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A short class with Sarah and her students. The other ways are under More.
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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.
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.
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.
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.
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.
Seven for balance is good to see, too many trucks just won't let it be.
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.
To recall cycle times: 'T L - T to L, make sure to balance well.'
BUST (Balance = Under/Over/Same Trucks) helps remember the effects of varying truck counts.
Term
Balance Number
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Term
Unit Production Cost
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Term
Truck Cycle Time
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Term
Loader Cycle Time
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The optimal number of trucks matched with a loader to achieve maximum productivity without unnecessary cost.
The total time taken for a truck to complete a cycle of loading, transporting, and unloading.
The amount of time taken for a loader to load a truck.
The cost incurred to produce a unit of output.
This section explains the balance number of trucks required for effective loader productivity and how unit production costs vary with changes in truck numbers.
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.
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.
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.
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.