3.1. Graphical Representation of Unit Production Cost

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 how many trucks are needed for one loader, we use the truck cycle time and loader cycle time. The truck cycle time is the total time it takes for a truck to complete its cycle, while the loader cycle time is how long it takes to load the truck. By dividing the truck cycle time (39.5) by the loader cycle time (5.5), we arrive at a balance number of approximately 7.18 trucks. This means if we have fewer than 7 trucks, the trucks would not work efficiently because they can't keep up with the loader's capacity.

Imagine you have a friend who is a server at a restaurant, and she can serve a maximum of 5 tables at a time. If you have only 3 tables set up, the restaurant isn't operating at full efficiency because your friend could potentially handle more. However, if you set up 8 tables, your friend becomes overwhelmed and can't serve customers effectively because she would be running back and forth without enough time to attend to each table properly.

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?

In this chunk, we explore how the number of trucks influences both productivity and unit production costs. If we were to analyze scenarios where we have 5, 6, 7, 8, or 9 trucks, we would notice a trend: as we increase the number of trucks, initially, productivity increases. However, once we hit the balance number (in this case, around 7 trucks), adding more trucks won't necessarily lead to increased productivity beyond what a single loader can handle.

Suppose you're a delivery driver with a truck capable of making 10 deliveries per hour. If you only have 3 packages, you won't make as many deliveries as possible because you're not maximizing your capacity. But as you add more packages, your deliveries increase. Once you hit the limit of your truck, adding more packages (like adding more trucks in our scenario) will not help you make more deliveries; it just creates extra waiting time.

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.

To calculate the total unit production cost, we need to consider the costs associated with both the loader and the trucks. The cost for the loader is rupees 2700 per hour, and the cost for each truck is rupees 1650 per hour. For any given number of trucks, we multiply the hourly truck cost by the number of trucks and then add the loader's hourly cost to find the total cost. This total cost can then be divided by the productivity to find the unit cost.

Think of running a small cafe. You need to factor in your hourly expenses like the rent for the cafe and the costs of ingredients. Let's say your rental cost is fixed, but as you serve more customers (like adding more trucks), your ingredient costs (similar to truck costs) rise. Just like in our calculations, you would determine how much each coffee costs you to make by dividing your total costs by the number of coffees sold.

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.

This point highlights a key relationship between the number of trucks, total costs, and unit cost. While the total costs might be lower with fewer trucks (like 5), the productivity also decreases, meaning that each truck is not fully utilized. The unit cost reflects this inefficiency: with lower productivity, the cost per unit becomes higher because you're spreading the costs over fewer delivered cubic meters of material. Therefore, there's a balance to find.

Imagine a factory. If the factory operates with fewer machines, it may spend less on utility costs, but the slower production speed means they can’t meet demand. You might think you’re saving money, but in the end, customers might turn to competitors, costing even more in lost sales. So, sometimes having more machines (or trucks, in our example) is worth the extra cost because they help produce more products, reducing the cost per product.

Graphically you can see this, so when the number of trucks or less your unit production cost is less when the number of trucks is 5, when the number of trucks is less the unit production cost is higher than the optimum value.

This visual representation helps students understand the relationship between the number of trucks and the unit production cost. Initially, as the number of trucks increases, the unit cost decreases due to better productivity. However, once we reach the balance number, the unit production cost hits an optimum level. Beyond this point, additional trucks lead to higher costs without real productivity gains. This illustrates the concept of 'diminishing returns' and the importance of choosing the right number of trucks for maximum efficiency.

Consider a team of students working on a project. At a certain point, adding more team members helps get work done faster and improves quality. But if the team continues to grow, coordinating becomes difficult and efficiency drops. In essence, there is an optimal team size at which performance peaks; going beyond this leads to chaos and slower productivity.

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