2.3. Productivity Limitations Beyond Balance Number

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. The truck cycle time is 39.5 and the loader cycle time is 5.5, which gives a balance number of 7.18. Here, I can round it to either 7 or 8, but I must also consider the economics of both cases.

To determine the balance number of trucks needed for a loader, you divide the truck cycle time by the loader cycle time. In this case, the truck cycle time is 39.5 minutes, and the loader cycle time is 5.5 minutes. Dividing these two numbers gives us a balance number of 7.18. Since we cannot have a fraction of a truck, we round this number to either 7 or 8. When deciding which number to use, it's essential to analyze the costs associated with each option.

Think of it like balancing the number of cars in a carpool. If you have one passenger van (the loader) that can take 7 people (balance number), adding more cars (trucks) might not make sense if they can't accommodate more passengers than the van can carry. You'd want to ensure that the total number of vehicles doesn't exceed the passenger capacity so that no one is left waiting.

As I increase the number of trucks (5, 6, 7, 8, 9), I will analyze how the productivity and unit production cost vary. For example, with 5 trucks, productivity is 62.65 cubic meters per hour; with 6, it's 75.18; with 7, it's 87.71; with 8, it's 100.24, yet the productivity cannot exceed 90 when those exceed the balance number.

As you increase the number of trucks used in conjunction with a loader, productivity increases up to a certain point. For example, with 5 trucks, the total productivity is 62.65 cubic meters per hour. By adding more trucks, this productivity increases until it reaches a maximum, which is determined by the loader's capacity. Beyond that balance point, even if more trucks are added, productivity will remain fixed at the loader's maximum output, which is 90 cubic meters per hour in this case.

Imagine a concert where only ten people can fit into a car (loader) to reach an event. If five friends arrive, it’s no problem; they all get in. If six arrive, it still works fine. But if there’s a sudden need for ten more friends to come along after everyone is in the car, they will have to wait outside indefinitely since the car can only take ten at a time. Adding more cars won’t help if they can't board the original car.

When the number of trucks exceeds the balance number, the trucks will wait for the loader. This results in inefficiency since trucks can’t work until the loader is available, limiting productivity to that of the loader, which is a maximum of 90 cubic meters per hour.

If too many trucks are operating beyond the established balance number, they will end up waiting for the loader to become available. This situation leads to inefficiency, as the overall productivity is restricted to the loader's maximum output rather than leveraging the extra trucks. It's crucial to recognize that while having more trucks might seem beneficial, it can actually become counterproductive when they cannot all be utilized simultaneously.

Consider a restaurant kitchen with a chef (the loader) cooking meals and several waiters (the trucks) waiting to serve them. If the chef can only handle a certain number of dishes at a time, having too many waiters waiting around won’t speed up the service; they’ll just be idle until the chef serves more dishes. Adding more waiters only clogs the space without increasing the number of meals prepared.

It is also essential to consider the economics of operating between the balance number and beyond it. Total costs increase as more trucks are added without a corresponding increase in productivity, which raises the unit production cost.

When you decide on the number of trucks to operate, it is not just about productivity but also about costs. If you go beyond the balance number, you incur additional costs for the extra trucks that do not enhance productivity. For instance, if your productivity caps at 90 cubic meters per hour due to the loader's capability, any extra truck operates at a cost without providing additional output, leading to higher unit production costs.

Think of a grocery store that hires extra cashiers to keep lines short. If only three customers are there at a time, hiring more cashiers than necessary just adds to the payroll without improving service. The additional employee costs contribute to overall expenses but don’t result in a higher number of customers served, thus increasing the cost per customer.

When determining whether to round the balance number up or down, consider both the unit production cost and operational efficiency. Opting for the lower number usually provides a more economical solution, like choosing 7 trucks with a lower unit cost over 8 trucks with increased costs but similar productivity.

It’s essential to evaluate whether to round down (7 trucks) or round up (8 trucks) based on the total costs associated. More trucks may lead to diminishing returns on productivity, causing costs to rise without any real benefit. Thus, selecting the lower number often brings savings in costs while maintaining adequate productivity, plus it allows for potential operational flexibility like scheduled breaks.

Picture a company deciding between two shipping strategies. One plan involves using fewer trucks that operate efficiently (7 trucks) while the other commits to more trucks (8) but with negligible efficiency gains. The company must analyze costs, and typically, opting for fewer trucks allows for better resource allocation, almost like choosing less but better quality delivery services versus more but less effective ones.

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