2.1. Cost Calculation for Different Combinations

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, here also I did not get the old number, so I have to do the rounding either I can round it to 7 or I can round it to 8.

To determine how many trucks are needed for one loader, we calculate the balance number of trucks. This number is found by dividing the truck cycle time (39.5 minutes) by the loader cycle time (5.5 minutes). This results in a balance number of 7.18. Depending on project considerations, we can round this number either up to 8 or down to 7, which will influence the efficiency of the operation.

Imagine you are organizing a shuttle service for your friends. If you can fit 4 people in your car and you have a total of 20 minutes for round trips, you would calculate how many cars you need based on how long it takes to fill up and take off. The balance number can help decide if you need more cars or if one car is sufficient to keep everyone moving efficiently.

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.

By analyzing different scenarios with various numbers of trucks (5, 6, 7, 8, and 9), we can understand how the productivity changes and its subsequent impact on costs. It helps us discover the optimal number of trucks needed to maximize efficiency and minimize costs. We will conduct an in-depth analysis of each scenario.

Think of a bakery increasing its staff as demand for bread rises. Initially, hiring more bakers boosts output significantly. However, if they exceed the optimal number, they might overcrowd the kitchen, making it harder for each baker to work effectively, thus reducing overall productivity.

So, basically how to estimate the job production? So, it is nothing but your single truck productivity multiplied by number of trucks, that will give you the job production. So, provided the number of trucks are a 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 estimate the job production, the productivity of a single truck is multiplied by the number of trucks used, but only if that number is less than or equal to the balance number. This means if we have, for example, 5 trucks and each truck can process 12.53 cubic meters per hour, our overall productivity would be straightforwardly calculated. As long as truck availability is below the balance number, the truck cycle time determines how efficiently the whole system works.

Imagine you’re at a concert with multiple food stands. Each stand can serve a certain number of customers per hour. If you have just the right amount of stands (trucks) for the number of attendees, each stand can operate smoothly. However, if you have fewer stands than needed, longer wait times will occur, reducing overall customer satisfaction (productivity).

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. This is what you got. Similarly, when the number of trucks is 6, 6 into 12.53-meter cube per hour that will give me the answer is 75.18.

As long as the number of trucks remains below or reaches the balance number, the overall productivity can be easily calculated by multiplying each truck's productivity with the number of trucks. For instance, if we have 5 trucks, each processing at a rate of 12.53 cubic meters per hour, our total productivity is straightforwardly 62.65 cubic meters if we stick with the trucks less than or equal to the balance number.

If a team of students working on a group project can only collaborate effectively when they're not overcrowded, having 5 or 6 members might be ideal for discussions and brainstorming. However, if more students join, it might lead to reduced productivity because too many voices can complicate things.

Beyond the balance number, so you can see that number of trucks are more so the truck will be waiting for the loader unless the loader is available your truck cannot do the job. So, the productivity here will be controlled by your loader. So, beyond the balance number you can see that you cannot go beyond the productivity of the loader because the load of cycle time will control the productivity of the system, for cases above the balance number.

When the number of trucks exceeds the balance number, they will wait for the loader to become available to continue working. As such, the productivity is no longer governed by the trucks but by the loader. This means that after a certain point, increasing trucks doesn't help and actually leads to inefficiencies as they sit idle.

Think of a school supply store that has a line of students (trucks) waiting to check out. If the checkout counter (loader) can only handle a certain number of students in a given time, adding more students to the line doesn’t increase the speed of service. Instead, it leads to longer waits for everyone.

So, 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.

In evaluating the costs of truck and loader combinations, we focus on the unit production cost since it significantly influences decision-making. The goal is to select the combination that yields the lowest cost per unit produced, which involves computing total costs based on different configurations.

Imagine a restaurant considering how many chefs to hire based on their food costs. Evaluating which combination of chefs and kitchen assistants results in the least cost per meal would help to maximize profits and efficiency. The restaurant would aim to balance staff numbers with customer demand and food quality.

Now let us estimate the total unit cost for the truck loader combinations for different number of trucks. Say for first for 5 number of trucks, how will you calculate the total cost? Total cost is nothing but 5 multiped what is the hourly cost of truck 1650 plus there is only one loader 1 multiplied by 2700.

To calculate total costs, we multiply the number of trucks by the hourly cost of each truck, then add the loader's hourly cost. For example, for 5 trucks costing 1650 each per hour and 1 loader costing 2700, we would calculate: (5 * 1650) + (1 * 2700) to get the total hourly cost of operation.

Consider running a lawn care business: if each mower costs $50 per hour and you have 5 mowers plus an assistant costing$40 per hour, you would calculate the total cost of running your operation each hour by multiplying the number of mowers by their cost and then adding the assistant's rate.

Unit cost of production is nothing but cost per hour divided by productivity per hour. So, for the number of trucks 5, so for 5 trucks what is the total cost 10950 divided by productivity is 62.65. So, this gives me the answer as rupees 174.78 per meter cube, this is the unit production cost associated with 5 trucks.

The unit cost of production is derived by dividing the hourly operational cost by the productivity achieved in that hour. For instance, if the total cost of having 5 trucks is 10,950 rupees and their combined productivity is 62.65 cubic meters, the cost per cubic meter is calculated as 10,950 / 62.65.

In a bakery, if the total cost of baking 100 loaves of bread is $200 and they produce 100 loaves in an hour, the cost per loaf would be$200/100, which is $2 per loaf. This helps the bakery determine if they are pricing their bread appropriately.

But as your number of trucks increases you can see that the productivity increases significantly, that is why your unit cost of production reduces, it is reducing. But beyond the balance number 7 when I try to increase the number of trucks, there is no increase in productivity. Because the productivity is limited by loader, I cannot go beyond 90, but your truck causes unnecessarily increasing.

As we increase the number of trucks up to the balance number, there’s a clear improvement in productivity and a decrease in unit production costs. However, pushing beyond the balance number yields no further productivity increase since the output is capped by the loader's capacity. This leads to rising costs without corresponding output advantages.

Think of a factory with a maximum production capacity due to staffing constraints. If adding more machines increases output, that's great; however, adding machines when staffing is insufficient leads to congestion without increasing total output, thereby driving up operational costs unnecessarily.

But when you try to increase number of trucks beyond the balance number, what is happening? There is no increase in productivity. Beyond the balance number the productivity is limited by the loader, so I cannot go beyond 90 meter cube per hour that was the productivity of the loader I cannot go beyond 90 meter cube per hour.

After surpassing the balance truck number, increasing trucks leads to no gain in productivity as the rate gets capped by the loader's efficiency. Thus, beyond this balance, any additional trucks merely contribute to increased costs without enhancing the total output.

Imagine a bus system: if the buses are filled to capacity and more buses are added, they will just idle at stops waiting for passengers to board. This doesn’t make the system more efficient; it only increases the transport costs without improving service.

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.

When finalizing the number of trucks, it’s often recommended to round down to the nearest whole number due to potential cost savings and operational efficiency, especially if the balance number is just above a whole number. Here, 7 is preferred over 8, as it keeps productivity high and costs low.

In a team project, if the ideal number of team members is 7.18, it might be more advantageous to stick with 7 to ensure everyone has meaningful work without overloading and confusing the group dynamics, thus fostering a productive environment.

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