the machine.
Detailed Explanation
In making decisions about the number of trucks and loaders, it's crucial to compute the economics or costs involved, focusing on the unit production costs. This allows operations to find a combination that minimizes costs while maximizing productivity, ensuring efficient use of equipment.
Examples & Analogies
Running a bakery, if you can afford several mixers and ovens, but the cost of ingredients and labor is high, you need to calculate how much each batch costs you. By analyzing expenses, you determine how many batches keep things profitable without overextending your budget.
Calculating Total Cost and Unit Cost of Production
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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 determine total costs of operation, we take the hourly costs of all trucks and the loader. This provides a base from which we can derive the unit cost of production by dividing total costs by productivity, allowing for a comparison of efficiency across different truck counts.
Examples & Analogies
Think of a gym membership. You pay a monthly fee (fixed costs), but if you work out more often, you get healthier, which is akin to understanding how costs relate to how much you produce or how fit you become based on the investment in that gym.
Understanding Unit Cost vs. Productivity
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But 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. But as your number of trucks increases you can see that the productivity increases significantly.
Detailed Explanation
It's crucial to understand the relationship between unit cost and productivity. Fewer trucks may result in lower total operational expenses initially, but due to their limited productivity, the cost per produced unit is higher. Conversely, with more trucks, while costs might increase, the productivity boosts lead to lower unit costs, showing efficiency gains.
Examples & Analogies
Imagine you’re selling cookies. If you bake only a few at a time, each cookie may cost more due to baking and marketing efforts. However, if you bake larger batches, your overall cost per cookie decreases, even with higher production-related expenses.
Optimal Number of Trucks and Its Economic Implications
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So, it is always preferable to go by the balance number, but in this case our balance number was 7.18, it was 7.18. So, whether to round it to lower number or round it to the higher number, whether I should go for 7 or whether I should go for 8. If I go for 7 my unit production cost is 162.47. If I go for 8 trucks my unit production cost is 176.67, so it is preferable to round it to the lower number.
Detailed Explanation
In deciding the number of trucks to deploy, it's vital to consider costs. Our analysis suggests rounding down from 7.18 to 7, which balances productivity and minimizes unit costs. Using 8 trucks leads to inefficient costs with no added benefit to productivity, making it advisable to keep a minimal yet efficient number of trucks active.
Examples & Analogies
Think of a carpool. If three friends need to drive to a concert, they can take one car instead of everyone driving separately. If they start inviting more friends without checking how many can fit comfortably, they’d end up with too many cars and wasted gas. Hence, it’s efficient to keep only what is necessary.
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 optimal number of trucks for a loader to minimize costs while maximizing productivity.
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Truck Cycle Time: The total time taken for a truck to perform a loading and unloading task.
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Loader Cycle Time: The time required for the loader to load the truck, affecting overall productivity.
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Unit Production Cost: Calculated by dividing the total cost by productivity; it informs economic decisions.
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Economics: The study of unit costs and productivity balance in engineering operations.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Using 5 trucks with a productivity of 62.65 cubic meters per hour results in a higher unit cost than using 7 trucks, where productivity reaches 87.71 cubic meters per hour.
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Choosing to operate with 8 trucks does not increase productivity beyond the loader's capacity of 90 cubic meters per hour, yet incurs higher costs.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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When truck numbers rise but loader stays, Productivity stalls, in many ways.
📖 Fascinating Stories
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Imagine an eager truck fleet boosting productivity but waiting in line for the single loader that limits their breakthroughs.
🧠 Other Memory Gems
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ROPE - Rounding Off Production Economically - to remember the importance of economics in truck decisions.
🎯 Super Acronyms
LIMP - Loader Is Maximum Productivity, to remind us that the loader ultimately controls productivity.
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 required for a truck to complete one full cycle of loading and unloading.
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Term: Loader Cycle Time
Definition:
The time it takes for a loader to load a truck.
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Term: Balance Number
Definition:
The optimal number of trucks needed for a loader to maximize productivity without excess.
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Term: Unit Production Cost
Definition:
The cost of production per unit, calculated as total cost divided by productivity.
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Term: Economic Analysis
Definition:
The assessment of costs associated with differing operational strategies.