4. Summary and Conclusion

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.

To calculate how many trucks are needed for one loader, we first need to use a formula which involves the truck cycle time and the loader cycle time. The truck cycle time (39.5 units) is divided by the loader cycle time (5.5 units). This calculation shows us that approximately 7.18 trucks are required for optimal performance, which means that to decide how many trucks to use, we should round this number either up to 8 or down to 7 based on economic factors.

Imagine you are managing a bakery with one oven (the loader) and several trays (the trucks) to bake cookies. If you have too few trays, you won't bake enough cookies quickly, but if you have too many trays, they will just sit and wait. Finding the 'balance number' is like figuring out the optimal number of trays you need to maximize cookie production without having them wait for the oven.

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, so that will get a clear picture on what is the effect of number of trucks, and what is the effect of increasing the number of trucks beyond the balance number on the unit production cost.

We then need to compare different scenarios with varying numbers of trucks (from 5 to 9) to see how they affect productivity and costs. By calculating productivity based on how many trucks are being used, we can observe the productivity increases up to the balance number (7.18), where they optimally support the loader. Beyond this number, additional trucks lead to diminishing returns on productivity since excess trucks lead to waiting times rather than additional work.

Think of a popular coffee shop. If the barista can serve 10 customers at a time efficiently, adding more baristas only helps up to a point. If you exceed that number, several baristas will be standing around with nothing to do because there's a limit to how many customers can be served at once.

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. So, whichever combination gives you lesser unit production cost we will advise that combination, so that is how we are supposed to follow.

Decisions about the number of trucks to use are deeply intertwined with their economic implications, particularly unit production costs. We'll calculate total costs based on various truck and loader combinations, considering their hourly rates, and then derive the unit cost of production by dividing total costs by productive output. This analysis helps us find the most cost-efficient configuration.

Imagine planning a road trip with a group of friends. You might need to consider how many cars to take. More cars can mean a more comfortable trip, but also higher gas costs and parking fees. Therefore, calculating costs per person can help you decide how many cars are ideal for both a pleasant ride and a manageable budget.

So, 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, that is why your unit cost of production reduces.

When we analyze the results, we notice a trend: having too few trucks results in higher unit costs due to low productivity. As we increase the number of trucks, productivity increases, leading to a decrease in unit costs. However, when we exceed the balance number, productivity gains level off, but costs continue to rise due to additional equipment, making it inefficient economically to add more than the balance number.

Consider a restaurant with a limited number of chefs. If there are too few chefs, they can’t cook enough meals quickly, leading to long wait times and frustrated customers. As you add more chefs, the service improves until you hit a sweet spot of efficiency. If you keep adding chefs beyond what the kitchen can handle, they’ll just get in each other's way, wasting time and resources.

Now, 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.

Finally, we need to make a decision on whether to use 7 or 8 trucks based on the calculations of unit production costs. Since using 7 trucks results in a lower unit cost than using 8 trucks, it is more economical to choose 7 trucks. This decision also factors in potential downtime for the loader to rest or address site needs, which can further improve efficiency.

It’s like buying a new computer. If you find one that meets your needs and is $500, but a fancier one is$600 with features you don't really need, it’s often better to stick with the one that best fits your use case and budget. More isn't always better!

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