1.2. Economics of Different Truck Numbers

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.

To determine the ideal number of trucks that should be used with one loader, you need two key values: the truck cycle time and the loader cycle time. In this case, the truck cycle time is 39.5 minutes and the loader cycle time is 5.5 minutes. The balance number of trucks needed is found by dividing the truck cycle time by the loader cycle time, giving us approximately 7.18. This means that ideally, you should have around 7 to 8 trucks for one loader, depending on rounding.

Imagine a restaurant kitchen where a chef (the loader) can prepare one plate of food every 5.5 minutes. If customers take 39.5 minutes to finish their meals, you can think of it as a ratio; for each chef, having around 7 to 8 waiters (trucks) ensures that food is served efficiently without the waiters (trucks) waiting around.

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.

Analyzing how productivity and unit production costs change with varying numbers of trucks provides important insights. When the number of trucks is below or equal to the balance number, productivity increases linearly as more trucks are added. However, once you reach the balance point of around 7 trucks, adding more trucks does not improve overall productivity significantly because they end up waiting for the loader, leading to potential increases in unit costs.

Consider a school where teachers (loaders) can only teach a certain number of students (trucks) at a time. If you have 5 students, they get personal attention but if you suddenly bring in 10, the new students will just sit and wait, thereby not increasing the class productivity.

The unit cost here will be calculated for the different combinations. Total cost is nothing but x multiped what is the hourly cost of truck + 1 multiped hourly cost of loader.

Unit production cost is calculated by dividing the total cost of using trucks and loaders by the productivity. For example, if 5 trucks cost ₹1650 each per hour and the loader costs ₹2700 per hour, the total cost becomes: 5 * 1650 + 2700. Then, divide this total cost by the productivity derived from the trucks to determine the unit production cost. Doing this for various truck counts shows how costs vary with productivity changes.

Think of it like throwing a birthday party. The total cost of the party includes the cost of food (like trucks) and entertainment (the loader). If you have a few friends (trucks) and everyone gets fed, your overall satisfaction (productivity) increases. But if more friends show up than there's food, costs go up without more happiness.

Beyond the balance number, the productivity will be controlled by your loader. So, it is not advisable to increase the number of trucks beyond the balance number because the trucks will be just waiting for the loader.

Once you exceed the optimal truck number, the additional trucks do not enhance the operation because they will be waiting for the loader to finish its tasks. Even if you have more trucks, the productivity is capped by how fast the loader can work. Therefore, it's crucial to recognize this limitation to avoid unnecessary increased costs.

Imagine a food truck festival where there's one chef making food and too many customers lining up. If more customers arrive than the chef can serve, those extra customers only create longer waiting times without increasing food output, thereby wasting resources.

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