1.5. Economics Analysis

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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