3.2. Optimum Unit Production Cost Discussion

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. 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 divide the truck's cycle time (39.5 seconds) by the loader's cycle time (5.5 seconds). This calculation results in a balance number of approximately 7.18 trucks. Therefore, you can either round this figure down to 7 or up to 8 when making a decision about equipment. It’s important to analyze the implications of both options economically.

Imagine you are planning a carpool. If four cars can drive every 30 minutes, while one driver takes 2 hours to complete their route, you would want to determine how many cars are needed during peak times. If your need is between four and five cars, you'd have to decide whether to use four and have some waiting at the destination or to use five and ensure no wait but at an extra cost.

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, 6, 7, 8 and 9 trucks, 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.

Analyzing the relationship between truck numbers and productivity helps us understand how efficiency changes with different configurations. For each number of trucks from 5 to 9, we can calculate how much material can be moved per hour, and how that correlates with the unit production cost. This analysis will clarify the viable number of trucks needed to maintain cost-effectiveness and productivity.

Consider a bakery. If a bakery were to produce pastries, having two ovens might result in a certain output. If you add a third oven, the productivity rises, but if you add too many more without enough bakers to use them, the benefit diminishes as workers may not keep pace, leading to wasted resources. Analyzing productivity helps find the sweet spot for resources.

Now let us work out the economics because most of the decisions are based upon the economics. The unit cost here will be calculated for the different combinations. The input data is given to you what is the cost associated with the loader and the truck.

To decide on the most economically viable number of trucks, we must calculate the unit production cost. This is determined by knowing the hourly cost of both the loader (2700 rupees) and the individual trucks (1650 rupees). By calculating the total cost associated with each number of trucks, we can effectively determine the cost per unit produced, guiding decision-making towards the most efficient and cost-effective arrangement.

Imagine you're organizing a lemonade stand. If the cost to run your stand is $10 per day and you sell 50 cups of lemonade, each cup effectively costs you 20 cents to make. If you only managed to sell 20 cups, each cup would then cost 50 cents. Understanding your costs helps you set prices appropriately and manage your operations efficiently.

But when the number of trucks is greater than the balance number, the productivity will be controlled by your loader. So, you cannot go beyond the productivity of the loader because the load of cycle time will control the productivity of the system.

When the number of trucks exceeds the balance number, productivity doesn't continue to grow due to limitations. The loader can only handle a specific output rate; thus, the extra trucks simply wait for their turn, leading to inefficiencies and ensuring that productivity caps at the loader's rate. This insight is critical for avoiding excess costs associated with idle resources.

Think of train cars waiting to be filled with cargo at a loading dock. If the crane can only load one car at a time, additional cars will simply end up waiting in line, leading to increased operational costs without any added benefits. Managing how many are loaded at once ensures everything runs smoothly and efficiently.

Unit cost of production is nothing but cost per hour divided by productivity per hour.

To determine unit production cost, the strategy is straightforward: divide total operational costs by the productivity achieved in that period. For instance, if operating costs for a specific number of trucks are determined to be 10950 rupees and the productivity output is 62.65 cubic meters, the unit cost becomes approximately 174.78 rupees per cubic meter, enabling comparisons across configurations.

Using the lemonade stand analogy again, if you spent $10 on lemons and cups and sold 50 cups, your cost per cup is$10/50 = $0.20 per cup. This shows the importance of understanding both sales volume and expenses to ensure you aren’t losing money on each sale.

So, 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.

In this analysis, it becomes evident that simply decreasing the number of trucks can result in reduced total costs; however, it also leads to lower productivity levels. This means every unit produced ends up costing more. Therefore, while balancing costs and productivity is crucial, it’s often more beneficial to increase the number of trucks to enhance overall productivity when a balance point is reached.

Imagine if a restaurant operated with fewer waitstaff to save labor costs. While expenses might drop, service could slow down, leading to unhappy customers, less repeat business, and ultimately less revenue in the long run. It’s important to find a stable number of workers to keep service speed and satisfaction high.

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