3. Graphical Analysis of Costs and Productivity

Now let us find the balance number of trucks needed for one loader. So, that depends upon your truck cycle time divided by loader cycle time. 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. This gives me the balance number of 7.18.

To determine how many trucks are needed for one loader, you need to consider the truck cycle time and the loader cycle time. The truck cycle time is how long it takes for a truck to complete its round trip, while the loader cycle time is how long it takes for the loader to load a truck. By dividing the truck cycle time (39.5 minutes) by the loader cycle time (5.5 minutes), you calculate the balance number, which is approximately 7.18 trucks. This means ideally, you need about 7 to 8 trucks to work efficiently with one loader.

Think of it like a restaurant where one chef (loader) can only cook a limited number of meals at a time, while multiple waiters (trucks) are taking the meals to customers. If there are too few waiters, customers wait too long; if there are too many, waiters are just standing around and not being productive.

We will work out the economics when I go for different numbers of trucks (5, 6, 7, 8, and 9) and see how the productivity will vary and how the unit production costs will vary.

By analyzing different scenarios where the number of trucks is varied, you can see how productivity changes. For example, with fewer than the balance number of trucks, productivity is limited by how quickly the trucks can cycle. But as you add more trucks, productivity increases until you reach the balance number. Beyond this point, having more trucks does not increase overall productivity because the loader cannot load more than a certain amount at a time.

Imagine a school bus scenario: If there are only two buses for a field trip, not all students can get on at once. With each additional bus, more students can be accommodated until you reach the maximum number that the school allows. If you get more buses than needed, they just end up parked, waiting for students to board the already full buses.

The total unit cost is calculated for the truck loader combination based on the hourly costs given for the loader and truck. For instance, for 5 trucks, the total cost is 5 multiplied by 1650 plus 1 multiplied by 2700, giving a cost of 10,950 rupees.

To know how much it costs to produce one unit (like a cubic meter) of output, you need to calculate the total cost associated with the trucks and loader. For each scenario (5 trucks, 6 trucks, etc.), you multiply the number of trucks by their hourly cost and add the loader's hourly cost. This gives you the total hourly cost. Then you divide this total cost by the productivity (how much output you can generate in that hour) to get the unit cost.

It's like a team of workers getting paid hourly: If you have two workers working hard (good productivity) compared to having five, where three are just standing around waiting for instructions (inefficient productivity), your cost per task completed would be much higher if the workers aren’t effectively used.

Beyond the balance number, the trucks will be waiting for the loader. Productivity will be controlled by your loader since you cannot go beyond its loading capacity of 90 cubic meters per hour.

Once you have more trucks than the balance number, those additional trucks do not contribute to the output because they will simply be waiting for the loader to be available. The loader's capacity limits how much can be produced, capping the productivity regardless of how many trucks you have.

This situation mirrors a bottleneck in a factory. If a machine can process only ten items an hour, having twenty workers will not speed up production; they will end up waiting for their turn to use the machine, just like trucks waiting for the loader.

Work out the economics for lower versus higher truck numbers. For instance, with 7 trucks, your unit production cost is better than with 8 trucks, where productivity does not significantly increase, but costs do.

Economic decisions must balance productivity and cost. As the number of trucks increases beyond the balance point, while productivity might look higher at first glance, the increase in costs due to additional trucks often outweighs the benefits when there’s no increase in production. A lower unit cost at the balance point is preferred because it signifies efficient resource use.

Consider a coffee shop: If you acquire too many coffee machines, you might think this will increase your output. However, if you only have one barista, the extra machines won't help. In fact, the cost of machines increases your overall operational cost without increasing sales, similar to having too many trucks with insufficient loader capacity.

We have discussed various topics including the balance number of trucks, their impacts on productivity, and the importance of cost analysis in decision-making.

In summary, understanding the balance between truck numbers and loader productivity is crucial for efficient operations. One must evaluate the productivity at different truck counts and analyze the associated costs to make informed decisions about the machinery setup that will yield the best economic results.

Just like optimizing any business operations, whether it is online retail or food delivery, aligning resources (like trucks and loaders) efficiently leads to better service and profitability, whereas mismanagement can lead to wasted resources and increased costs.

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