1. Balance Number of Trucks for One Loader

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 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 needed for one loader, we first calculate it by dividing the truck cycle time by the loader cycle time. In this case, the truck cycle time is given as 39.5 minutes and the loader cycle time is 5.5 minutes. Thus, when we perform the calculation (39.5 / 5.5), we arrive at a value of approximately 7.18. This indicates that ideally, around 7 trucks should be utilized to effectively balance the loading operations with one loader.

Think of balancing a seesaw with weights. If one side has too many weights (trucks) compared to the other (loader), the seesaw won't function effectively. Similarly, to achieve optimal productivity in loading, we need to ensure we have the right number of trucks aligned with the loader's capacity.

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. So, but the logical thing is you have to work with the economics of both the cases and then take the decision.

After calculating the balance number of 7.18, we face the decision of rounding it. We can either round down to 7 or up to 8. The decision should be based on an analysis of the economic implications of each option. If we choose 7, we might maintain efficiency but potentially miss out on some productivity, while selecting 8 could increase costs without a corresponding increase in productivity.

Consider ordering food for a group. If you're expecting 8 people but you're worried about costs, you might round down to 7 dishes. On the other hand, rounding up might ensure everyone is satisfied, but you risk wasting food and spending more. The key is to weigh the costs against the benefits, just as we do with truck numbers.

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?

To understand the impact of varying the number of trucks, we will evaluate different scenarios: using 5, 6, 7, 8, and 9 trucks. This involves calculating how productivity changes with each additional truck and how that influences the unit production cost. The analysis will show that while increasing the truck numbers may initially raise productivity, there is a point where the additional trucks don’t contribute to further efficiency due to limitations imposed by the loader's cycles.

Imagine you're hosting a party and have just enough chairs for guests. At first, as you add more seats, more guests can sit comfortably. But when you have too many chairs compared to available table space, adding more doesn't help; some will still stand. Similarly, we need to find just the right number of trucks that meets loading demands effectively.

So, basically how to estimate the job production? So, it is nothing but your single truck productivity multiplied by the number of trucks, that will give you the job production. 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.

Job production can be estimated by multiplying the productivity of a single truck by the total number of trucks, under the condition that the total truck count is less than or equal to the balance number. When we’re within this range, the cycle time of the trucks dictates the overall productivity, meaning that we won’t be fully utilizing the loader's capabilities yet. For example, if each truck operates at a productivity of 12.53 cubic meters per hour and we have 5 trucks, total expected production would be 62.65 cubic meters per hour.

It’s like a team of workers picking apples. If there are only 5 baskets but the apple trees produce more than the baskets can handle, then some of the apples will just sit there unpicked until the baskets are freed up. This means productivity is limited until there’s enough capacity to handle the workload.

So, when the number of trucks is your balance number say 7, the 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 number of trucks equals the balance number (in this case, 7), we achieve maximum efficiency. If we increase the number of trucks beyond this point, while it may seem advantageous at first, the additional trucks will become idle because they will have to wait for the loader. The loader's cycle time limits the productivity even if we have more trucks. So, beyond the balance number, the total productivity will remain capped at what the loader can handle, which is 90 cubic meters per hour in this scenario.

Picture a factory assembly line. If you have the perfect number of workers (trucks) stationing parts precisely but then you add too many workers without extra assembly stations (the loader), everyone will just stand around waiting. Hence, even with more workers, the output doesn’t increase because the assembly line is constrained by the pace of just one station.

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.

Decisions in operations often revolve around economics and the unit production cost, which reflects the cost of producing one unit of output based on the resources used. We need to evaluate how changing the number of trucks impacts the unit production cost by analyzing the total costs associated with maintaining the trucks and the loader versus the productivity level achieved. The goal is to find a combination that minimizes the unit production cost while ensuring effective operation.

Consider shopping for groceries. You want to buy enough to feed your family without overspending. If you buy too little, you’ll have to make multiple trips, costing more in the long run. But if you buy too much, food might go to waste. Similarly, in using trucks and loaders, we must balance costs to optimize productivity.

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.

The total cost for operating a truck-loader combination is determined by adding the costs associated with the trucks and the loader. For example, if each truck costs 1650 per hour and there are 5 trucks, the total cost for the trucks would be 5 x 1650 = 8250. Then, adding the loader's cost of 2700 gives a total of 10950 per hour for that setup. We can repeat this for different numbers of trucks (6, 7, etc.) to see how costs change.

Think of it like calculating the total price of various snacks for your movie night. If popcorn costs $3, sodas$2, and you plan for 5 friends, you will need to multiply the cost of each item by the number of friends to determine how much to spend overall versus only buying one item. It’s prudent to handle different combinations to find the best value.

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.

The unit cost of production calculates how much it costs to produce one unit of output. This is achieved by dividing the total cost by the productivity. Continuing with the previous example of 5 trucks, if the total cost is 10950 and the output is 62.65 cubic meters per hour, the unit cost would be 10950 divided by 62.65, yielding approximately 174.78 per unit. This helps in assessing the efficiency of resources and optimizing costs.

It resembles a school project where you total the costs for materials and then divide by the number of projects completed to see how efficient you were. If you spent more on one project than others, it signals a need for evaluating spending to ensure you're not overshooting your budget.

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.

This highlights an important consideration: even if the total operational cost is lower with fewer trucks (like 5), if productivity is also low, the unit cost remains high. As we analyze different configurations, we generally see that if we increase truck numbers, productivity rises, thereby reducing the unit production cost until we reach the balance point. After this point, adding more trucks doesn’t yield any productivity increase but raises costs, emphasizing the need for balanced operations.

Imagine running a small coffee shop. If you have insufficient staff during peak hours (like just one barista), you might save on salary costs, but customers leave unhappy and your sales are low. Hire more staff and costs rise, but sales and customer satisfaction can also increase, which is ideal. Your goal is to find the right staff balance to maximize profit.

So, it is always preferable to go by the balance number, but in this case, our balance number 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.

Ultimately, the aim is to decide whether to use 7 or 8 trucks based on the economic analysis carried out. As we’ve seen, rounding to 7 helps control costs while ensuring productivity is optimized—operating right at or below the balance number maintains efficiency without incurring unnecessary expenses from idle trucks. Hence, it’s advisable to make careful calculations to derive the most effective solution.

Picture a carpool with friends aiming to attend a concert. If you choose to drive one car with the correct amount of seats (like your 7 trucks), costs are shared optimally. However, if everyone jumps in and two people have to sit on laps (like having 8 trucks), it becomes uncomfortable and more costly, hence it’s better to keep it balanced.

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